Payday loan shop, Soho, London

Unit 9 The credit market: Borrowers, lenders, and the rate of interest

Introduction

The market town of Chambar in southeastern Pakistan serves as the financial centre for 2,400 farmers in surrounding villages. At the beginning of the kharif planting season in April, when the farmers sow cotton and other cash crops, they buy fertilizer and other inputs. Months have passed since they sold the last harvest, and so the only way they can buy inputs is to borrow money, promising to repay at the next harvest. Others borrow to pay for medicines or doctors.

But few farmers have ever walked through the shiny glass and steel doors of the JS Bank on Hyderabad Road. Instead, they visit one of approximately 60 moneylenders.

If they are seeking a first-time loan, they will be questioned intensively by the moneylender, asked for references from other farmers known to the lender, and in most cases given a small trial loan as a test of creditworthiness. The lender will probably visit to investigate the condition of a farmer’s land, animals, and equipment.1

The lenders are right to be wary. If the farmer’s crop fails due to drought or lack of attention, the lender will make a loss. Unlike many financial institutions, lenders do not usually require that the farmer set aside some property or belongings—for example, some gold jewelry—that would become the lender’s property if the farmer does not repay the loan.

If the would-be first-time borrower looks reliable or trustworthy enough, the farmer is offered a loan. In Chambar, this is at an average interest rate of 78% per annum. If the borrower pays the loan back in four months (the growing period of the crop prior to harvest), 100 rupees borrowed before planting is paid back as 126 rupees. But, knowing that more than half the loan applications are refused, the borrower would feel fortunate.

And indeed, the borrower in Chambar would be, at least compared to some people 12,000 km away in New York, who take out short-term loans to be repaid when their next paycheck comes in. These payday loans bear interest rates ranging from 350% to 650% per annum, much higher than the legal maximum interest rate in New York (25%). In 2014, the ‘payday syndicate’ offering these loans was charged with criminal usury in the first degree.2

Given the interest rates charged, is the business of lending in Chambar or of payday loans in New York likely to be exceptionally profitable? The evidence from Chambar suggests it is not. Some of the funds lent to farmers are borrowed from commercial banks, like the JS Bank, at interest rates averaging 32% per annum, representing a cost to the moneylenders. And the costs of the extensive screening of borrowers and collection of the debts further reduces the profits made by the moneylenders.

Partly as a result of the careful choices made by the moneylenders in Chambar, default is rare—fewer than one in 30 borrowers fail to repay. By contrast, default rates on loans made by commercial banks are much higher—one in three. The moneylenders’ success in avoiding default is based on their accurate assessment of the likely trustworthiness of their clients.

Not everyone passes the trustworthiness tests set by the moneylenders and the payday lenders—some would-be borrowers find it impossible to get a loan. And, in Chambar and New York, some of those who do, pay much higher interest rates than others.

Long before there were the employers, employees, and the unemployed that we studied in the previous unit, there were lenders and borrowers. Some of the first written records of any kind were records of debts. Differences in income between those who lend—like the farmers in Chambar and those seeking payday loans in New York—and those who borrow—like the money lenders in Chambar and the payday lenders in NY—remain an important source of economic inequality today.

In this unit, we study borrowers and lenders and the workings of the market for credit. We examine the nature of the benefits that arise from lending and borrowing; we also show how the nature of credit markets can limit those benefits. Like the labour market, the credit market is essential to the functioning of a capitalist economy, and also like the labour market the credit market differs in important ways from the markets for bread, language courses, and the other goods and services studied in Unit 7.

9.1 Income, consumption, and wealth

In everyday language, terms like ‘money’, ‘wealth’ and ‘investment’ are often used loosely. We hear people say: ‘I want a job that pays good money,’ or: ‘I want to invest some money for when I retire,’ or: ‘I need to borrow some money to see me through to the end of the month.’

To understand the credit market, we need to clarify how these terms are used in economics.

It turns out that, for economists, one of the trickiest things to define precisely is money. Economists like to define money in terms of what it does. They point to a number of functions that money fulfils. Some of these functions are also fulfilled by other things, but only money fulfils all these functions. We shall delve deeper into these functions in Unit 10.

But at this stage, we only need to think about one function of money—money is a ‘store of value’. In simple terms, this means that anyone who has money can turn it into goods and services. When people say they want more money, what they really want is more of the goods and services that money will buy.

Thus:

consumption (C)
Expenditure on both short-lived goods and services and long-lived goods, which are called consumer durables.

Why are our paraphrases more precise than the original sentences? In each case, they focus on the person’s motivation. One way to show this is to note that money itself does not play a unique role in the original sentences. Thus:

investment (I)
Expenditure on newly produced capital goods (machinery and equipment) and buildings, including new housing.
wealth
Stock of things owned or value of that stock. It includes the market value of a home, car, any land, buildings, machinery or other capital goods that a person may own, and any financial assets, such as bank deposits, shares, bonds, or loans made to others. Debts to others are subtracted from wealth—for example, the mortgage owed to the bank.

In this unit, we shall postpone any further discussion of money. We first focus on consumption and investment directly in terms of goods and services, and on wealth as potential spending power. We then analyse the role of borrowing and lending in allowing us to shift spending in time. We return to the topic of what money is and does in Unit 10.

Wealth

One way to think about the amount of wealth that you have as a household is that it is the largest amount that you could spend without borrowing, after having paid off your debts and collected any debts owed to you—for example, if you sold your house, car, and everything you owned.

income
The amount of labour earnings, dividends, interest, rent, and other payments (including transfers from the government) received by an economic actor, net of taxes paid, measured over a period of time, such as a year. The maximum amount that you could consume and leave your wealth unchanged. Also known as: disposable income. See also: pre-tax income.
human capital
The stock of knowledge, skills, behavioural attributes, and personal characteristics that determine the labour productivity or labour earnings of an individual. Investment in this through education, training, and socialization can increase the stock, and such investment is one of the sources of economic growth. Part of an individual’s endowments. See also: endowment.

The term wealth is also sometimes used in a broader sense to include immaterial or intangible aspects, such as your health, skills, and ability to earn an income (your human capital). But we will use the narrower definition of material wealth in this unit since we focus on forms of wealth that can potentially be turned into spending on goods and services. Since the abolition of human slavery, human capital cannot be bought and sold.

Income

earnings
Wages, salaries, and other income from labour.

Income is the amount of money you receive over some period of time, whether from market earnings, assets that you own, or as transfers from the government.

flow
A quantity measured per unit of time, such as annual income or hourly wage.
stock
A quantity measured at a point in time. Its units do not depend on time. See also: flow.

Since it is measured over a period of time (such weekly or yearly), it is a flow variable illustrated below in Figure 9.1. Wealth is a stock variable, meaning that it has no time dimension. At any moment of time it is just there. In this unit, we only consider after-tax income, also known as disposable income.

To highlight the difference between wealth and income, think of filling a bathtub, as in Figure 9.1. Wealth is the amount (stock) of water in the tub, while income is the flow of water into the tub. The inflow is measured by litres (or gallons) per minute; the stock of water is measured by litres (or gallons) at a particular moment in time.

Wealth, income, depreciation, and consumption: The bathtub analogy.

Figure 9.1 Wealth, income, depreciation, and consumption: The bathtub analogy.

depreciation
The loss in value of a form of wealth that occurs either through use (wear and tear) or the passage of time (obsolescence).

As we have seen, some wealth takes physical forms, such as a house, or car, or office, or factory. The value of physical wealth tends to decline, either due to use or simply the passage of time. This reduction in the value of a stock of wealth over time is called depreciation. Using the bathtub analogy, depreciation is the amount of evaporation of the water. In economics, an example of depreciation is the fall in the value of a car with mileage and with age. Like income, depreciation is a flow (you could measure it in for a car in dollars per year), but a negative one.

When we take account of depreciation, we must distinguish between net income and gross income. Gross income is the flow of disposable income into the bathtub. It either adds to wealth, is used for consumption spending or is lost as depreciation. Before the income enters the bathtub, taxes are subtracted and transfers are added, such as pension payments from the government. Net interest receipts are part of the flow into the bathtub, and so are net receipts of transfers from others (such as gifts).

income net of depreciation
Disposable income minus depreciation. See also: disposable income, gross income, depreciation.

Income net of depreciation is the maximum amount that you could consume and leave your wealth unchanged.

Consumption, saving, and investment

Water also flows out of the tub. The flow through the drain is called consumption, and it reduces wealth just as net income increases it.

Measured consumption includes spending on goods that provide services over long periods of time, like screens, bicycles and cars. Where the services are provided over a very long period as for new housing, the spending is classified as investment.

saving
When consumption expenditure is less than net income, saving takes place and wealth rises. See also: wealth.

An individual (or household) saves when consumption is less than net income, so wealth increases. Wealth is the accumulation of past and current saving. Saving can take a number of forms—for example, in bank deposits, or in financial assets, such as shares (or stocks) in a company or a government bond. These are often held indirectly by investing in a pension fund. In everyday language these purchases are sometimes referred to as ‘investment’, but in economics investment means spending on capital goods that provide services over long periods of time, such as equipment or buildings.

