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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