Unit 9 Lenders and borrowers and differences in wealth

9.6 Lending and storing: 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 9.5 we showed a hypothetical indifference curve for Julia if she had $100 now. Marco’s reservation indifference curve is shown in Figure 9.7.

Marco and Julia have the same degree of intrinsic impatience, but they have very different degrees of situational impatience. Julia wishes to bring forward some consumption; Marco could use all of his $100 to buy goods to consume now but, as the analysis from previous sections suggests, 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 (we assume the price level in the economy doesn’t change).

Figure 9.7 shows 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 9.7 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. Therefore, the MRT of current consumption into future consumption is just 1.

In this diagram, the horizontal axis shows consumption now, in dollars, and ranges between 0 and 120. The vertical axis shows consumption later, in dollars, and ranges between 0 and 150. Marco’s endowment point has coordinates (100, 0). A downward-sloping, convex curve passes through Marco’s endowment point, and is labelled Marco’s reservation indifference curve. There are two parallel, downward-sloping, convex curves that lie above Marco’s reservation indifference curve at all points. The upper of the two is labelled Marco’s indifference curve (medium utility). The lower of the two is labelled Marco’s indifference curve (low utility). A downward-sloping, straight line connects points (0, 100) and (100, 0) and is labelled FF (store money in drawer). Marco’s indifference curve (low utility) is tangential to the FF at point M (60, 40) where MRS = MRT. The vertical distance between points (60, 0) and (60, 40) is labelled consumption later (storing).
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Figure 9.7 Smoothing consumption by storing.

Marco’s preferences: In this diagram, the horizontal axis shows consumption now, in dollars, and ranges between 0 and 120. The vertical axis shows consumption later, in dollars, and ranges between 0 and 150. Marco’s endowment point has coordinates (100, 0). A downward-sloping, convex curve passes through Marco’s endowment point, and is labelled Marco’s reservation indifference curve.
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Marco’s preferences

Marco’s reservation indifference curve goes through his endowment.

Marco’s preferences: In this diagram, the horizontal axis shows consumption now, in dollars, and ranges between 0 and 120. The vertical axis shows consumption later, in dollars, and ranges between 0 and 150. Marco’s endowment point has coordinates (100, 0). A downward-sloping, convex curve passes through Marco’s endowment point, and is labelled Marco’s reservation indifference curve. There are two parallel, downward-sloping, convex curves that lie above Marco’s reservation indifference curve at all points. The upper of the two is labelled Marco’s indifference curve (medium utility). The lower of the two is labelled Marco’s indifference curve (low utility).
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Marco’s preferences

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

Marco’s feasible frontier: In this diagram, the horizontal axis shows consumption now, in dollars, and ranges between 0 and 120. The vertical axis shows consumption later, in dollars, and ranges between 0 and 150. Marco’s endowment point has coordinates (100, 0). A downward-sloping, convex curve passes through Marco’s endowment point, and is labelled Marco’s reservation indifference curve. There are two parallel, downward-sloping, convex curves that lie above Marco’s reservation indifference curve at all points. The upper of the two is labelled Marco’s indifference curve (medium utility). The lower of the two is labelled Marco’s indifference curve (low utility). A downward-sloping, straight line connects points (0, 100) and (100, 0) and is labelled FF (store money in drawer). Marco’s indifference curve (low utility) is tangential to the FF.
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Marco’s feasible frontier

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

Marco’s decision to store: In this diagram, the horizontal axis shows consumption now, in dollars, and ranges between 0 and 120. The vertical axis shows consumption later, in dollars, and ranges between 0 and 150. Marco’s endowment point has coordinates (100, 0). A downward-sloping, convex curve passes through Marco’s endowment point, and is labelled Marco’s reservation indifference curve. There are two parallel, downward-sloping, convex curves that lie above Marco’s reservation indifference curve at all points. The upper of the two is labelled Marco’s indifference curve (medium utility). The lower of the two is labelled Marco’s indifference curve (low utility). A downward-sloping, straight line connects points (0, 100) and (100, 0) and is labelled FF (store money in drawer). Marco’s indifference curve (low utility) is tangential to the FF at point M (60, 40) where MRS = MRT. The vertical distance between points (60, 0) and (60, 40) is labelled consumption later (storing).
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Marco’s decision to store

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

In Figure 9.7, some part of Marco’s feasible frontier lies above 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.

The figure shows 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 intrinsic 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 9.8 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.

Figure 9.8 shows that 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.