The distinction between investment and purchasing shares or bonds (sometimes called financial investment) is illustrated by a sole proprietor business. At the end of the year, the owner decides what to do with her net income. Out of the net income, she decides on her consumption expenditure for the year ahead and saves the remainder, so her wealth rises.

With her savings, she could buy financial assets that provide funds to businesses or the government, such as shares or bonds. Contributions to a personal pension fund are an example of the use of savings to buy financial assets. Or, instead, she could spend on new assets such as computers to expand her business, which would be investment expenditure.

To summarize—in this example, the wealth of the owner of the small business has increased. The form the increase in wealth takes is a combination of money (bank deposits), financial assets (bonds, shares, and pension fund assets), and physical assets (computer equipment for her business).

Lending and borrowing

Households borrow from banks, finance companies, payday lenders, or from other individuals to spend on consumer durables and nondurables and for the purchase of housing. Businesses and governments also borrow; when a household buys bonds with their savings, they are making a loan to the government (a government bond) or to a business (a corporate bond).

Question 9.1 Choose the correct answer(s)

Which of the following statements are correct?

  • Your material wealth is the largest amount that you can consume without borrowing; it includes the value of your house, car, financial savings, and human capital.
  • Income net of depreciation is the maximum amount that you can consume and leave your wealth unchanged.
  • In economics, investment means saving in financial assets, such as stocks and bonds.
  • Depreciation is the loss in your financial savings due to unfavourable movements in the market.
  • Human capital, such as your health, skills, and ability to earn an income, is immaterial wealth.
  • Income net of depreciation is the flow that corresponds to your stock of wealth, so if you consume it all, your wealth is unchanged.
  • Although in everyday language this is sometimes referred to as investment, in economics, investment means expenditure on capital goods, such as machinery, equipment, and housing.
  • Depreciation is the loss in value through wear and tear or the passage of time.

Question 9.2 Choose the correct answer(s)

Mr Bond has wealth of £500,000. He has a market income of £40,000 per year, on which he is taxed 30%. Mr Bond’s wealth includes some equipment, which depreciates by £5,000 every year. Based on this information, which of the following statements are correct?

  • Mr Bond’s disposable income is £40,000.
  • Mr Bond’s net income is £28,000.
  • The maximum amount of consumption expenditure possible for Mr Bond is £23,000.
  • If Mr Bond decides to spend 60% of his net income on consumption and the rest on investment, then his investment is £9,200.
  • Mr Bond’s disposable income is his market income less tax, which is £40,000 × 0.7 = £28,000.
  • Mr Bond’s net income is his disposable income minus depreciation, which is £28,000 – £5,000 = £23,000.
  • £23,000 is Mr Bond’s net income. Consuming this amount does not alter his wealth. However, Mr Bond can also consume all of his wealth, so his maximum possible consumption expenditure is £500,000 + £23,000 = £523,000.
  • Sixty per cent of his net income is £13,800, leaving £9,200 to spend on investment.

9.2 Borrowing: Bringing consumption forward in time

Borrowing and lending are about shifting consumption and production over time. The moneylender offers funds to the farmer to purchase fertilizer now, to pay back after the crop matures, as long as the harvest is good. The payday borrower will be paid at the end of the month but needs to buy food now. The borrower brings some future buying power to the present.

indifference curve
A curve of the points which indicate the combina­tions of goods that provide a given level of utility to the individual.
preferences
A description of the benefit or cost we associate with each possible outcome.

To understand borrowing and lending, we will use feasible sets and indifference curves. In Units 4 and 5, you studied how Alexei and Angela make choices between conflicting objectives, such as free time and grades or grain. They made choices from the feasible set, based on preferences described by indifference curves that represented how much they valued one objective relative to the other.

opportunity cost
When taking an action implies forgoing the next best alternative action, this is the net benefit of the foregone alternative.

Here, you will see that the same feasible set and indifference curve analysis apply to choosing between having something now and having something later. In earlier units we saw that giving up free time is a way of getting more goods, or grades, or grain. We shall see that giving up some goods to be enjoyed now will sometimes allow us to have more goods later. The opportunity cost of having more goods now is having fewer goods later.

Borrowing and lending allow us to rearrange our capacity to buy goods and services across time. Borrowing allows us to buy more now, but constrains us to buy less later. To see how this works, think about Julia, who needs to consume now but has no money today. She may be a payday borrower in New York City or a farmer in Chambar at planting time; perhaps she has just graduated and needs to finance a period before her first job begins.

Julia knows that, in the next period (‘later’), she will have $100 from her paycheck or harvest. Julia’s situation is shown in Figure 9.2. Each point in the figure shows a given combination of Julia’s consumption—now (measured on the horizontal axis) and later (measured on the vertical axis).

We will use a figure like this throughout the unit, and often refer to the ‘slope’ of lines and curves that we draw. You may remember from studying geometry that, when a line slopes downwards from left to right, the slope is negative. This is logical—to get more income now (a positive change), Julia accepts less income later (a negative change).

When economists talk about the ‘slope’ of the trade-off between now and later, they usually simplify things in the descrition by using the positive value of this number. This is called taking the absolute value of the slope. When we refer to the ‘slope’ of a line or curve in this unit, we will refer to the absolute value, and so the slope is always a positive number. You will find this is easier when you are describing the trade-off that borrowers make.

Julia is not free to simply pick any combination of consumption now and later. The institutions relevant to her consumption—consumption goods are private property and can be acquired only by purchase, not by theft, gift, or government provision—mean that she has to buy what she consumes.

Borrowing, the interest rate, and the feasible set.

Figure 9.2 Borrowing, the interest rate, and the feasible set.

Julia has nothing

Julia has no money now but she knows that, in the next period, she will have $100. Given this state of affairs, her consumption now is $0 and $100 later. This point is labelled as her endowment. It is what she has now or expects to get before any other interaction, such as borrowing.

Figure 9.2a Julia has no money now but she knows that, in the next period, she will have $100. Given this state of affairs, her consumption now is $0 and $100 later. This point is labelled as her endowment. It is what she has now or expects to get before any other interaction, such as borrowing.

Bringing future income to the present

Julia could, for example, borrow $91 now and promise to pay the lender the $100 that she will have later, assuming an interest rate of 10%.

Figure 9.2b Julia could, for example, borrow $91 now and promise to pay the lender the $100 that she will have later, assuming an interest rate of 10%.

Borrowing less

At the same interest rate (10%), she could also borrow $70 to spend now, and repay $77 at the end of the year. In that case, she would have $23 to spend next year.

Figure 9.2c At the same interest rate (10%), she could also borrow $70 to spend now, and repay $77 at the end of the year. In that case, she would have $23 to spend next year.

Borrowing even less

At the same interest rate (10%), she could also borrow $30 to spend now, and repay $33 at the end of the year. In that case she would have $67 to spend next year.

Figure 9.2d At the same interest rate (10%), she could also borrow $30 to spend now, and repay $33 at the end of the year. In that case she would have $67 to spend next year.

Julia’s feasible set

By repeating these hypothetical borrowing and repayment combinations, the boundary of Julia’s feasible set—called her feasible frontier—is formed. This is shown for the assumed interest rate of 10%.

Figure 9.2e By repeating these hypothetical borrowing and repayment combinations, the boundary of Julia’s feasible set—called her feasible frontier—is formed. This is shown for the assumed interest rate of 10%.

Julia’s feasible frontier

If Julia can borrow at 10%, she can move from her endowment by borrowing now and choose any combination on her feasible frontier.

Figure 9.2f If Julia can borrow at 10%, she can move from her endowment by borrowing now and choose any combination on her feasible frontier.

A higher interest rate

If, instead of 10%, the interest rate is 78%, Julia can only borrow a maximum of $56 now.

Figure 9.2g If, instead of 10%, the interest rate is 78%, Julia can only borrow a maximum of $56 now.

The feasible set

The feasible set with the interest rate of 78% is the dark shaded area, while the feasible set with an interest rate of 10% is the dark shaded area plus the light shaded area.

Figure 9.2h The feasible set with the interest rate of 78% is the dark shaded area, while the feasible set with an interest rate of 10% is the dark shaded area plus the light shaded area.

A closer look at borrowing

In Figure 9.2, Julia is at the point labelled ‘Julia’s endowment’. To consume at least something now, Julia considers taking out a loan, as shown.

interest rate
The price of bringing some buying power forward in time. See also: nominal interest rate, real interest rate.

If the interest rate were 10%, Julia could, for example, borrow a bit less than $91 now and promise to pay the lender the whole $100 that she will have later. Her total repayment of $100 would include the principal (how much she borrowed, namely $91) plus the interest charge ($9) at the rate r, or:

And if ‘later’ means in one year from now, then the annual interest rate, r, is:

You can think of the interest rate as the price of bringing some spending power forward in time.

At the same interest rate (10%), Julia could also borrow $70 to spend now, and repay $77 at the end of the year, that is:

In this case, she would have $23 to spend next year. Another possible combination is to borrow and spend just $30 now, which would leave Julia with $67 to spend next year, after repaying her loan.

feasible frontier
The curve made of points that defines the maximum feasible quantity of one good for a given quantity of the other. See also: feasible set.

