Macroeconomic Theory (AS.440.602) Fall 2021 Midterm Exam
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Macroeconomic Theory (AS.440.602)
Fall 2021
Midterm Exam
Monday, October 18, 2021
1) The following questions should be answered based on the relevant materials that we studied in class. Assume that net taxes (T) are not function of output (Y). Explain your answers clearly.
a. Based on the IS-LM model, when will the rise in government spending (G) surely lead to a rise in investment (I)? Explain. Your answer should be backed by an accurate graph.
b. Based on the IS-LM model, explain when will the rise in government spending (G) leave both consumption (C) and Investment (I) unchanged.
c. Our analysis in the class indicates that raising government spending (G) and cutting net taxes (T) by the same amount are equally effective in raising output (Y). True/False?
Explain your answer using the right equations!
d. Your are giving the following information:
C = 460 + 0.6YD
I = 200+ 0.15Y-2500i
G = 200
T = 100
(M/P)d=0.5Y- 10000i
Ms=600
Find the AD Curve.
2) The representative agent lives for infinite periods (0, 1, 2, …) and receives exogenous incomes of y0 , y1 , y2 ,..., respectively. The lifetime present discounted value of utility is given by:
with β(< 1) being the discount factor and ct is consumption at time t. The agent is allowed to save or borrow at the real interest rate r , but she cannot die with debt or wealth. Assume also that the initial wealth is zero.
a. Solve the optimization problem of the agent using the period-by-period budget constraints. In particular, show the Euler equation.
b. Using the given functional form, write the Euler equation between time 1 and time 3. In other words, show how c1 and c3 are related.
c. Write the present discounted value of optimal lifetime consumption as a function of c0 (and, potentially, other parameters or exogenous variables).
d. Write the present discounted value of optimal lifetime utility as a function of c0 (and, potentially, other parameters or exogenous variables).
e. Find the present discounted value of lifetime income as a function of y0 (and, potentially, other parameters or exogenous variables) when income is growing each period at the rate ofy , where 0 <y < r . Your final answer should be as simple as possible and it may not involve any summations.
f. Can saving at time zero be zero (i.e. S0 = 0 ) if β(1+ r) = 1andy > 0 ? Explain!
2023-12-22