11 Jun WHAT ARE THE INDIVIDUAL CHOICES FOR C1 AND C2 UNDER UTILITY MAXIMIZATION?
Economics 1. In a ceratin economy, the production function is given by by: where Y is output, N is the number of workers. The supply of labor (SN) is given by: Where W is the nominal wage and P is the price level. a. Find the demand for labor for the profit maximizning firm. b. Find the equilibrium in the labor market (real wage, number of workers and output). c. If full employemnt is set at 100 workers, find the unemployement rate. d. If an incomes policy is successful/not succesful in this economy what do you think will happen with the equilibrium level in this economy. Explain your answer using a diagram. 2. Consider an individual who lives for two periods and whose utility function (constant-relative-risk-aversion) is given as: where P1 and P2 denote the prices of consumption (C ) in the two periods with W being the value of lifetime income. a. What are the individual choices for C1 and C2 under utility maximization? b. Find ; c. c. If P1 = P2, find d. If Saving at the end of period 1 is: , find 3. The following information describes an economy: Y = C+I + G, (Y = national income) C = 170 + 0.6(Y ? T) (C = consumption) T = 200 (T = taxes) I = 100 “ 4r (I = investment; r = interest rate) G = 350 (G = government spending) L(r, Y) = 0.75Y ? 6r MS = M/P (M/P = money supply) (a) Derive the equation for the IS curve. (b) Derive the equation for the LM curve. (c) Derive the equation for the Aggregate Demand curve (d) Calculate the equilibrium level of income (Y), consumption (C), investment (I), interest rate (r); and the velocity of money (V), if the money supply (M/P) is 735. (e) If the money supply is increased in this model, draw an IS/LM model showing the expected changes in the equilibrium level of income and interest rates as well as the expected effect on aggregate demand. Identify the multiplier. (f) If the productivity in this economy increases causing output to increase, explain what the effects this change will have on the IS/LM and aggregate supply and demand models. Use a diagram to help explain your answer. 4. The following information describes an economy: Y = C+I +G (Y = national income) C = c(Y- t(Y)) + a (C = consumption) a = B/rP (T = taxes); a = wealth; B = bonds; r = interest rate; I = I(r) (I = investment) M/P = L(r) + k(Y- t(Y)) (M/P = money supply) 1.0 Find dy/dB. 2.0 Find dr/ dB. 3.0 Explain how a fall in prices will affect consumption and the IS curve. 5. Given the following model: 1. Y* = c(Y- t(Y) + M/P)) + I( r ) + G 2. M/P = k(Y*) + L(r) With Y* representing full employment such that dY* = 0. (a) Find dP/dM and dr/dM, given that P and r are endogenous variables with dG = 0. (b) How do you interpret your results in relation to money neutrality.
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