All of her possible combinations of consumption now and consumption later, for example ($91, $0), ($70, $23) ($30, $67), are the points that make up the feasible frontier shown in Figure 9.2. This is the boundary of the feasible set when the interest rate is 10%.

The fact that Julia can borrow means that she does not have to consume only in the later period. She can borrow now and choose any combination on her feasible frontier. But the more she consumes now, the less she can consume later. With an interest rate of r = 10%, the opportunity cost of spending one dollar now is that Julia will have to spend 1.10 = 1 + r dollars less later.

One plus the interest rate (1 + r) is the marginal rate of transformation of goods from the future to the present, because to have one unit of the good now, you have to give up 1 + r goods in the future. This is the same concept as the marginal rate of transformation of goods, grain, or grades into free time that you encountered in Units 4 and 5.

We have thus far referred simply to ‘the interest rate’. But in relating it so explicitly to the price of future consumption, we have implicitly been using what economists refer to more precisely as the real interest rate—since what Julia cares about is her loss of real spending power.

Economists contrast this to the nominal interest rate, which is the rate that is typically actually paid on loans. When the price of goods and services is rising—that is, if there is a positive inflation rate—the nominal interest rate overstates the true (real) interest rate. For the moment, we will not worry about this. We will return to inflation and the nominal interest rate in Unit 10.

A higher interest rate raises the price of bringing buying power forward

Suppose that, instead of 10%, the interest rate is 78%, the average rate paid by the farmers in Chambar. At this interest rate, Julia can now only borrow a maximum of $56, because the interest on a loan of $56 is $44, using up all $100 of her future income. Her feasible frontier therefore pivots inward and the feasible set becomes smaller. Because the price of bringing buying power forward in time has increased, the capacity to consume in the present has fallen, just as your capacity to consume grain would fall if the price of grain went up (unless you are a producer of grain).

conflict of interest
The situation which arises if in order for one party to gain more from the interaction, another party must do less well.

Of course, the lender will benefit from a higher interest rate (as long as the loan is repaid) so there is a conflict of interest between the borrower and the lender.

Exercise 9.1 Julia’s feasible frontier

We construct Julia’s feasible frontier by finding all the combinations of consumption now and next period, given her endowment and the interest rate.

  1. Complete the table below, using the information given. Round your answers to the nearest dollar.
  2. Using your completed table, draw a diagram similar to Figure 9.2, showing the feasible frontier, consumption amounts and the amount of repayment.
Point on the feasible frontier Consumption now = Amount borrowed Consumption later = Income later − Repayment = Income later − (1 + r) × Amount borrowed Repayment = Income later − Consumption later
Endowment point (0, 100) 0 100 0
Interest rate = 10%
(91, 0) 91 100 − (1.1)91 = 0 100
(70, 23)
(30, 67) 30 33
Interest rate = 78%
(56, 0) 56 100 − (1.78)56 = 0 100
30
33

9.3 Reasons to borrow: Smoothing and impatience

consumption smoothing
Actions taken by an individual, family, or other group in order to sustain their customary level of consumption. Actions include borrowing or reducing savings to offset negative shocks, such as unemployment or illness; and increasing saving or reducing debt in response to positive shocks, such as promotion or inheritance.

Given the opportunities for bringing forward consumption shown by the feasible set, what will Julia choose to do? How much consumption she will bring forward depends on how impatient she is. She could be impatient for two reasons:

Smoothing

The first reason is that she would like to smooth her consumption because she enjoys an additional unit of something more when she has not already consumed a lot of it. Think about food—the first few bites of a dish are likely to be much more pleasurable than bites from your third serving. This is a fundamental psychological reality, sometimes termed the law of satiation of wants.

diminishing marginal returns to consumption
The value to the individual of an additional unit of consumption declines, the more consumption the individual has. Also known as: diminishing marginal utility.

More generally, the value to the individual of an additional unit of consumption in a given period declines the more that is consumed. This is called diminishing marginal returns to consumption. You have already encountered something similar in Unit 4, when Alexei experienced diminishing marginal returns to free time. Holding his grade constant, the more free time he had, the less each additional unit was worth to him, relative to how important the grade would be. We can apply this to consumption in general. Diminishing marginal returns imply that we prefer to smooth our consumption. We would optimally choose to consume similar amounts now and later, as Figure 9.3 shows.

Consumption smoothing: Diminishing marginal returns to consumption.

Figure 9.3 Consumption smoothing: Diminishing marginal returns to consumption.

Julia’s choices

The dashed line shows the combinations of consumption now and consumption later from which Julia can choose.

Figure 9.3a The dashed line shows the combinations of consumption now and consumption later from which Julia can choose.

Diminishing marginal returns to consumption

Julia’s indifference curve is bowed toward the origin as a consequence of diminishing marginal returns to consumption in each period. The more goods she has in the present, the less she values an additional one now relative to more in the future. The slope of the indifference curve is the marginal rate of substitution (MRS) between consumption now and consumption later.

Figure 9.3b Julia’s indifference curve is bowed toward the origin as a consequence of diminishing marginal returns to consumption in each period. The more goods she has in the present, the less she values an additional one now relative to more in the future. The slope of the indifference curve is the marginal rate of substitution (MRS) between consumption now and consumption later.

What choices would Julia make?

The MRS at C is high (the slope of her indifference curve is steep)—Julia has little consumption now and a lot later, so diminishing marginal returns mean that she would like to move some consumption to the present. The MRS at E is low. She has a lot of consumption now and less later, so diminishing marginal returns mean that she would like to move some consumption to the future. So she will choose a point between C and E.

Figure 9.3c The MRS at C is high (the slope of her indifference curve is steep)—Julia has little consumption now and a lot later, so diminishing marginal returns mean that she would like to move some consumption to the present. The MRS at E is low. She has a lot of consumption now and less later, so diminishing marginal returns mean that she would like to move some consumption to the future. So she will choose a point between C and E.

MRS falls

We can see that the MRS is falling as we move along the indifference curve from C to E. The slope is steeper at C than at E.

Figure 9.3d We can see that the MRS is falling as we move along the indifference curve from C to E. The slope is steeper at C than at E.

Julia’s optimal choice

Given the choice shown by the line CE, Julia will choose point F. It is on the highest attainable indifference curve. She prefers to smooth consumption between now and later.

Figure 9.3e Given the choice shown by the line CE, Julia will choose point F. It is on the highest attainable indifference curve. She prefers to smooth consumption between now and later.

Pure impatience, or how impatient you are as a person

If Julia knows she can have two meals tomorrow but she has none today, then diminishing marginal returns to consumption could explain why she might prefer to have one meal today and one tomorrow. Note that Julia would opt for the meal now, not because she is an impatient person, but because she does not expect to be hungry in the future. She prefers to smooth her consumption of food.

pure impatience
This is a characteristic of a person who values an additional unit of consumption now over an additional unit later, when the amount of consumption is the same now and later. It arises when a person is impatient to consume more now because she places less value on consumption in the future for reasons of myopia, weakness of will, or for other reasons.

But there is a different reason for preferring the good now, called pure impatience. To see whether someone is impatient as a person, we ask whether, if she initially had the same amount of the good in both periods, would she would value having more of the good now more highly than more of the good later? Two reasons for pure impatience are:

We saw that Julia, who will earn $100 in the future, wants to borrow. The situation that she is in gives her a strong desire to smooth by borrowing. Think about what Julia’s indifference curve, passing through her endowment point, might look like. As shown in Figure 9.4, she has a strong preference for increasing consumption now.

reservation indifference curve
A curve that indicates allocations (combinations) that are as highly valued as one’s reservation option.

This is called Julia’s reservation indifference curve, because it is made of all the points at which Julia would be just as well off as at her reservation position, which is her endowment with no borrowing or lending (Julia’s endowment and reservation indifference curves are similar to those of Angela, the farmer, in Unit 5). At point A, with no expenditure at all on consumption now, we assume Julia has some way of maintaining herself.

Julia’s indifference curves.

Figure 9.4 Julia’s indifference curves.

Figure 9.4 shows Julia’s indifference curves:

impatience
Any preference to move consumption from the future to the present. This preference may be derived either from pure impatience or diminishing marginal returns to consumption.

For any particular point in the figure, the individual’s impatience can be seen from the steepness of the indifference curve. At her endowment point—$100 later, nothing now—shown by point A, her indifference curve is very steep. Because she has nothing now, she is very impatient. It means she would be willing to give up a substantial amount of consumption later to gain a little bit of consumption now. This could be illustrated by a move from point A to A’.

discount rate
A measure of the person’s impatience: how much the person values an additional unit of consumption now relative to an additional unit of consumption later. It is the absolute value of the slope of the person’s indifference curve for consumption now and consumption later, minus one. Also known as: subjective discount rate.

We define a person’s discount rate, (economists use the Greek letter rho, which rhymes with ‘toe’), as the slope (remember, we take the absolute—positive—value) of the indifference curve minus one. It is a measure of impatience, namely how much Julia values an extra unit of consumption now, relative to an extra unit of consumption later.

smooth consumption
No definition available.

Her discount rate , which measures her impatience, depends both on her desire to smooth consumption and on her degree of pure impatience. A high discount rate means a high degree of impatience.

