2 solve all of them.

(8) [10 points] Suppose that the central bank strictly followed a rule of keeping the real interest rate at 3% per year. That rate happens to be the real interest rate consistent with the economy's initial equilibrium (a) [5 points] Assume that the economy is hit by a money demand shock only. Under the central bank's rule, how will the money supply respond to a money demand shock? Will the rule make aggregate demand more stable or less stable than it would be if the money supply were constant? (b) [5 points] Assume that the economy is hit by IS shocks only. Under the central bank's rule, how will the money supply behave? Will the interest-rate rule make aggregate demand more stable or less stable than it would be if the money supply were constant?

2. This problem is based on the Einev and Finkelstein JEP 2013 model of adverse selection.

Assume that there are 10,000 people in a market to be insured. The number of people wanting to buy insurance (the demand for insurance) is

N = 10000 - pi

where pi is the premium. a) What is the highest premium that anyone is willing to pay to buy insurance? At a zero premium, how

many people in the market buy health insurance?

b) Solve for the inverse demand function that expresses Premium as a function of number of enrollees N.

c) Assume that the marginal cost of people as they start to buy insurance is as follows MC = 3000 - N/2

Draw the marginal cost function on the same axes as the demand function. Do the two cross? What is the significance of this crossing point?

d) Calculate the average cost function for people in this plan as a function of N and add it to the diagram. At what quantity N does it cross the demand curve? What is the premium at this quantity?

e) If there is no government regulation or interference in this market, and premiums are based on the average cost of enrollees, then how many people will buy insurance and what will be the preumium?

f) At what subsidy will the socially optimal number of people buy health insurance in this market?

g) At what fixed dollar tax will everyone want to buy insurance in this market? That is, people choose to either pay the tax or pay the premium. How much revenue will the government raise through this tax at this rate?

h) How does this problem relate to US Health insurance problems?

10) Consider a consumer with preferences U = Z 1 0 e tu(ct)dt; where is the subjective discount rate, c is consumption, and u(c) = ln c. She receives an exogenous ow of income y and can borrow or lend freely at a constant interest rate r; subject to a no-Ponzi-game condition that rules out innite debt. Her ow budget constraint is a_ = ra + y c; where a represents nancial wealth and a0 is the initial value. (a) Derive the rst-order conditions for optimal consumption. (b) At what rate does consumption change? Interpret its sign. (c) Derive the optimal decision rule for consumption. Provide an interpretation for the case = r: 2. (20) Consider the following optimal growth model. Agentspreferences are given by E0 "X1 t=0 tAt ln ct # The term At denotes an i:i:d: demand shock. Output is a concave function of beginning of period capital and a technology shock. That is, yt = ztkt It is assumed that zt is i:i:d:both over time and with respect to At . (That is, the two shocks are independently distributed.) The depreciation rate of capital is 100%. Within this environment, do the following (a) Set up the social planner problem as a dynamic programming problem and derive the necessary conditions. (b) Conjecture a solution to the policy functions for consumption and savings. Derive the equations that determine these optimal policy functions and characterize their qualitative behavior. (c) Suppose one period (real) bonds were introduced into this economy. How do demand shocks aect interest rates in this economy? Explain.

You decide to short 100 shares of GME at $300 as you believe the stock price is overvalued. The initial margin and maintenance margin requirement is 50% and 30% respectively. Ignoring margin interests.

a) Construct the account balance sheet once the short selling position is set.

b) Calculate the annual percentage return (APR) and the effective annual return (EAR) of your trading strategy if you settle your position at the price of $270 in 20 days later, assuming

that a year has 360 days. c) Calculate the price level that you will receive margin call. d) Explain why short selling may not be a good 'investment'.

(20) Consider the basic real business cycle model in which the representative agent maximizes the expected value of discounted utility given by: E0 "X1 t=0 t (ln ct ht) # Technology is given by a standard Cobb-Douglas production function, i.e. yt = ztk t h 1 t in which zt is an i:i:d: technology shock with c:d:f: given by G (zt): The depreciation rate of capital is 100%. Do the following: (a) Solve the model as a social planner problem and derive the optimal policy functions. (b) Discuss how well the implied time series characteristics of the model match those seen in the data. (Restrict your discussion to those features discussed in class.) Discuss a minimal set of changes in the model environment that could produce better consistency between the model and business cycle da