Unit 9 Lenders and borrowers and differences in wealth

9.8 Conflicts over the gains made possible by borrowing and lending

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 intrinsic impatience, are identical. They differ only according to their situation. Marco’s reservation indifference curve is superior to Julia’s (further away from the origin). Julia borrows because she is poor in the present, which is why she is more impatient than him now. She wants to smooth her consumption by bringing some buying power to the present, and he wants to smooth his consumption by shifting buying power to the future.

Julia and Marco are on opposite sides of the credit market

The fact that Marco would like 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 9.14 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). Remember, in this unit what we call the ‘slope’ will always be a positive number, even though the line slopes downwards from left to right. 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.

The r in the above equations is what Marco gets and what Julia pays. This is why Marco’s feasible frontier is uniformly outside Julia’s; his larger feasible set means that 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.

In this diagram, the horizontal axis shows consumption now in dollars, and ranges between 0 and 110. The vertical axis shows consumption later in dollars, and ranges between 0 and 180. Coordinates are (consumption now, consumption later). Point (0, 100) is Julia’s endowment. Point (100, 0) is Marco’s endowment. There are two sets of two parallel, straight, downward-sloping lines. In one set, one line connects points (0, 100) and (83, 0). The other line connects points (0, 120) and (100, 0). In the other set, one line connects points (100, 0) and (56, 0). The other line connects points (0, 178) and (100, 0).
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Figure 9.14 On opposite sides of the market: an increase in the interest rate improves Marco’s welfare and reduces Julia’s.

Julia’s feasible frontier: In this diagram, the horizontal axis shows consumption now in dollars, and ranges between 0 and 110. The vertical axis shows consumption later in dollars, and ranges between 0 and 180. Coordinates are (consumption now, consumption later). Point (0, 100) is Julia’s endowment. A straight downward-sloping line connects points (0, 100) and (83, 0).
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Julia’s feasible frontier

The dark red line connecting the points (0, 100) and (83, 0) shows Julia’s feasible frontier when the interest rate is 20%.

Marco’s feasible frontier: In this diagram, the horizontal axis shows consumption now in dollars, and ranges between 0 and 110. The vertical axis shows consumption later in dollars, and ranges between 0 and 180. Coordinates are (consumption now, consumption later). Point (0, 100) is Julia’s endowment. Point (100, 0) is Marco’s endowment. There are two parallel, straight, downward-sloping lines. One connects points (0, 100) and (83, 0). The other connects points (0, 120) and (100, 0).
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Marco’s feasible frontier

The bright red line connecting the points (0, 120) and (100, 0) shows Marco’s feasible frontier when the interest rate is 20%.

Effect of an interest rate rise on Julia’s frontier: In this diagram, the horizontal axis shows consumption now in dollars, and ranges between 0 and 110. The vertical axis shows consumption later in dollars, and ranges between 0 and 180. Coordinates are (consumption now, consumption later). Point (0, 100) is Julia’s endowment. Point (100, 0) is Marco’s endowment. There are two parallel, straight, downward-sloping lines. One connects points (0, 100) and (83, 0). The other connects points (0, 120) and (100, 0). Another straight, downward-sloping line connects points (0, 100) and (56, 0).
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Effect of an interest rate rise on Julia’s frontier

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

Effect of an interest rate rise on Marco’s frontier: In this diagram, the horizontal axis shows consumption now in dollars, and ranges between 0 and 110. The vertical axis shows consumption later in dollars, and ranges between 0 and 180. Coordinates are (consumption now, consumption later). Point (0, 100) is Julia’s endowment. Point (100, 0) is Marco’s endowment. There are two sets of two parallel, straight, downward-sloping lines. In one set, one line connects points (0, 100) and (83, 0). The other line connects points (0, 120) and (100, 0). In the other set, one line connects points (100, 0) and (56, 0). The other line connects points (0, 178) and (100, 0).
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Effect of an interest rate rise on Marco’s frontier

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

Figure 9.14 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 moves:

  • Marco’s feasible frontier outwards, thereby expanding his set of choices
  • Julia’s feasible frontier inwards, thereby shrinking her set of choices.

Let’s return to how Marco differs from Julia. They have identical preferences, except for the following:

conflict of interest
The situation that arises in an economic interaction if in order for one party to gain more, another party must do less well.
  • Marco starts with wealth while Julia starts with nothing. Julia has the guarantee of a similar asset later, but this puts the two on opposite sides of the credit market.
  • Because of this difference in their situation, they can both benefit by participating in the credit market, Julia by borrowing and Marco by lending.
  • Because Marco’s feasible frontier is entirely outside Julia’s, he can end up on a higher indifference curve than can Julia.
  • Because the cost of moving consumption forward in time by borrowing (the rate of interest) is the same as the gain to Marco by postponing his consumption (by lending), they have a conflict of interest over how the mutual gains from exchange are shared. Marco gains from a higher interest rate and Julia loses.

Question 9.12 Choose the correct answer(s)

Figure 9.14 shows the effect of an interest rate rise on Marco and Julia’s feasible frontiers. Suppose that Marco and Julia’s initial endowments are the same as in Figure 9.14, but the interest rate was initially 10% and increased to 45%. Based on this information, read the following statements and choose the correct option(s).

  • With a 45% interest rate, Marco can consume $80 now and $29 later.
  • With a 45% interest rate, Julia can consume $58 now and $18 later.
  • If Marco were to save all of his initial endowment, he would have $35 more to consume later under a 45% interest rate compared to a 10% interest rate.
  • If Julia were to borrow and consume all of her endowment now, she would have $20 less to consume now under a 45% interest rate compared to a 10% interest rate (rounded to the nearest whole number).
  • If Marco consumes $80 now, he will have 20 × 1.45 = $29 for consumption later.
  • If Julia consumes $58 now, she can consume at most 100 – (58 × 1.45) = $16 later (rounded to the nearest whole number).
  • If Marco were to consume his entire endowment later, he would have $110 to spend if the interest rate were 10% and $145 if the interest rate were 45%, so his maximum consumption later has increased by $35.
  • When the interest rate rises from 10% to 45%, Julia’s maximum consumption now has decreased from $91 to $69, so she has $22 less to consume now.

Exercise 9.8 Lifetime income

Consider an individual’s income over their 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 intrinsic impatience remains unchanged over their lifetime).