Notice in Figure 9.4 that if Julia hypothetically had the $100 now (point B), she would be much less impatient; at B, her indifference curve is very flat, which means that she would like to have more consumption in the future and less now and would be willing to give up a dollar now, even if she got less than a dollar in return later.

Not only would Julia be less impatient at point B (with $100 now) than at point A (in her initial situation of having $100 later), but she would also be better off. In Figure 9.4, the indifference curve through B is above the indifference curve through A. This is because, as a person, she has a degree of pure impatience.

utility
A numerical indicator of the value that one places on an outcome, such that higher valued outcomes will be chosen over lower valued ones when both are feasible.

To see this, notice that when Julia’s utility is at the same level as when she has the $100 in the future, she must be on the same indifference curve, that is, the one going through A. You can see that on that indifference curve at B′, her consumption is much lower than $100. For the indifference curves shown in Figure 9.4, she values $100 later the same as she values half that amount now (B′ is one half of B).

Question 9.3 Choose the correct answer(s)

Figure 9.3 depicts Julia’s indifference curves for consumption in periods 1 (now) and 2 (later). Based on this information, which of the following statements are correct?

  • The slope of the indifference curve is the marginal rate of substitution between the consumption in the two periods.
  • The marginal return to consumption in period 1 is higher at E than at C.
  • Julia’s consumption is more equal (more ‘smoothed’) at C than at E. Therefore, she prefers consumption choice C to E.
  • Consuming exactly the same amount in the two periods is Julia’s most preferred choice.
  • In order to stay on the same indifference curve, the change in utility due to a marginal change in consumption now must be precisely offset by the change in utility due to the change in consumption later.
  • At E, Julia is consuming more now than at C. Due to diminishing marginal returns to consumption, Julia’s marginal return to consumption now is lower at E than at C.
  • The two points are on the same indifference curve. Therefore, she is indifferent between the two.
  • This depends on the interest rate (one plus interest rate is the slope of the feasible frontier) and the shape of the indifference curves. Julia’s preferred choice is at F, where the consumption in the two periods is not necessarily equal.

9.4 Borrowing allows smoothing by bringing consumption to the present

How much will Julia borrow? If we combine Figures 9.2 and 9.3 we will have the answer. As in the other examples of a feasible set and indifference curves, Julia wishes to get to the highest possible indifference curve but is limited by her feasible frontier. The highest feasible indifference curve when the interest rate is 10% will be the one that is tangent to the feasible frontier, shown as point E in Figure 9.5. This means that Julia borrows just enough so that:

We know that:

Therefore:

If we subtract 1 from both sides of this equation, we have:

Here, Julia chooses to borrow and consume $56 and repay $62 later, leaving her $38 to consume later.

Now consider how much she would borrow if she had to pay not 10%, but the 78% that was the average among the Chambar farmers. Figure 9.5 shows that, as before, finding the point of tangency between the new feasible frontier given by the 78% interest rate and one of Julia’s indifference curves, she will choose point G, meaning that she will borrow much less—$35—to consume now, paying $62 with interest, and having $38 to consume later.

The higher ‘price’ of moving consumption forward in time means two things:

In the example, her consumption later does not change. But, depending on the shape of her indifference curves, it could be lower or higher. With the higher interest rate, she is less well off, so this would tend to push down her consumption later. But the higher interest rate makes it costlier to bring consumption forward, which would tend to push up her consumption later.

Use the analysis in Figure 9.5 to see how Julia will choose consumption when the interest rate is 10% and when it is 78%.

Moving consumption over time by borrowing.

Figure 9.5 Moving consumption over time by borrowing.

Julia’s feasible frontier

Julia wishes to get to the highest indifference curve but is limited by her feasible frontier.

Figure 9.5a Julia wishes to get to the highest indifference curve but is limited by her feasible frontier.

Julia’s best option

When the interest rate is 10%, the highest attainable indifference curve is the one that is tangent to the feasible frontier shown as point E.

Figure 9.5b When the interest rate is 10%, the highest attainable indifference curve is the one that is tangent to the feasible frontier shown as point E.

MRS and MRT

At this point, MRS = MRT.

Figure 9.5c At this point, MRS = MRT.

The decision to borrow

At point F, her discount rate, , exceeds r, the interest rate, so she would like to bring consumption forward in time. This means that the benefits to her of bringing some consumption forward to the present () are greater than the costs (r), so she will borrow more to finance current consumption. Similar reasoning eliminates all points except E on the feasible frontier.

Figure 9.5d At point F, her discount rate, , exceeds r, the interest rate, so she would like to bring consumption forward in time. This means that the benefits to her of bringing some consumption forward to the present () are greater than the costs (r), so she will borrow more to finance current consumption. Similar reasoning eliminates all points except E on the feasible frontier.

An increase in the interest rate

If the interest rate at which she can borrow increases, the feasible set gets smaller.

Figure 9.5e If the interest rate at which she can borrow increases, the feasible set gets smaller.

The effect of a higher interest rate

The best Julia can do now is to borrow less ($35 instead of $56), as shown by point G.

Figure 9.5f The best Julia can do now is to borrow less ($35 instead of $56), as shown by point G.

Question 9.4 Choose the correct answer(s)

Figure 9.5 depicts Julia’s choice of consumptions in periods 1 and 2. She has no income in period 1 (now) and an income of $100 in period 2 (later). The current interest rate is 10%. Based on this information, which of the following statements are correct?

  • At F, the interest rate exceeds Julia’s discount rate (degree of impatience).
  • At E, Julia is on the highest possible indifference curve, given her feasible set.
  • E is Julia’s optimal choice, as she is able to completely smooth out her consumption over the two periods and consume the same amount.
  • G is not a feasible choice for Julia.
  • At F, the slope of the indifference curve is steeper than that of the feasible frontier. Therefore, Julia’s discount rate exceeds the interest rate.
  • E is on the highest feasible indifference curve because any higher indifference curves would not touch the budget constraint line.
  • At E, Julia consumes 56 in period 1 and 38 in period 2.
  • G is in Julia’s feasible set. She does not choose it because it is not the optimal choice (it is on a lower indifference curve).

9.5 Storing or lending allows smoothing and moving consumption to the future

Now think about Marco, an individual otherwise identical to Julia, but facing a very different situation. Marco has wealth of $100 but does not (yet) anticipate receiving any income later.

By identical, we mean that Marco’s preferences between consumption now and later are the same as Julia’s. For example, in Figure 9.4 we showed a hypothetical indifference curve for Julia if she had $100 now. This is Marco’s reservation indifference curve in Figure 9.6.

Marco and Julia have the same degree of pure impatience but are in very different situations. Julia wishes to bring forward some consumption; Marco could use all of his $100 to buy goods to consume now, but as we have seen, this would probably not be the best he could do given the circumstances. In order to smooth his consumption over time, he wishes to move some consumption to the future.

Marco’s options for smoothing: Storing

Marco could do this by just putting some of his wealth in cash in a drawer, not spending it now, and having it later. We assume that his $100 will not be stolen and that $100 will purchase the same amount of goods now and later because there is no inflation (that is, the price level in the economy doesn’t rise).

In Figure 9.6, we see that Marco’s endowment is on the horizontal axis, as he has $100 available now. His reservation indifference curve includes the point $100 on the horizontal axis.

Figure 9.6 analyses Marco’s decision. The dark line shows Marco’s feasible frontier if he just ‘stores’ his wealth in cash in the drawer, and the dark shaded area shows his feasible set. The frontier shows that, for every dollar that Marco stores, he will have a dollar later—for example, if he stored $50 he could consume $50 of his wealth now and $50 later. Thus, the marginal rate of transformation (MRT) of current consumption into future consumption is just 1.

Smoothing consumption by storing.

Figure 9.6 Smoothing consumption by storing.

Marco’s preferences

Marco’s reservation indifference curve goes through his endowment.

Figure 9.6a Marco’s reservation indifference curve goes through his endowment.

Marco’s preferences

Indifference curves to the right of Marco’s reservation curve indicate higher levels of utility.

Figure 9.6b Indifference curves to the right of Marco’s reservation curve indicate higher levels of utility.

Marco’s feasible frontier

With storage, there is a one-to-one trade-off between consumption now and consumption later.

Figure 9.6c With storage, there is a one-to-one trade-off between consumption now and consumption later.

Marco’s decision to store

Point H on Marco’s indifference curve denotes the amount of storage that he will choose.

Figure 9.6d Point H on Marco’s indifference curve denotes the amount of storage that he will choose.

In Figure 9.6, some part of Marco’s feasible frontier lies above and to the right of his reservation indifference curve, so he can do better by storing. If storing were the only option, he would definitely store some of his $100.

In Figure 9.6 the figure we see that he stores less than half, so he ends up consuming more now than later. This means that Marco, like Julia, has some degree of pure impatience. If this were not the case, he would store half of his endowment and have the same levels of consumption now and later.

Marco’s options for smoothing: Lending

A better plan, if Marco could find a trustworthy borrower who would repay for sure, would be to lend some of his wealth. If he did this and could be assured of repayment of (1 + r) for every $1 lent, then he could have feasible consumption of 100 × (1 + r) later, or any of the combinations along his new feasible frontier. The light line in Figure 9.7 shows the feasible frontier when Marco lends at 20%. By lending, Marco has raised the marginal rate of transformation of current spending into future spending. With storing it was just 1. Now it is 1.2.

