Unit 6 The financial sector: Debt, money, and financial markets

6.2 Bilateral debt: Marco and Julia

There is good evidence that debt has existed in human societies for millennia, and possibly pre-dates anything we might call money.

We start with a simple example to illustrate how debt allows people to consume and invest when they do not have an income—even in a world without money, or a financial sector.

In this example, there are two characters, Marco and Julia (who also appear in Unit 9 of the microeconomics volume), and only two periods—now and later. And there is only one good—grain—which can be eaten, stored, or used to produce more grain. We assume:

• Marco has wealth—that is, a pile of grain. He can consume it now, but he wants to ensure he can also consume ‘later’.
• Julia, in contrast, has no wealth. But if she could borrow some grain, she could consume some now; she could also grow more for consumption later. Unless she can rely on her family to support her, this is the only way she can avoid starvation.

Land is freely available in Marco and Julia’s world, so the production of new grain requires two inputs: grain itself for planting, and labour. Marco has no wish to spend any time working, but Julia is able and willing to work. So if Marco is prepared to lend some grain to Julia, then she will be able to invest some of it (by planting it now) and pay Marco back in future from the grain she produces.

This requires her to take on a debt, also known as a liability, or an IOU (‘I owe you’): a promise to pay Marco back, also in grain, in the future. For now, we assume that Marco trusts Julia’s promise. So Marco hands over an agreed amount of grain to Julia; in exchange, she promises to repay a fixed amount of grain next period. This is called a bilateral debt contract.

The benefit for Julia of entering into a debt contract is clear—without it she cannot consume. What about Marco? He needs to consume in the second period. So he needs some kind of ‘store of value’: a way of transferring consumption into the future. Or he can save by lending some to Julia, in the expectation that she will repay him later. If he can trust her to do so, this may also be a good deal for him. Firstly, he may be concerned about the difficulties of storing grain safely; in that case, Julia’s promise to repay her loan acts as an alternative store of value. An added incentive for Marco would be a promise from Julia to pay back more grain in the future than she borrows now: in other words, Julia’s liability may require her to pay a positive amount of interest.

Marco and Julia’s balance sheets

balance sheet

A record of all the current assets and liabilities, and the net worth, of an economic actor such as a household, bank, firm, or government. See also: net worth, liability.

asset

Something that is owned, and has value.

liability

A debt; an amount that is owed, with a contractual obligation to repay it in future.

To understand the relationship between an individual’s assets and liabilities, we represent them in a balance sheet. A balance sheet is a device that summarizes assets and liabilities—things that are owned, and things that are owed—at a particular point in time. We can construct balance sheets for individuals, or for institutions such firms or banks, or for the economy as a whole. Assets are listed on the left-hand side, and liabilities on the right.

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 human capital, through education, training, and socialization can increase the stock. Human capital is part of an individual’s endowment. See also: endowment.

net worth

The net worth (or equivalently, wealth) of an individual, household, or organization is the difference between the total value of its assets and the total value of its liabilities.

wealth

The stock of things owned, or value of that stock; it may generate income, or contribute to the owner’s well-being in some other way; 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 shares or bonds. To calculate wealth, debts are subtracted—for example, the mortgage owed to the bank. Debts owed to the person are added.

The difference between a person’s assets and liabilities is their net worth, which is also known as their wealth. The ‘net’ indicates that something has been subtracted: in this case, the total value of what you owe now (liabilities, red) is subtracted from the value of what you own (assets, blue) to give the size of your wealth, (net worth, green) as represented in the balance sheet in Figure 6.2.

Or in words:

\[\textbf{net worth (or wealth) equals assets } \mit{minus} \textbf{ liabilities}\]

Your net worth measures the amount you could consume now if all your debts were paid.

unit of account

A standard unit that is used to measure and compare the market value of different goods and services. One of the functions of money in the economy is to act as a unit of account.

For Marco and Julia, assets, liabilities, and net worth are all measured in terms of grain. Economists would refer to grain as the unit of account in this model, meaning that we measure consumption, wealth, and debt in terms of grain.

Suppose Marco starts out with 100 units of grain, but then agrees to lend 50 units of grain to Julia. (The units could be pounds or kilograms of grain, for example.)

How does the debt contract between Macro and Julia affect their individual wealth? And how does it affect their combined wealth?

Figure 6.3 shows the balance sheets just before, and just after, the loan takes place, for Marco and Julia as individuals (in the first and second slides) and in aggregate (in the third slide).

A key message of Figure 6.3 is that since, at an individual level, neither Marco’s nor Julia’s net worth is changed by the loan, the same is true for their combined net worth.

Therefore, in terms of Marco’s and Julia’s joint net worth, debt cancels out. And once we think about it, this is not a surprising result. A debt contract transfers grain between the lender and the borrower, so it makes no difference to the sum of their current wealth. Nevertheless, it can benefit both parties—Julia can invest to produce more grain in future, and she and Marco can each consume more over the two periods than they could otherwise have done.

While our model is highly stylized, these features of debt and wealth apply to the economy as a whole. To see this, imagine an economy populated only by Marco and Julia. Since for every borrower there must be a lender, then in such an economy, debt would have no direct effect on aggregate wealth.

The second period: Interest rates, investment, and consumption

interest rate, rate of interest

The price of bringing buying power forward in time, by borrowing; it is the additional amount that the borrower promises to repay; the rate of interest is the amount of interest to be repaid per period, as a proportion of the loan. See also: nominal interest rate, real interest rate.

Most debt contracts include an agreement to pay interest; in other words, to pay back more than is borrowed. Suppose that the contract between Julia and Marco specifies an interest rate of 10%. Then if Marco lends Julia 50 units of grain in period 1, she will be required to pay back 55 units (the original loan plus 10% more) in period 2. The rate of interest is the extra amount that the borrower must pay, per period, as a proportion of the loan:

\[\text{rate of interest} = \frac{\text{extra amount borrower promises to pay back}}{\text{loan}}\]

For Marco, the effect of the loan to Julia is that he can consume his remaining 50 units of grain now, and 55 units in the second period.

What about Julia? She needs to invest some of the loan to grow more grain, both for her own future consumption and to repay Marco. Suppose Julia decides to consume 20 units now, and plant 30 units. After long hours of working in the fields, she will harvest her grain at the beginning of period 2, pay 55 units back to Marco, and consume the remainder.

For example if Julia produces 90 units of grain, she will have 35 units left for her own consumption in period 2. Figure 6.4 summarizes the outcome.

Overall, the debt contract has helped Marco to smooth his consumption over the two periods. It has enabled Julia both to consume and invest in the first period. And, because the investment led to grain production, it has enabled both Julia to consume in the second period, and Marco to consume more than he could have done by storing grain.

Of course, the outcome could be very different for both of them, depending on the size of the grain harvest. We shall return to this problem in Section 6.4.