Q: If a household receives an unexpected increase in bequests $$B$$, which of the following best describes the effect on first-period consumption $$C_0$$?

First-period consumption increases by $$MPC \times \Delta B$$

Question 1

Which of the following best describes the household's intertemporal budget constraint for two periods, given first-period income $$Y_0$$, second-period income $$Y_1$$, initial wealth $$B$$, and real interest rate $$r$$?

Accepted Answer

$$C_0$$ + \frac{$$C_1$$}{1 + r} = $$Y_0 + B$$ + \frac{$$Y_1$$}{1 + r}$$

Question 2

Given the utility function $$u(C_0$, C_1$) = \frac{C_0$^{1-\sigma}}{1-\sigma} + \beta \frac{C_1$^{1-\sigma}}{1-\sigma}$$, what does the parameter $$\sigma$$ represent?

Accepted Answer

The elasticity of intertemporal substitution

Question 3

If the household maximizes $$u(C_0$, C_1$)$$ subject to its budget constraint, which condition must hold at the optimum?

Accepted Answer

$$\frac{\partial u}{\partial C_0$} = (1 + r) \frac{\partial u}{\partial C_1$}$$

Question 4

Suppose $$\sigma = 2$$, $$\beta = 0.98$$, and $$r = 0.04. $$What is the marginal propensity to consume (MPC) out of bequests in the first period, using the formula $$MPC = \frac{1}{1 + [\beta (1 + r)]^{1/\sigma}}$$?

Accepted Answer

$$0.5728$$

Question 5

If the real interest rate $$r$$ increases, holding all else constant, what happens to the present value of future income $$\frac{Y_1$}{1 + r} in $$the household's budget constraint?

Accepted Answer

It decreases

Question 6

Given the consumption function $$C_0$$ = \frac{A}{D} B$$, where A$$ = [1 + r]^\frac{1}{\sigma}$$ and D = 1$$ + [\beta (1 + r)]^{1/\sigma}$$, what does $$\frac{\partial $$C_0$$}{\partial B}$$ represent?

Accepted Answer

The marginal propensity to consume out of bequests

Question 7

If a household receives an unexpected increase in bequests $$B$$, which of the following best describes the effect on first-period consumption $$C_0$$?

Accepted Answer

First-period consumption increases by $$MPC 	imes \Delta B$$

Question 8

Which of the following is NOT a step in solving the household's optimization problem for endogenous choice variables?

Accepted Answer

Ignore the budget constraint and maximize utility directly

Question 9

If $$\beta$$ increases, holding $$r$$ and $$\sigma$$ constant, what is the effect on the marginal propensity to consume (MPC) out of bequests in the first period?

Accepted Answer

MPC decreases

Question 10

Suppose the household's utility function is $$u(C_0$, C_1$) = \frac{C_0$^{1-\sigma}}{1-\sigma} + \beta \frac{C_1$^{1-\sigma}}{1-\sigma}$$ and $$\sigma = 1. $$What does the utility function simplify to?

Accepted Answer

$$u(C_0$, C_1$) = \ln C_0$ + \beta \ln C_1$

Question 11

In the context of the two-period model, what does the parameter $$\beta$$ represent?

Accepted Answer

The subjective discount factor for future utility

Question 12

If the household faces uncertainty in future income $$Y_1$$, which of the following is a likely effect on current consumption $$C_0$$?

Accepted Answer

Current consumption $$C_0$$ may decrease due to precautionary saving

Question 13

Which mathematical technique is used to maximize the utility function subject to the budget constraint in the two-period model?

Accepted Answer

Substitution and differentiation

Question 14

If the household's first-period consumption is given by $$C_0$$ = \frac{[1 + r]^{1/\sigma} ($$Y_0 + B$$) + \beta (1 + $$r)^{1/\sigma}$$ $$Y_1$$}{1 + [\beta (1 + r)]^{1/\sigma}}$$, what happens to C_0$ if Y_1$ increases?

Accepted Answer

Current consumption $$C_0$$ increases

Question 15

Which of the following best explains why the marginal propensity to consume (MPC) out of bequests is less than one in the two-period model?

Accepted Answer

Households spread additional wealth over both periods, not just the first

Question 16

If the household's utility function is $$u(C_0$, C_1$)$$ and the budget constraint is $$C_0$$ + \frac{$$C_1$$}{1 + r} = $$Y_0 + B$$ + \frac{$$Y_1$$}{1 + r}$$, which variable is endogenous in the optimization problem?

Accepted Answer

$$C_0$$

Question 17

Suppose the household's first-period consumption function is $$C_0$$ = \frac{A}{D} B$$, and $$\frac{\partial $$C_0$$}{\partial B} = \frac{A}{D}$$. If A = 1.0396$ and D = 1.1032672$, what is $$\frac{\partial $$C_0$$}{\partial B}$$?

Accepted Answer

$$0.9428$$

Question 18

If the household's utility function is $$u(C_0$, C_1$)$$ and the first derivative with respect to $$C_0 is$$ $$u'(C_0$) = C_0$^{-	heta}$$, what does $$	heta$$ represent?

Accepted Answer

The coefficient of relative risk aversion

Question 19

In the two-period model, if the household is more patient (higher $$\beta$$), what is the effect on the allocation of consumption between periods?

Accepted Answer

More consumption is allocated to the second period

Intertemporal Choice, Budget Constraints, and Consumption in Macroeconomics

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