As you can see from Figure 9.7, Marco’s feasible set is now expanded by the opportunity to lend money at interest, compared to storing the cash (putting it in his drawer). Anything that expands a person’s feasible set so that the old feasible set is entirely inside the new one must allow that person to be better off. Marco is able to reach a higher indifference curve by lending rather than storing.

As we shall see in Unit 10, there are a variety of financial instruments in a contemporary economy that Marco can use to shift consumption to the future by lending—such as term deposits or bonds issued by companies or by the government. Note that, in recent years, returns of 20%, as in Figure 9.7, have been very unusual indeed.

Smoothing consumption by storing and lending.

Figure 9.7 Smoothing consumption by storing and lending.

Marco’s decision to lend

The light line shows the feasible frontier when Marco lends at 20%.

Figure 9.7a The light line shows the feasible frontier when Marco lends at 20%.

The effect of the decision to lend

Marco is now able to reach a higher indifference curve.

Figure 9.7b Marco is now able to reach a higher indifference curve.

But how much will Marco lend? Like Julia, he will seek the highest feasible indifference curve by finding the point of tangency between the indifference curve and the feasible frontier. This is point J, at which Marco has equated his MRS between consumption now and in the future to the MRT, which is the cost of moving goods from the present to the future.

In the example, the amount Marco lends does not change. But it could be lower or higher. When he lends, he is better off, so this would tend to push up his consumption now and push down his lending. But when he can earn interest, this increases his return from postponing consumption. This would tend to push up his lending and raise his consumption later. The case in the diagram assumes that these cancel out, leaving lending and consumption now unchanged.

Exercise 9.2 Marco’s feasible frontier

As we did with Julia, we construct Marco’s feasible frontier under storing or lending by finding all the combinations of consumption now and in the next period, given his endowment and the interest rate.

  1. Complete the table below, using the information given. Round your answers to the nearest dollar.
  2. Using your completed table, draw a diagram similar to Figure 9.7, showing the feasible frontier, consumption, and lending options.
Point on the feasible frontier Consumption now
= Income now – Amount stored or lent
Consumption later
= Amount stored
or = Amount lent including interest on the loan
or =(1 + r) × Amount lent
Amount stored or lent (excluding interest)
Endowment point (100, 0) 100 0 0
Store money in a drawer
91 9 9
50
30
Lend at an interest rate of 20%
(56, 53) 56 (1 + 0.2)(100 − 56) = 53 44
30
33

9.6 Mutual gains and conflicts over their distribution in the credit market

In the initial situation, Julia and Marco would both get $100 eventually, but time creates a difference. In the present, Marco’s wealth, narrowly defined, is $100. Julia’s wealth is zero.

Marco and Julia’s indifference curves, and hence their pure impatience, are identical. They differ according to their situation, not their preferences. Marco’s reservation indifference curve is superior to Julia’s (farther away from the origin) because he has wealth now, and she has the same amount, but later. Julia borrows because she is poor in the present, unlike Marco, which is why she is more impatient than him. She wants to smooth her consumption by bringing some buying power to the present.

The fact that Marco is in exactly the opposite situation—he is looking for ways to move some consumption to the future—explains why they can mutually benefit, Marco by lending and Julia by borrowing. We are not assuming that they are borrowing and lending directly to each other. Rather, they are borrowing and lending on the same market.

The solid lines in Figure 9.8 show the borrowing opportunities for Julia and lending opportunities for Marco, both measured by their feasible frontiers.

The feasible frontiers of the two both have a slope of (1 + r). For Julia, the cost of moving $1 from the future to the present by borrowing is 1 + r, while for Marco the gain from moving $1 from the present to the future by lending is also 1 + r. They face the same ‘price’ of moving consumption in time, but they are moving their buying power in different directions.

Remember, in this unit what we call the ‘slope’ will always be a positive number, even though the line slopes downwards.

This is why Marco’s feasible frontier is uniformly outside Julia’s; he has more choices open to him than she does. Because they have identical indifference curves, we know that he will be able to enjoy a higher level of utility than Julia will.

On opposite sides of the market: An increase in the interest rate improves Marco’s welfare and reduces Julia’s.

Figure 9.8 On opposite sides of the market: An increase in the interest rate improves Marco’s welfare and reduces Julia’s.

Julia’s feasible frontier

The dark red line shows Julia’s feasible frontier when the interest rate is 20%.

Figure 9.8a The dark red line shows Julia’s feasible frontier when the interest rate is 20%.

Marco’s feasible frontier

The bright red line shows Marco’s feasible frontier when the interest rate is 20%.

Figure 9.8b The bright red line shows Marco’s feasible frontier when the interest rate is 20%.

Effect of an interest rate rise on Julia’s frontier

When the interest rate rises to 78%, Julia’s feasible set shrinks.

Figure 9.8c When the interest rate rises to 78%, Julia’s feasible set shrinks.

Effect of an interest rate rise on Marco’s frontier

When the interest rate rises to 78%, Marco’s feasible set expands.

Figure 9.8d When the interest rate rises to 78%, Marco’s feasible set expands.

Figure 9.8 also shows the effect of an increase in the rate of interest from r = 0.20 to r = 0.78. The increase in the rate of interest makes both feasible frontiers steeper, but this:

Let’s return to how Marco differs from Julia. They have identical preferences, but:

conflict of interest
The situation which arises if in order for one party to gain more from the interaction, another party must do less well.

Exercise 9.3 Lifetime income

Consider an individual’s income over his or her lifetime, from leaving school to retirement. Using the concepts in this unit, explain in words how an individual may move from a situation like Julia’s to one like Marco’s over the course of their lifetime (assume that their pure impatience remains unchanged over their lifetime).

Question 9.5 Choose the correct answer(s)

Figure 9.7 depicts Marco’s choice of consumption in periods 1 (now) and 2 (later). He has $100 in period 1 and no income in period 2. Marco has two choices: he can store the money that he does not spend in period 1, or he can lend the money he does not consume at an interest rate of 20%. Based on this information, which of the following statements are correct?

  • With storage, if Marco consumes $68 in period 1, he can consume $32 in period 2.
  • With lending, if Marco consumes $68 in period 1, he can consume $35 in period 2.
  • The marginal rate of transformation is higher when storing than when lending.
  • Marco will always be on a higher indifference curve when lending than when storing.
  • Under storage, Marco’s consumption in both periods must sum to $100.
  • He lends $32, which then increases in value by 20% to $38.40.
  • The MRT is 1 when storing, and 1.2 when lending.
  • The budget constraint when lending is higher than in scheme 1 at any positive level of storing.

9.7 Borrowing may allow investing: Julia’s best hope

Like Julia in our model, payday borrowers in New York often buy groceries or clothes for their children with their borrowed funds; farmers in Chambar also often borrow for purposes of consumption, for example, to pay for a wedding. But both the Chambar farmers and New York payday borrowers sometimes use the borrowed funds for an investment. For the Pakistani farmers, this could be the purchase of equipment that would improve the crop yield.

collateral
An asset that a borrower pledges to a lender as a security for a loan. If the borrower is not able to make the loan payments as promised, the lender becomes the owner of the asset.

Now suppose that Julia is considering becoming a Lyft driver and to qualify needs to make some cosmetic repairs on her brother’s car that she will drive. She cannot use the car as collateral (it is not hers), so she finds it difficult to get a conventional loan. She goes to a payday lender, who, as in the example above, will charge her an interest rate of 78%. Figure 9.9 shows Julia’s feasible set and frontier based on borrowing at this rate.

Julia has a new option—she can borrow and then split how much she has borrowed between consuming some now and investing the rest. This is her plan:

Suppose it is the case that every dollar Julia spends on the car will result in $3 more in income next year (that is, a rate of return of 200%). Then she can move along the new dashed feasible frontier with investment.

To see the full range of her new options, if she invested the entire $56 (so that she would have no consumption now), she would have $168 (3 × 56) next year. All the points on the dashed feasible frontier with investment are now open to her. The slope of the feasible frontier with investment is 3, which is the ratio of income later to amount invested. The steeper the slope is, the better for Julia. This slope is the marginal rate of transformation of current investment into future income.

Options for the individual (Julia) who starts without assets but can borrow and invest.

Figure 9.9 Options for the individual (Julia) who starts without assets but can borrow and invest.

Julia’s options

She can borrow at an interest rate of 78% and can also choose to invest some of her income with a return of 200%. The dotted line shows her feasible frontier when she chooses to borrow and invest.

Figure 9.9a She can borrow at an interest rate of 78% and can also choose to invest some of her income with a return of 200%. The dotted line shows her feasible frontier when she chooses to borrow and invest.

How much will Julia invest?

She will use the same rule that she used in deciding how much to borrow when there was no option to invest. She will find the highest feasible indifference curve by finding the tangency of an indifference curve and the feasible frontier, or what is the same thing, equating the MRT (slope of the feasible frontier) with the MRS (slope of the indifference curve.)

Figure 9.9b She will use the same rule that she used in deciding how much to borrow when there was no option to invest. She will find the highest feasible indifference curve by finding the tangency of an indifference curve and the feasible frontier, or what is the same thing, equating the MRT (slope of the feasible frontier) with the MRS (slope of the indifference curve.)