In this diagram, the horizontal axis shows consumption now (in dollars) and ranges between 0 and 120. The vertical axis shows consumption later (in dollars) and ranges betweeb 0 and 150. Coordinates are (consumption now, consumption later). A downward-sloping straight line connects points (0, 100) and (100, 0) and is labelled FF (store money in drawer). Another downward-sloping straight line connects points (0, 120) and (100, 0) and is labelled FF (lend at 20%). Point (100, 0) is Marco’s endowment. There are three parallel, downward-sloping, convex curves. The upper-most is labelled Marco’s IC (medium utility) and is tangential to FF (lend at 20%) at point D (60, 48). The middle is labelled Marco’s IC (low utility) and is tangential to FF (store money in drawer) at point M (60, 40) where MRS = MRT. The lower-most is labelled Marco’s reservation IC and passes through point (100, 0). The vertical distance between point M and the horizontal axis is consumption later (storing). The vertical distance between point D and the horizontal axis is consumption later (lending). The horizontal distance between the vertical axis and point M is consumption now. The horizontal distance between point M and point (100, 0) is amount stored.
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Figure 9.8 Smoothing consumption by storing and lending.

Marco’s decision to lend: In this diagram, the horizontal axis shows consumption now (in dollars) and ranges between 0 and 120. The vertical axis shows consumption later (in dollars) and ranges betweeb 0 and 150. Coordinates are (consumption now, consumption later). A downward-sloping straight line connects points (0, 100) and (100, 0) and is labelled FF (store money in drawer). Another downward-sloping straight line connects points (0, 120) and (100, 0) and is labelled FF (lend at 20%). Point (100, 0) is Marco’s endowment. There are three parallel, downward-sloping, convex curves. The upper-most is labelled Marco’s IC (medium utility) and is tangential to FF (lend at 20%) at point D (60, 48). The middle is labelled Marco’s IC (low utility) and is tangential to FF (store money in drawer) at point M (60, 40) where MRS = MRT. The lower-most is labelled Marco’s reservation IC and passes through point (100, 0). The vertical distance between point M and the horizontal axis is consumption later (storing). The horizontal distance between the vertical axis and point M is consumption now. The horizontal distance between point M and point (100, 0) is amount stored.
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Marco’s decision to lend

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

The effect of the decision to lend: In this diagram, the horizontal axis shows consumption now (in dollars) and ranges between 0 and 120. The vertical axis shows consumption later (in dollars) and ranges betweeb 0 and 150. Coordinates are (consumption now, consumption later). A downward-sloping straight line connects points (0, 100) and (100, 0) and is labelled FF (store money in drawer). Another downward-sloping straight line connects points (0, 120) and (100, 0) and is labelled FF (lend at 20%). Point (100, 0) is Marco’s endowment. There are three parallel, downward-sloping, convex curves. The upper-most is labelled Marco’s IC (medium utility) and is tangential to FF (lend at 20%) at point D (60, 48). The middle is labelled Marco’s IC (low utility) and is tangential to FF (store money in drawer) at point M (60, 40) where MRS = MRT. The lower-most is labelled Marco’s reservation IC and passes through point (100, 0). The vertical distance between point M and the horizontal axis is consumption later (storing). The vertical distance between point D and the horizontal axis is consumption later (lending). The horizontal distance between the vertical axis and point M is consumption now. The horizontal distance between point M and point (100, 0) is amount stored.
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The effect of the decision to lend

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 an indifference curve and the feasible frontier. In the figure, this is point D, 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 when the feasible set expands. But depending on his indifference curves, 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 two effects cancel out, leaving lending and consumption now unchanged. Recall from Section 3.6, that the first effect is the ‘income effect’ and the second one is the ‘substitution effect’.

Exercise 9.6 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 9.8, showing the feasible frontier, consumption, and lending options.
Point on the feasible frontier Consumption now Consumption later Amount stored or lent (excluding interest)
Calculation = income now – amount stored or lent = amount stored or = amount lent including interest on the loan
Endowment point (100, 0)
Store money in a drawer
(91, 9)
(50, 50)
(30, 70)
Lend at an interest rate of 30%
(56, 57)
(30, 91)
(67, 43)

Question 9.8 Choose the correct answer(s)

Figure 9.8 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 consume in period 1, or he can lend the money he does not consume at an interest rate of 20%. Based on this information, read the following statements and choose the correct option(s).

  • 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 up to $35 in period 2.
  • The marginal rate of transformation is higher when storing than when lending.
  • Marco can always be on a higher indifference curve when lending than when storing, provided that Marco finds a trustworthy borrower.
  • Under storage, Marco’s consumption in both periods must sum to $100.
  • Marco lends $32, which then increases in value by 20% to $38.40. Therefore the maximum Marco can consume in period 2 is $38.40.
  • The MRT is 1 when storing, and 1.2 when lending.
  • The feasible frontier for lending is higher than the feasible frontier for storing, at any positive level of storing.