Econ 4520, Spring 2023 Problem Set 3
Hello, dear friend, you can consult us at any time if you have any questions, add WeChat: daixieit
Problem Set 3
Econ 4520, Spring 2023
Due Date: Friday, March 24, 2023 by 5 pm via canvas
Important notes about the problem set
• Your answers must be submitted as a single pdf file via canvas.
• Please write clearly and concisely, show your work, and properly label all plots.
• Late problem sets will not be accepted and receive a grade of zero
• Please note that SGUW refers to the text book, “International Macroeconomics” by Schmitt-Grohe, Uribe and Woodford. Please refer to the version on canvas for the problems and not any other version (including the physical textbook).
Question 1 (30 points)
Consider a closed economy that lasts for two periods, t = 1,2. In period 2 there are two states of the world, s 2 {sL , sH}. Each state is realized with probability 1/2. The representative household has preferences
log (c1 ) + β X 
log (c2 (s))
s=sH ,sL
The household receives labor income y1 = 1 in period 1 and
y2 (s) = 
1 if s = sH
in period 2. The household is endowed with 100% of the shares of the two firms in the economy: firm A and firm B. Firm A and B do not pay out dividends in period 1 but they pay dividends Ri (s) is period 2.
R2(A) (s) = 
∆
:0
In particular
if s = sH if s = sL ,
R2(B) (s) = <0
if s = sH
if s = sL
Assume that ∆ > 0 and 1 - 2∆ > 0.
There are three assets in this economy: firm A’s stock (let !A be the holdings at the end of the period), firm B’s stock (!B ), and risk free debt (b). The definition of an equilibrium is the following:
An equilibrium is an allocation for the household, (c1 , c2 (s) , !A , !B , b), and prices (qA , qB ,1 + r) such that
• given prices, the allocation solves
(c1 ,c2 ( s()!(a)xA , !B ,b) log c1 + β [ 
log c2 (sH ) + 
log c2 (sL )]
subject to
c1 + qA !A + qB !B + b 6 y1 + qA + qB ,
c2 (s) 6 y2 (s) + (1 + r) b + !A RA (s) + !B RB (s) s = sL , sH • asset markets clear in that:
!A = 1 , !B = 1, b = 0
1. (20 points) Derive an expression for the expected returns of the stock of each firm and one for the risk free interest rate in terms of exogenous variables.
2. (10 points) “Assets with more volatile payouts must earn a higher expected return than risk free assets to compensate for the risk.” Though the lens of our model, is the statement correct? Or is it wrong? (If you can, motivate your answer using the expressions you derived in part 1.)
Question 2 (30 points)
I have posted a document on canvas titled twindeficits_chapter.pdf. Please complete exercise 7.3 from that document. (Each part worth 15 points)
Question 3 (40 points)
Please complete Exercise 6.4 in SGUW. (Each worth 5 points).
2023-04-07