Julia’s optimal choice

Doing this, Julia chooses point I in the figure. How does this work out for her? Having borrowed the maximum—$56—she invests $21 and consumes $35 now. The investment of $21 will yield her an income of $63 later.

Figure 9.9c Doing this, Julia chooses point I in the figure. How does this work out for her? Having borrowed the maximum—$56—she invests $21 and consumes $35 now. The investment of $21 will yield her an income of $63 later.

The investment opportunity has greatly increased Julia’s wellbeing. She consumes the same amount now that she did when only the borrowing opportunity was available—$35—but she can now consume $63 later, rather than only $38. Note that she will only invest if she has an investment project with a rate of return higher than 78%—the rate of return has to be higher than the borrowing rate in order to expand her feasible set.

In our example, Julia consumes the same amount now under the borrowing only and borrowing and investment options; her current consumption could be either greater than or less than in the case without the investment opportunity. What is certain is that she is better off with the investment opportunity because her feasible set is expanded.

We can thus contrast three situations in which Julia might have found herself:

Question 9.6 Choose the correct answer(s)

Figure 9.9 depicts two possible feasible frontiers for Julia, who has no income in period 1 (now) and $100 in period 2 (later). The solid line (option 1) shows her feasible frontier if she borrows at an interest rate of 78%. The dotted line shows her feasible frontier if she borrows at an interest rate of 78% and can invest for a return of 200% (option 2). Based on this information, which of the following statements are correct?

  • When borrowing only, Julia is worse off than at her initial endowment (point A) because of the high interest rate.
  • The consumption choice G can only be attained under option 1.
  • If the interest rate for borrowing increases to 100%, ceteris paribus the feasible frontiers become steeper and the vertical axis intercept under option 2 is now $150.
  • If the return on investment increases to 250%, ceteris paribus the vertical axis intercept under option 2 is now $200.
  • Julia is on a higher indifference curve at G than at her endowment point. Therefore, she is better off when borrowing.
  • G is in the feasible set of options 1 and 2, so it is a possible choice under both options. However, G is only optimal under option 1.
  • With an interest rate of 100%, Julia can borrow a maximum of $50 in period 1, so her maximum consumption in period 2 is 50 + 2(50) = $150.
  • With a return of 250%, Julia’s maximum consumption in period 2 is 56 + 2.5(56) = $196.

9.8 Credit market constraints: Another principal–agent problem

Lending is risky

Up until now, we have said nothing about the elephant in the room—lending is risky. A loan is made now and must be repaid in the future. Between now and then, unanticipated events beyond the control of the borrower can occur.

If the crops in Chambar, Pakistan were destroyed by bad weather or disease, the moneylenders would not be repaid, even though the farmers worked hard. The obsolescence of the skill you have invested in using your student loan is an unavoidable risk and will mean the loan may not be repaid.

The greater the risk of default due to unavoidable events, the greater the interest rate set by a bank or a moneylender. This is one explanation for why an interest rate of 78%, as is the case in Chambar, is not highly profitable. Two other reasons were noted in the introduction:

Differences of interest, and information problems

But lenders face two further problems. When loans are taken out for investment projects, the lender cannot be sure that a borrower will exert enough effort to make the project succeed. Remember, if the borrower has not put any of her own money into the project, it is the lender, not the borrower, who loses money if the project fails and the loan is not repaid.

Moreover, often the borrower has more information than the lender about the quality of the project and its likelihood of success.

These problems arise in turn from a difference (or conflict) of interest between the borrower and lender, and from the difference between the information the borrower and the lender have about the borrower’s project and actions. The problems impose costs of monitoring and loan enforcement that will push up the interest rate on loans.

If the project doesn’t succeed because the borrower made too little effort or because it just wasn’t a good project, the lender loses money. If the borrower were using only her own money, it is likely that she would have been more conscientious or maybe not engaged in the project at all.

The borrower may decide to use the borrowed funds for a much riskier project than the one that she told the lender she would use it for. To illustrate this (with an extreme example), she could simply buy lottery tickets with the money she has borrowed—if one of them pays off, she is rich; if not, the lender does not get repaid.

principal–agent relationship
This is an asymmetrical relationship in which one party (the principal) benefits from some action or attribute of the other party (the agent) about which the principal’s information is not sufficient to enforce in a complete contract. See also: incomplete contract. Also known as: principal–agent problem.

The relationship between the lender and the borrower is a principal–agent problem similar in many ways to the relationship between the employer and employee studied in the previous unit. The lender is the ‘principal’ and the borrower is the ‘agent’.

The principal–agent problem between borrower and lender is also similar to the ‘somebody else’s money’ problem discussed in Unit 6. In that case, the manager of a firm (the agent) makes decisions about the use of the funds supplied by the firm’s investors (the principals), but they cannot contractually require the manager to act in a way that maximizes their wealth, rather than pursuing her own objectives.

Incomplete contracts

In the case of borrowing and lending, it is often not possible for the lender (the principal) to write a contract that ensures a loan will be repaid by the borrower (the agent). The reason is that it is impossible for the lender to ensure by contract that the borrower will use the funds in a prudent way and repay according to the terms of the loan.

The table in Figure 9.10 compares two principal–agent problems.

Actors Conflict of interest over Enforceable contract covers Left out of contract (or unenforceable) Result
Labour market (Unit 6) Employer
Employee
Wages, work (quality and amount) Wages, time, conditions Work (quality and amount), duration of employment Effort under-provided; unemployment
Credit market (Unit 9) Lender
Borrower
Interest rate, conduct of project (effort, prudence) Interest rate Effort, prudence, repayment Too much risk, credit constraints

Principal–agent problems: The credit market and the labour market.

Figure 9.10 Principal–agent problems: The credit market and the labour market.

Lenders will attempt to secure repayment of a loan through legal measures but this will often be difficult if the borrower is poor or declares bankruptcy. In the introduction to this unit, we reported an example of a method of improving compliance in car loan repayments—companies install devices that disable the ignition of the car if the repayments are not made as required.

If legal methods fail, lenders may use illegal ones, such as threatening physical violence.

The role of collateral in lending

equity
An individual’s own investment in a project. This is recorded in an individual’s or firm’s balance sheet as net worth. See also: net worth. An entirely different use of the term is synonymous with fairness.

One response of the lender to the conflict of interest in the credit market is to require the borrower to put some of her wealth into the project (this is called equity). The more of the borrower’s own money that is invested in the project, the more closely aligned her interests are with those of the lender. Another common response is to require the borrower to set aside property that will be transferred to the lender if the loan is not repaid (this is called collateral).

Collateral is used in loans for houses (called mortgages) and for cars. For many people, these are the only large loans they can get, and that is because of the collateral—the house, or the car reverts to the lender if repayments are not made.

The pawnbroker is a common example of collateral in small-scale lending and borrowing that has existed for thousands of years. The pawnbroker, found today on shopping streets under the slogan ‘Cash converter’ or similar, extends a loan to the borrower with a date and amount of repayment specified. And the borrower turns over some item of his or her property to the pawnbroker, which will be returned to the borrower when the loan is repaid. Items commonly lodged with a pawnbroker because they can easily be sold include jewelry, computers and other electronic equipment, cameras, or valuable household items.

A loan with collateral is called a secured loan because, as long as the collateral (the house or the pawned item) can readily be sold for more than the amount of money owed, the lender is secure. With a secured loan, the lender does not run any risk.

conflict of interest
The situation which arises if in order for one party to gain more from the interaction, another party must do less well.

Equity or collateral reduces the conflict of interest between the borrower and the lender. The reason is that, when the borrower has some of her money (either equity or collateral) at stake:

Credit rationing and inequality

But there is a hitch. If the borrower had been wealthy, she could either have used her wealth as collateral and as equity in the project, or she could have been on the other side of the market, lending money. Often the reason why the borrower needs a loan is that, like Julia, she is not wealthy. As a result, she may be unable to provide enough equity or collateral to sufficiently reduce the conflict of interest and hence the risk faced by the lender, and the lender refuses to offer a loan.

Adam Smith had credit rationing in mind when he wrote: ‘Money, says the proverb, makes money. When you have got a little it is often easy to get more. The great difficulty is to get that little.’ Adam Smith. 1776. ‘Of the profits of stock’. In An Inquiry into the Nature and Causes of the Wealth of Nations.

credit rationing
The process by which those with less wealth borrow on unfavourable terms, compared to those with more wealth.

This is called credit rationing—those with less wealth borrow on unfavourable terms compared with those with more wealth or are refused loans entirely.

credit-excluded
A description of individuals who are unable to borrow on any terms. See also: credit-constrained.
credit-constrained
A description of individuals who are able to borrow only on unfavourable terms. See also: credit-excluded.

Borrowers whose limited wealth makes it impossible to get a loan at any interest rate are termed credit-excluded. Those who borrow, but only on unfavourable terms, are termed credit-constrained. Both are sometimes said to be wealth-constrained, meaning that their lack of wealth limits their credit market opportunities.

The relationship between wealth and credit is summarized in Figure 9.11.

Wealth, project quality, and credit.

Figure 9.11 Wealth, project quality, and credit.

