Reference no: EM132490746

Problem 1

Consider the banking model from Chapter 18. There are three periods and a unit mass of agents as well as the bank. Each of the agent has an initial funds of 1 at the initial date 0. Each agent can be one of the two types: patient or impatient. The type is revealed at date t = 1. A fraction p = 0.2 of agents are impatient and consume only at t = 1. The remaining fraction are patient and indifferent between consuming at either t = 1 or t = 2. As in a textbook version of the model the agent's type is her private information. Funds, which are invested for two periods earn a gross return R = 1.65, funds invested for one period yield zero return (i.e. the agent just gets their funds back). Each agent has the following utility:

U (c) = c^1-σ/1 - σ

where σ = 3.

a. Write down the optimization problem, which gives rise to the efficient risk sharing (optimal insurance scheme) between patient and impatient agents, i.e. set up the problem of maximizing the agents utility subject to the proper resource constraint and incentive constraint.

b. Solve the problem for the consumptions of the patient c∗P and impatient agents c∗I using the imposed numerical values.

c. The optimal insurance can be implemented by the deposit contract with the bank, that pays out (d1, d2) at time 1 and 2. Explain how to implement the efficient risk sharing arrangement from points (a)-(b). Solve for the values of d1 and d2.

d. Calculate the ex ante (period 0) expected utility of the agent who enters into this deposit contract with the bank. Is it higher or lower than the ex ante expected utility of the agent who invests by himself (autarky)? Explain. How would your answer change if the agents are risk neutral, i.e. their utility is U (c) = c.

e. Suppose that individuals are trying to withdraw their funds get them de- pending on their place in the queue for deposits. Suppose that the fraction of consumers who withdraw early is e ≥ p then the constraint that the bank is facing is

r₂(e) = max [0, R (1 - ed₁)/(1-e)]

Argue why this bank is prone to runs. Suppose that the first period payout d1 is given by the value computed in (c). Compute the maximum number of withdrawals e beyond which any individual patient agent will find it optimal to withdraw early?

Problem 2

Suppose that the rate of return on asset is 15 percent. The asset was purchased for 100 dollars, and price has increased by 10 percent. How large was the dividend payment?

Problem 3

Consider the small-open economy model with investment and production (Chapter 16). Suppose there is an increase in current total factor productivity z. Answer the following Problems and carefully explain your answers. Illustrate your answers with a graph.
a) What is the effect on the aggregate supply curve Y^s?

b) What is the effect on the absorption curve A?

c) What is the effect on the aggregate demand curve Y d?

d) Explain what happens to C, I, Y , A, and CA.

Problem 4

Consider the US economy in 2008, i.e. an economy in market clearing equilibrium, which is also in a liquidity trap. Suppose that the economy is hit with the credit market shock, which increases uncertainty in the financial markets and damages the collateral used to borrow against. Use the sticky-price model from Chapter 14 to answer the following Problems.

a. How do the uncertainty and collateral shocks manifest themselves in the model? Argue whether they shift the supply or the demand curve. Illustrate your answer with the appropriate figure.

b Discuss and illustrate in the figure the stabilizing role of the monetary policy. Carefully explain what it can and can not achieve in case the economy is in a liquidity trap, in particular whether the economy can be brought back to the initial equilibrium. Explain what happens with output, employment, consumption, investment and wages following the policy intervention. State clearly any assumptions that you make.

c Discuss and illustrate in the figure the stabilizing role of the fiscal policy. Carefully explain what it can and can not achieve in case the economy is in a liquidity trap, in particular whether the economy can be brought back to the initial equilibrium. Explain what happens with output, employment, consumption, investment and wages following the policy intervention. State clearly any assumptions that you make.

Problem 5

Consider the current Coronavirus Pandemic and use the sticky-price model from Chapter 14 to analyze it. In particular suppose that the pandemic is modelled as a combination of two shocks: negative demand shock and negative supply shock, which hit the economy at the same time.

a. Illustrate in the figure the impact of these shocks on the economy, starting from the market clearing equilibrium. Carefully explain what happens in the output and the money market assuming central bank target interest rate is unchanged. Con- sider two cases, the first one where the supply shock dominates the demand shock, the second one where the demand shocks dominates the supply shock. Use a separate figure for each case.

b. Discuss and illustrate in the figure the stabilizing role of the monetary policy in both cases from part (a). Carefully explain what it can and can not achieve, in particular whether the economy can be brought back to the initial equilibrium. Explain what happens with output, employment, consumption, investment and wages following the policy intervention. State clearly any assumptions that you make.

c. Discuss and illustrate in the figure the stabilizing role of the fiscal policy in both cases from part (a). Carefully explain what it can and can not achieve, in particular whether the economy can be brought back to the initial equilibrium. Explain what happens with output, employment, consumption, investment and wages following the policy intervention. State clearly any assumptions that you make.

d. Imagine you are the main economic advisor to the prime minister of Canada. Design the five point economic policy plan that should be implemented to alleviate the economic crisis. Back up your arguments with the analysis conducted in parts (a)-(c). Come up with policies, which can achieve outcomes not attainable by monetary and fiscal policies.