Q: Suppose the productivity process in the RBC model is given by: $ A_t = \exp(\varepsilon^A_t) A_{t-1}^{\rho_A} $ where $\varepsilon^A_t \sim N(0, \sigma^2_{\varepsilon})$ and $|\rho_A| < 1$. What is the economic interpretation of $\rho_A$?

$\rho_A$ measures the persistence of productivity shocks over time.

Q: In the representative firm's profit maximization problem, the Cobb-Douglas production function is: $ Y_{j,t} = A_t K_{j,t}^{\alpha} L_{j,t}^{1-\alpha} $ If the firm chooses $K_{j,t}$ and $L_{j,t}$ optimally, what is the expression for the real wage $W_t$?

$W_t = (1-\alpha) Y_{j,t} / L_{j,t}$

Q: Which of the following statements about the equilibrium condition in the RBC model is correct?

The equilibrium condition is $Y_t = C_t + I_t$ because all output is either consumed or invested.

Q: Suppose the depreciation rate $\delta$ increases in the RBC model. Holding all else constant, what is the immediate effect on the law of motion for capital? $ K_{t+1} = (1 - \delta) K_t + I_t $

A higher $\delta$ reduces the amount of capital carried over to the next period, lowering $K_{t+1}$ for a given $I_t$.

Q: In the RBC model, which of the following is NOT a typical assumption?

Monetary policy has strong real effects in the long run.

Q: Suppose a positive technology shock occurs in the RBC model (i.e., $A_t$ increases unexpectedly). According to the model, what is the likely effect on output $Y_t$ and investment $I_t$ in the short run?

Both output $Y_t$ and investment $I_t$ increase.

Q: Which of the following best explains why the RBC model is considered a general equilibrium model?

It analyzes the goods, capital, and labor markets simultaneously, with most variables determined endogenously.

Q: In the context of the RBC model, what is the economic meaning of the Lagrange multiplier $\lambda_{j,t}$ in the household's optimization problem?

$\lambda_{j,t}$ represents the marginal utility of wealth or the shadow price of relaxing the household's budget constraint.

Question 1

Which of the following best describes the main innovation of Real Business Cycle (RBC) models compared to standard Keynesian macroeconomic models?

Accepted Answer

RBC models introduce microfoundations and rational expectations, emphasizing technology shocks as the main source of economic fluctuations.

Question 2

In the standard RBC model, which of the following is assumed to be the only source of uncertainty?

Accepted Answer

Stochastic productivity shocks

Question 3

Consider the household's intertemporal Euler equation in the RBC model:

$
C_{j,t}^{-\sigma} = \beta E_t \left[ C_{j,t+1}^{-\sigma} (1 + R_{t+1} - \delta) \right]
$

What does this equation represent?

Accepted Answer

The intertemporal choice between consumption today and consumption tomorrow

Question 4

Suppose the productivity process in the RBC model is given by:

$
A_t = \exp(\varepsilon^A_t) A_{t-1}^{\rho_A}
$

where $\varepsilon^A_t \sim N(0, \sigma^2_{\varepsilon})$ and $|\rho_A| < 1$. What is the economic interpretation of $\rho_A$?

Accepted Answer

$\rho_A$ measures the persistence of productivity shocks over time.

Question 5

In the representative firm's profit maximization problem, the Cobb-Douglas production function is:

$
Y_{j,t} = A_t K_{j,t}^{\alpha} L_{j,t}^{1-\alpha}
$

If the firm chooses $K_{j,t}$ and $L_{j,t}$ optimally, what is the expression for the real wage $W_t$?

Accepted Answer

$W_t = (1-\alpha) Y_{j,t} / L_{j,t}$

Question 6

Which of the following statements about the equilibrium condition in the RBC model is correct?

Accepted Answer

The equilibrium condition is $Y_t = C_t + I_t$ because all output is either consumed or invested.

Question 7

Suppose the depreciation rate $\delta$ increases in the RBC model. Holding all else constant, what is the immediate effect on the law of motion for capital?

$
K_{t+1} = (1 - \delta) K_t + I_t
$

Accepted Answer

A higher $\delta$ reduces the amount of capital carried over to the next period, lowering $K_{t+1}$ for a given $I_t$.

Question 8

In the RBC model, which of the following is NOT a typical assumption?

Accepted Answer

Monetary policy has strong real effects in the long run.

Question 9

Given the household's intratemporal first-order condition:

$
C_t^{\sigma} L_t^{\phi} = W_t
$

If the wage $W_t$ increases, what is the predicted effect on labor supply $L_t$, holding consumption $C_t$ constant?

Accepted Answer

Labor supply $L_t$ increases.

Question 10

Suppose a positive technology shock occurs in the RBC model (i.e., $A_t$ increases unexpectedly). According to the model, what is the likely effect on output $Y_t$ and investment $I_t$ in the short run?

Accepted Answer

Both output $Y_t$ and investment $I_t$ increase.

Question 11

Which of the following best explains why the RBC model is considered a general equilibrium model?

Accepted Answer

It analyzes the goods, capital, and labor markets simultaneously, with most variables determined endogenously.

Question 12

In the context of the RBC model, what is the economic meaning of the Lagrange multiplier $\lambda_{j,t}$ in the household's optimization problem?

Accepted Answer

$\lambda_{j,t}$ represents the marginal utility of wealth or the shadow price of relaxing the household's budget constraint.

Question 13

Consider the steady-state condition for capital in the RBC model:

$
K^* = \left( \frac{R^*}{\alpha} \right)^{\frac{1}{\alpha-1}}
$

If the steady-state return on capital $R^*$ increases, what happens to the steady-state capital stock $K^*$?

Accepted Answer

$K^*$ decreases.

Question 14

Which of the following is a key reason for log-linearizing the non-linear RBC model around the steady state before solving it computationally?

Accepted Answer

To obtain a system of linear equations that is easier to solve and interpret.

Question 15

Suppose you are using RISE to implement an RBC model. Which of the following blocks is NOT compulsory in the model file?

Accepted Answer

@planner objective

Question 16

In the RBC model, Ricardian equivalence implies which of the following?

Accepted Answer

Government debt has no effect on consumption because agents anticipate future taxes.

Question 17

A student is asked to simulate the effect of a permanent increase in the discount factor $\beta$ in the RBC model. Which of the following is the most likely long-run effect?

Accepted Answer

A higher $\beta$ increases the steady-state capital stock, as households become more patient and save more.

Question 18

Which of the following is a plausible real-world application of the RBC model?

Accepted Answer

Analyzing the impact of a sudden improvement in information technology on GDP and employment.

Question 19

Suppose you are calibrating an RBC model for South Africa using RISE. Which of the following would be an appropriate first step?

Accepted Answer

Specify the model's equations and parameters in a .rs or .dsge file.

The Real Business Cycle Model and Dynamic Stochastic General Equilibrium (DSGE) Models

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