The exclusion of those without wealth from credit markets or their borrowing on unfavourable terms is evident in these facts:

Question 9.7 Choose the correct answer(s)

Which of the following statements regarding the principal–agent problem are correct?

  • A principal–agent problem exists in loans due to a positive possibility of the principal not being repaid.
  • The principal–agent problem can be resolved by writing a binding contract for the borrower to exert full effort.
  • One solution for the principal–agent problem in loans is for the borrower to provide equity.
  • The principal–agent problem leads to credit rationing in the loans market.
  • A principal–agent problem exists in loans due to the asymmetric information regarding the borrower’s effort or the quality of the project.
  • The principal–agent problem exists because one cannot write a binding contract for full effort.
  • Equity implies that the agent has more to lose if the project fails, reducing the difference in the incentives between the principal and the agent.
  • This occurs because some otherwise-viable projects will not be funded owing to the principal–agent problem. In particular, those with few assets or little wealth who cannot afford to put in equity or provide collateral are more likely to be credit rationed because of the principal agent problem.

Exercise 9.4 Microfinance and lending to the poor

Read the paper ‘The Microfinance Promise’.5

The Grameen Bank in Bangladesh makes loans available to groups of individuals who together apply for individual loans, under the condition that the loans to the group members will be renewed in the future if (but only if) each member has repaid the loan on schedule.

  1. Explain how you think such an arrangement would affect the borrower’s decision about what to spend the money on, and how hard she will work to make sure that repayment is possible.
  2. Use the concepts in this section to explain how the Grameen Bank’s lending method could affect credit rationing and credit exclusion.
  3. Find evidence about whether or not microfinance has been effective in increasing investment by groups who would normally be excluded from the credit market.

9.9 Inequality: Lenders, borrowers, and those excluded from credit markets

We can analyse inequalities between borrowers and lenders (and among borrowers) using the same Lorenz curve and Gini coefficient model that we used to study inequality among employers and employees in Unit 8, and farmers and landowners in Unit 5.

Lenders and borrowers in the Lorenz curve diagram

Here is an illustration. An economy is composed of 90 farmers who borrow from 10 lenders and use the funds to finance the planting and tending of their crops. The harvest (on average) is sold for an amount greater than the farmer’s loan, so that for every euro borrowed and invested, the farmer receives 1 + R when the crop is sold after the harvest. This is the farmer’s revenue.

Following the harvest, the farmers repay the loans with interest, at rate i. To focus on the Lorenz curve model, we simplify in this section by assuming that all of the loans are repaid and that all lenders lend the same amount to the farmers at the same interest rate. The main message would not be altered if we included the probability that loans were not repaid (as in the Chambar case study), but the mathematics would be a lot more complicated.

Thus, if i = 0.10 and R = 0.15, then the lender’s share of total income is two-thirds and the borrower’s is one-third.

Inequality in this economy is shown by the dark-shaded area bordered by a solid line in Figure 9.12. The Gini coefficient is 0.57.

Excluded borrowers raise the Gini coefficient

In the previous sections, we showed why some would-be borrowers (those unable to post collateral or lacking their own funds to finance a project) might be excluded entirely from borrowing even if they would be willing to pay the interest rate. How does this affect the Lorenz curve and the Gini coefficient?

To explore this, imagine that 40 of the prospective borrowers are now excluded. Since they cannot borrow, they receive no income at all. For the other famers, i and R remain unchanged.

The dashed line in Figure 9.12 shows the new situation. The new Gini coefficient is 0.70, showing an increase in inequality when the poor are excluded from the credit market.

Inequality in a borrowing and lending economy. The Gini coefficient when everyone in the population can borrow is 0.57. When 40% of would-be borrowers are excluded from the credit market, it is 0.70.

Figure 9.12 Inequality in a borrowing and lending economy. The Gini coefficient when everyone in the population can borrow is 0.57. When 40% of would-be borrowers are excluded from the credit market, it is 0.70.

A model economy of lenders and borrowers

An economy is composed of 90 farmers who borrow from 10 lenders. Since i = 0.10 and R = 0.15, the lenders’ share of total income is two-thirds and the borrowers’ is one-third. The Gini coefficient is 0.57.

Figure 9.12a An economy is composed of 90 farmers who borrow from 10 lenders. Since i = 0.10 and R = 0.15, the lenders’ share of total income is two-thirds and the borrowers’ is one-third. The Gini coefficient is 0.57.

Some borrowers are credit market excluded

Suppose that 40 of the prospective borrowers are excluded. Since they cannot borrow, they receive no income at all.

Figure 9.12b Suppose that 40 of the prospective borrowers are excluded. Since they cannot borrow, they receive no income at all.

Inequality increases

When some prospective borrowers are excluded, the Gini coefficient increases to 0.70.

Figure 9.12c When some prospective borrowers are excluded, the Gini coefficient increases to 0.70.

Question 9.8 Choose the correct answer(s)

In an economy with a population of 100, there are 80 farmers and 20 lenders. The farmers use the funds to finance the planting and tending of their crops. The rate of profit for the harvest is 12.5%, while the interest rate charged is 10%. Compare the following two cases:

  1. Case A: All farmers are able to borrow.
  2. Case B: Only 50 farmers are able to borrow.

Based on this information, which of the following statements are correct?

  • The share of total output received by the farmers who can borrow is 25%.
  • The Gini coefficient for case A is 0.5.
  • The Gini coefficient for case B is 0.6.
  • There is a 10% increase in the Gini coefficient in case B compared to case A.
  • The farmers keep 12.5 – 10 = 2.5% of the 12.5% profit rate. This is a 2.5/12.5 = 20% share.
  • The Gini coefficient for case A is 0.6.
  • The Gini coefficient for case B is 0.66.
  • 0.66 is 10% higher than 0.6.

The credit market can provide mutual gains but perpetuates inequalities

This example illustrates the fact that one cause of inequality in an economy is that some people (like Marco) are in a position to profit by lending, just as others (like Bruno in Unit 5) are in a position to profit by employing others.

Bruno and Marco are probably not the best-loved characters that you have met so far in this course. For similar reasons, banks are not the most popular or trusted institutions. In the US, for example, 73% of people expressed ‘a great deal’ or ‘quite a lot’ of confidence in the military in 2016, exactly the same as the level a decade earlier. In contrast, in 2016, only 27% expressed a degree of confidence in banks, down from 49% a decade earlier. Surveys show that the public in Germany, Spain and many other countries hold their banks in low esteem. This has particularly been the case since the financial crisis of 2008. In Unit 10, we look at banks as economic actors in a modern economy.

It is sometimes said that rich people lend on terms that make them rich, while poor people borrow on terms that make them poor. Our example of Julia and Marco made it clear that one’s view of the interest rate—as a cost for Julia and as a source of income for Marco—depends on one’s wealth. People with limited wealth are credit-constrained, which limits their ability to profit from the investment opportunities that are open to those with more assets.

mutual gains
An outcome of an interaction among two or more people, in which all parties are better off as a result than they would have been without the interaction (or at least some parties are better off and none are worse off).

It is also true that, in determining the rate of interest at which an individual borrows, the lender often has superior bargaining power, and so can set a rate that enables him to capture most of the mutual gains from the transaction.

Like other profit-making firms, banks are owned by wealthy people and they often transact on terms (rates of interest, wages) that perpetuate the lack of wealth of borrowers and employees. But as we saw in the Chambar case, the profitability of the lending also depends on the extent of competition among lenders. The interest rate charged by the moneylenders in Chambar would have been even higher if—as in many villages—there is only a single moneylender.

Like the labour market, the credit market provides opportunities for mutual gains

But even those who dislike banks do not think that the less wealthy would be better off in their absence, any more than that the less wealthy would benefit if firms ceased to employ workers. Access to credit is essential to a modern economy—including access of the less well off to economic opportunities—because it provides opportunities for mutual gains that occur when people can benefit by moving their buying power from one time period to another, either borrowing (moving it to the present) or lending (the opposite).

Exercise 9.5 Unpopular banks

Why do you think that banks tend to be more unpopular than other profit-making firms (Honda or Microsoft, for example)?

Exercise 9.6 Limits on lending

Many countries have policies that limit how much interest a moneylender can charge on a loan.

  1. Do you think these limits are a good idea?
  2. Who benefits from the laws and who loses?
  3. What are the likely long-term effects of such laws?
  4. Contrast this approach to helping the poor gain access to loans with the Grameen Bank in Exercise 9.4.

9.10 The credit market and the labour market

The credit and labour markets share similarities. We use a principal–agent model to describe both.

The two markets are not only similar, they are related to each other, the credit market providing the funds allowing some (but not others) to become employers in the labour market. This is shown in Figure 9.13.

The credit and labour markets shape the relationships between groups with different endowments.

Figure 9.13 The credit and labour markets shape the relationships between groups with different endowments.

A model economy

Consider an economy with wealthy individuals and employees.

Figure 9.13a Consider an economy with wealthy individuals and employees.

Credit market excluded

Those without wealth (collateral) or insufficient wealth are excluded from the credit market.

Figure 9.13b Those without wealth (collateral) or insufficient wealth are excluded from the credit market.

