provide detailed solutions for each
1. (50 points) Consider the closed-economy one-period macroeconomic model developed in class. The consumer is endowed with h units of time, and chooses consumption C and leisure ( to maximize U = log(C) + 0log((), subject to the budget constraint C = w/* + *. Production is described by Y = =N. Government spending G is financed with a proportional revenue tax (tax rate 7) on the firm. (a) (10) Do you expect the competitive equilibrium of this economy to be Pareto Optimal? Explain why. (b) (10) Find the firm's optimal demand for labor Nd, as a function of w and r. (c) (10) Find the consumer's optimal levels of consumption, leisure, and labor, given the real wage w and firm profits . (d) (20) Solve for the equilibrium allocation (C, (, Y, N), equilibrium wage w, and equilibrium tax rate 7 using the conditions that must be satisfied by an equilib rium: i) (C. (, N) must be optimal for the consumer, given w and ; ii) N must maximize the firm's profits, given w and r; iii) the government budget constraint is satisfied; and iv) market clearing (Y = C + G, and No = N'). Note: you should be solving for C, 4, Y, N, r, and w as functions of exogenous variables and parameters.Quasar Corporation is set to release its latest video game system which utilizes the newest game technology. In fact, the release date is sooner than that of its only rival Orion. This gives Quasar Corporation "first-move" ability. The demand for video game systems is: Q" = 150 - 0.1P P =1,500-10 04. Orion's marginal revenue curve is: MRO (qo, qQ ) = 1,500-20q0 - 10qQ. The marginal cost functions are: MCQ (qQ) = 0.590 MCO (90) = 0.590 Determine Orion's reaction function. Given that Quasar Corporation has this information and moves first, Quasar's marginal revenue function is: MRQ (qQ) 31,500 420 41 41 40. Calculate Quasar Corporation's optimal output level. Does the "first-move" ability of Quasar Corporation allow it to capture a larger market share?3. 15-LM Model (Based on Mankiw Ch. 12 #3). Use the information about the following economy to build the IS-LM model. a. The consumption function is given by C = 300 + 0.6(Y - 7). The investment function is / = 700 - 80r. Government spending and taxes are both 500. Graph the IS curve for this economy. Be sure to label the x- and y-axes. b. The money demand function is (M/P)* = Y - 200r. The money supply M is 3,000 and the price level P is 3. On the same graph as in part a.), graph the LM curve. c. Find the equilibrium interest rate r and the equilibrium level of income Y. Label the equilibrium values on your graph. d. Suppose that government spending is increased from 500 to 700. How does the IS curve shift? What are the new equilibrium interest rate and level of income? Show the shift and the new equilibrium on your graph. e. Suppose instead that the money supply is increased from 3,000 to 4,500. How does the LM curve shift? What are the new equilibrium interest rate and level of income? On a new graph, show the original 15 and LM curves and then show the shift and the new equilibrium. f. With the initial values for monetary and fiscal policy, suppose that the price level rises from 3 to 5. What happens? What are the new equilibrium interest rate and level of Income? On a new graph, show the original 15 and LM curves and then show the shift and the new equilibrium. For the initial values of monetary and fiscal policy, derive and graph an equation for the aggregate demand curve (Hint: Solve the 15 and LM curves in terms of r. Then combine them and solve for I' in terms of P.). What happens to this aggregate demand curve if fiscal or monetary policy changes, as in parts d.) and e.) (simply state which direction the aggregate demand curve shifts in each case)
