Question 1

Suppose a consumer has an endowment of $$m_1 in $$period 1 and $$m_2 in $$period 2. If the interest rate is $$r$$, what is the equation for the intertemporal budget constraint in present value terms?

Accepted Answer

$$c_1$$ + \frac{$$c_2$$}{1+r} = $$m_1$$ + \frac{$$m_2$$}{1+r}$$

Question 2

If the interest rate increases, what happens to the opportunity cost of current consumption in the two-period intertemporal choice model?

Accepted Answer

It increases, making current consumption more expensive relative to future consumption.

Question 3

A consumer faces a two-period budget constraint with zero interest rate. If their endowment is $$(m_1$, m_2$)$$, what is the slope of the budget line?

Accepted Answer

$$-1$$

Question 4

In the case where borrowing and lending rates differ (borrowing rate $$r_B$$ and lending rate $$r_L$$), what happens to the budget constraint?

Accepted Answer

It becomes kinked at the endowment point.

Question 5

If a consumer chooses $$c_1$$ \u003e $$m_1 in $$the two-period model, what does this imply?

Accepted Answer

The consumer is a borrower.

Question 6

Which of the following best describes the effect of an increase in the interest rate on a net borrower’s consumption?

Accepted Answer

The substitution effect is negative, and the income effect reinforces it, leading to lower current consumption.

Question 7

If a consumer’s indifference curves are L-shaped in the intertemporal choice model, what does this imply about their preferences?

Accepted Answer

They regard consumption in the two periods as perfect complements.

Question 8

Suppose the present value of an investment’s income stream is $$PV_{income}$$ and the present value of the payments is $$PV_{payments}. $$When is the investment worthwhile?

Accepted Answer

If $$PV_{income} \u003e PV_{payments}$$

Question 9

In the two-period intertemporal choice model, what is the maximum possible second period consumption ($$c_2) if $$the consumer consumes nothing in the first period and the interest rate is $$r$$?

Accepted Answer

$$(1+r)m_1$ + m_2$

Question 10

If the consumer’s indifference curves are straight lines with slope $$-1$$, what does this imply about their preferences?

Accepted Answer

They regard consumption in the two periods as perfect substitutes.

Question 11

A consumer has $$m_1 = 100$ and m_2$ = 110. $$The interest rate is $$r = 0.1. $$What is the present value of their endowment?

Accepted Answer

$$100 + \frac{110}{1.1}$$

Question 12

If the price of first period consumption is 1 and the price of second period consumption is $$\frac{1}{1+r}$$, what does this mean in terms of present value?

Accepted Answer

Future consumption is discounted by the interest rate.

Question 13

Which of the following statements is true about the intertemporal budget constraint in the presence of a capital market with a single interest rate?

Accepted Answer

The consumer can borrow and lend freely at the same interest rate.

Question 14

Suppose a consumer’s optimal choice is at the intersection of their indifference curve and the budget constraint, and $$c_1$$ \u003c $$m_1. $$What does this indicate?

Accepted Answer

The consumer is a lender or saver.

Question 15

If the interest rate between periods 1 and 2 is $$r_1$$ and between periods 2 and 3 is $$r_2$$, what is the present value of $$m_3$$ received in period 3?

Accepted Answer

$$\frac{m_3$}{(1+r_1$)(1+r_2$)}$$

Question 16

A consumer’s endowment is $$(m_1$, m_2$)$$ and the interest rate is $$r. If $$the consumer consumes all their endowment in each period, what is their borrowing or lending status?

Accepted Answer

They neither borrow nor lend.

Question 17

Which of the following is the correct condition for optimal intertemporal consumption in present value terms?

Accepted Answer

$$c_1$$ + \frac{$$c_2$$}{1+r} = $$m_1$$ + \frac{$$m_2$$}{1+r}$$

Question 18

If a consumer prefers to smooth consumption over time, what do their indifference curves look like in the $$(c_1$, c_2$)$$ space?

Accepted Answer

They are convex to the origin.

Question 19

If the interest rate falls and the consumer is a lender, what is the likely effect on their consumption?

Accepted Answer

The substitution effect is negative, but the income effect is positive, so the overall effect is ambiguous.

Intertemporal Choice: Consumption, Saving, and Interest Rates

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