Wealthy individuals and successful borrowers

These people can purchase capital goods so as to become employers.

Figure 9.13c These people can purchase capital goods so as to become employers.

Those who are not wealthy

These are employees or unemployed.

Figure 9.13d These are employees or unemployed.

Employers hire employees on the labour market

This excludes the unemployed.

Figure 9.13e This excludes the unemployed.

Starting at the upper left of Figure 9.13, wealthy individuals can use their wealth to purchase the capital goods to become employers and they can also lend to others. Among the less wealthy, there will be some successful borrowers who can, as a result, also become employers. Those with even less wealth cannot borrow (they are the credit market excluded or can only borrow where the house provides the collateral for the mortgage), and must seek work as employees. Employers then hire employees from among the less wealthy, with some remaining unemployed (due to the workings of the labour market that you studied in Unit 8).

Horizontal arrows (‘lend to’ and ‘hire’) indicate a principal–agent relationship. Lenders and employers are the principals in Figure 9.13; their common orange colour indicates this similarity. Agents—successful borrowers, and employees—are coloured green to distinguish them from would-be agents (credit market excluded and unemployed), who are coloured purple. You definitely do not want to be in the purple boxes. But even if you are an agent lucky enough to be in one of the green boxes, the principal can put you back in the purple box just by refusing to deal with you. This is why lenders and employers have power over borrowers and employees.

Figure 9.13 helps us understand why some people end up as principals (employers, for example), while others end up as agents (employees). If one is wealthy, one can be both a lender and an employer. There is some truth to the saying that ‘people are born into their position in the economic order’. This was literally true in some economies of the past, for example, when the position of the slave was perpetuated in the slave’s children as a matter of law.

If you want to study this topic in more detail, you can read about it in Unit 19 of The Economy, which is all about the causes and effects of economic inequality.

Something similar can occur in places where wealth is inherited from parent to child. The children of employees (who inherit little wealth) are also more likely to become the next generation’s workers than are the children of employers. The children of well off parents in the US also tend to have high incomes when they become adults.

9.11 Conclusion

wealth
Stock of things owned or value of that stock. It includes the market value of a home, car, any land, buildings, machinery or other capital goods that a person may own, and any financial assets, such as bank deposits, shares, bonds, or loans made to others. Debts to others are subtracted from wealth—for example, the mortgage owed to the bank.
stock
A quantity measured at a point in time. Its units do not depend on time. See also: flow.
saving
When consumption expenditure is less than net income, saving takes place and wealth rises. See also: wealth.
income
The amount of labour earnings, dividends, interest, rent, and other payments (including transfers from the government) received by an economic actor, net of taxes paid, measured over a period of time, such as a year. The maximum amount that you could consume and leave your wealth unchanged. Also known as: disposable income. See also: pre-tax income.
flow
A quantity measured per unit of time, such as annual income or hourly wage.
human capital
The stock of knowledge, skills, behavioural attributes, and personal characteristics that determine the labour productivity or labour earnings of an individual. Investment in this through education, training, and socialization can increase the stock, and such investment is one of the sources of economic growth. Part of an individual’s endowments. See also: endowment.
income net of depreciation
Disposable income minus depreciation. See also: disposable income, gross income, depreciation.
consumption (C)
Expenditure on both short-lived goods and services and long-lived goods, which are called consumer durables.
constrained choice
No definition available.

This unit has looked at how credit markets, like labour markets, shape the relationship between groups with different endowments. To do so, we began by differentiating between wealth (a stock of accumulated savings) and income (a flow affected by direct taxes and transfers). Wealth can include money, financial assets, and physical assets. A broader definition of wealth includes human capital. While holding other things constant, greater income net of depreciation increases wealth, while greater consumption decreases it.

Using our constrained choice toolkit, we have developed a model of borrowing and lending to analyse how individuals decide to allocate their consumption across time periods.

preferences
A description of the benefit or cost we associate with each possible outcome.
feasible frontier
The curve made of points that defines the maximum feasible quantity of one good for a given quantity of the other. See also: feasible set.
interest rate
The price of bringing some buying power forward in time. See also: nominal interest rate, real interest rate.
indifference curve
A curve of the points which indicate the combina­tions of goods that provide a given level of utility to the individual.
utility
A numerical indicator of the value that one places on an outcome, such that higher valued outcomes will be chosen over lower valued ones when both are feasible.
discount rate
A measure of the person’s impatience: how much the person values an additional unit of consumption now relative to an additional unit of consumption later. It is the absolute value of the slope of the person’s indifference curve for consumption now and consumption later, minus one. Also known as: subjective discount rate.
smooth consumption
No definition available.
diminishing marginal returns to consumption
The value to the individual of an additional unit of consumption declines, the more consumption the individual has. Also known as: diminishing marginal utility.
pure impatience
This is a characteristic of a person who values an additional unit of consumption now over an additional unit later, when the amount of consumption is the same now and later. It arises when a person is impatient to consume more now because she places less value on consumption in the future for reasons of myopia, weakness of will, or for other reasons.
Constraint Preferences
The feasible frontier—consumption now and in the future cannot exceed one’s present and future income.

The slope of the feasible frontier is determined by the interest rate r, which affects the opportunity cost of consuming today. The marginal rate of transformation (MRT) is (1 + r), indicating that one must forgo (1 + r ) units of consumption in the future in order to consume one more unit today.

Indifference curves join together all combinations of present and future consumption that provide the same level of utility.

The slope of the indifference curves is determined by the discount rate , which reflects both a preference to smooth consumption (there are diminishing marginal returns to consumption in a given period) and pure impatience (be it due to myopia or prudence). The MRS is given by (1 + ).

Optimal choice: MRT = MRS
(1 + r) = (1 + )
r = 

mutual gains
An outcome of an interaction among two or more people, in which all parties are better off as a result than they would have been without the interaction (or at least some parties are better off and none are worse off).
conflict of interest
The situation which arises if in order for one party to gain more from the interaction, another party must do less well.
principal–agent relationship
This is an asymmetrical relationship in which one party (the principal) benefits from some action or attribute of the other party (the agent) about which the principal’s information is not sufficient to enforce in a complete contract. See also: incomplete contract. Also known as: principal–agent problem.
asymmetric information
Information that is relevant to the parties in an economic interaction, but is known by some but not by others. See also: adverse selection, moral hazard.
hidden actions (problem of)
This occurs when some action taken by one party to an exchange is not known or cannot be verified by the other. For example, the employer cannot know (or cannot verify) how hard the worker she has employed is actually working. Also known as: moral hazard. See also: hidden attributes (problem of).
incomplete contracts
No definition available.
equity
An individual’s own investment in a project. This is recorded in an individual’s or firm’s balance sheet as net worth. See also: net worth. An entirely different use of the term is synonymous with fairness.
collateral
An asset that a borrower pledges to a lender as a security for a loan. If the borrower is not able to make the loan payments as promised, the lender becomes the owner of the asset.
credit rationing
The process by which those with less wealth borrow on unfavourable terms, compared to those with more wealth.

While the different situations of borrowers and lenders give rise to mutual gains from interacting in the credit market, there is a conflict of interest over how these are distributed. An increased interest rate expands a lender’s feasible set but shrinks that of a borrower.

Differences in interest motivate us to model this as a principal–agent relationship in which:

Having some of one’s own wealth at stake (be it as equity in a project or collateral on a loan) not only signals to the lender a high-quality project, but also helps align interests because the borrower has less incentive to misuse the funds. Individuals with limited wealth, however, may not have access to loans because they cannot provide equity or collateral, or they can only borrow at high interest rates. This credit rationing can perpetuate inequalities as it limits the ability of less wealthy people to profit from the investment opportunities that are open to those with more assets.

9.12 Doing Economics: Credit-excluded households in a developing country

In Sections 9.8 and 9.9, we outlined the principal–agent problem in credit markets, which leads to some households being credit-constrained or credit-excluded.

In Doing Economics Empirical Project 9, we will use survey data from a developing country (Ethiopia) to identify households that face credit constraints and look at how borrowing conditions vary with household characteristics.

Go to Doing Economics Empirical Project 9 to work on this project.

Learning objectives

In this project you will:

  • identify credit-constrained and credit-excluded households using survey information
  • create dummy (indicator) variables
  • create and format time variables in Excel
  • explain why selection bias is an important issue.

9.13 References

  1. Irfan Aleem. 1990. ‘Imperfect information, screening, and the costs of informal lending: A study of a rural credit market in Pakistan’The World Bank Economic Review 4 (3): pp. 329–349.  

  2. Jessica Silver-Greenberg. 2014. ‘New York prosecutors charge payday loan firms with usury’. DealBook. Updated 11 August 2014. 

  3. David Gross and Nicholas Souleles. 2002. ‘Do liquidity constraints and interest rates matter for consumer behavior? Evidence from credit card data’. The Quarterly Journal of Economics 117 (1) (February): pp. 149–185. 

  4. Samuel Bowles. 2006. Microeconomics: Behavior, Institutions, and Evolution (The Roundtable Series in Behavioral Economics). Princeton, NJ: Princeton University Press.  

  5. Jonathan Morduch. 1999. ‘The Microfinance Promise’Journal of Economic Literature 37 (4) (December): pp. 1569–1614.