Solve. the following questions as attached below.

Question 1

Suppose that the economy only produces pizza, and 1,200 pizzas are sold in a given year at a unit price of $15. The quantity of money in the economy is $6,000.

a. Calculate the velocity of money.

b. Use the result from part a. What is the new price of pizza if there is an increase in the quantity of money to $8,000, holding everything else constant? What is the new nominal GDP?

c. Explain the relationship between the money supply and price.

Now use the version of the quantity theory of money in growth rates to answer questions d-g, assuming that the real interest rate is fixed at 2 percent.

d. Calculate the inflation rate and nominal interest rate if the growth rate of money supply is 5 percent and the growth rate of real GDP is 2 percent.

e. Calculate the inflation rate if the Fed increases the growth rate of money supply to 10 percent, but the growth rate of real GDP is still 2 percent.

f. Calculate the nominal interest rate based on part (e). What is the Fisher effect? What happens to the demand for money as a result? Explain.

g. Calculate the growth rate of the money supply if the Fed wants to achieve zero inflation?

5) In this question, we're going to use a game tree and backward induction to analyze a Stackelberg problem. In this case, each firm has 3 options: to produce a low level of output, a medium level of output, or a high level of output. The payoffs to each firm given each firm's output choice are: (KA, KB) B: High B:Medium B: Low A: High (0,0) (75,50) (112.50, 56.25) A: Medium (50,75) (100, 100) (125, 93.75) A: Low (56.25, 112.50) (93.75, 125) (112.50, 112.50) a) What is the Nash equilibrium when both firms choose their output at the same time? Explain. You must prove that your answer satisfies the definition of Nash equilibrium. b) Now assume that firm A can choose its output first. Fill in the following game tree for this sequential game. Each of the 9 payoff combinations above corresponds to one of the 9 endpoints of the game tree. I've filled in (Med, High) to get you started. A chooses L M H B chooses L M H M H M H A M. B-H (50,75) c) Now that you've filled in the tree, use backward induction to find the equilibrium for this game. Briefly describe why your answer is different than in 6a. Figure out B's best response to each of A's possible actions. Then, pick the one of those three options that maximizes A's profit, given how B will respond.1. Question 1: the Real Business Cycle Model Consider an economy consisting of a constant population of infinitely-lived in- dividuals. The representative individual maximises the expected value The instantaneous utility function u(Ct) = C; 6 (Ct + 02, 6 > 0. Assume that C is always in the range where u' (C) is positive, and that Q's are i.i.d. taste shocks with mean zero. Output is linear in capital: Y; = AKt. There is no depreciation; thus Kt\" = Kt + Y; Ct, and the interest rate is A. Assume A = p. (a) Find the rst-order condition (Euler equation) relating Cr and the expecta- tions of CH1 and explain its meaning. (20 points, 200 words) (b) Guess that consumption takes the form Ct = a + Kt + 75.5. Given this guess, What is K+1 as a function of Kt and Q? Interpret your results. (20 points, 200 words) (c) What values must the parameters a, ti, and 7 have for the rst-order con- dition in part (a) to be satisfied for all values of Kt and Q? Interpret your results. (20 points, 200 words) (d) What are the effects of a one-time positive shock to (t equal to (1 + A) on the paths of Yt, Kr, and Ct? Interpret your results. (20 points, 200 words) (8) Interpret the Covid-19 Pandemic as a (negative) taste shock, i.e. people have a lower appetite for consumption. How would you adjust your answer in part (d)? (20 points, 200 words)