Econ 422 Monetary Economics Assignment 3
Hello, dear friend, you can consult us at any time if you have any questions, add WeChat: daixieit
Econ 422 Monetary Economics
Assignment 3
Fall 2022
Question 1
Consider the same model in Question 2 of Assignment 2. Let σ = 1. Use the results you previously derived to calibrate a steady state of the model using the following information from data: (i) government spending is 20% of GDP; (ii) nominal interest rate is 4%; (iii) ináation rate is roughly 2%; and (iv) income velocity of money is y/x = 1:5. Solve for the following: 1. the real interest rate; 2. the welfare cost of raising the ináation target from 2% to 2.5%. [No need to calculate the Önal number. An expression similar to the one we derived in class will do.]
Question 2
Consider the search model we studied in class. Explain how low and steady ináation can be welfare-maximizing.
Question 3
Consider the model of Diamond and Dybvig (1983). We learnt in class that there exist two types of equilibria, one with bank runs and the other without. These equilibria are driven by self-fulÖlling beliefs. Note that if agents believe that there will be bank runs, then none of them will choose to deposit in the bank in the Örst place. Therefore, now let us explore the following question: Under what beliefs will agents choose to deposit in the bank?
Assume that agents have the following belief of the likelihood of the bank-run equilib-rium:
f = { t;
w.p. q
w.p. 1 ━ q
That is, bank runs occur with probability q and thus no bank runs with probability 1 ━ q . Given this belief, the expected utility of an agent depositing in the bank at T = 0 is given by:
F (q) = q [t + (1 ━ t)β] ┌ 
u (r* ) + (1 ━ 
)u(0)┐
+(1 ━ q) ┌tu(r* ) + β(1 ━ t)u(
R)┐
where r* = C1(H)* is solved in class and is the Örst-best allocation in T = 1.
1. Explain the terms in F (q).
2. Prove that so long as the public is not too pessimistic (i．e., q being su¢ ciently high), they will be willing to deposit in the bank, despite a positive chance of bank runs. That is, prove there exists an open set to the right neighborhood of q = 0 (i．e., as long as q is not too high) such that all the values of q within this set satisfy
F (q) > tu(1) + (1 ━ t)βu(R);
by showing the following:
(a) F (q) is a strictly decreasing function. That is, F\ (q) < 0.
(b) The function value at q = 0 is strictly above the value of an agent self-investing in her own project. That is, F (0) > tu(1) + (1 ━ t)βu(R).
3. Explain the central bankís role as the lender-of-the-last-resort.
2022-12-15