Answer the following attached questions.
(Production function) Condsider a representitive rm with a. production function which is ( i) twice continuously dierentiable; (ii) exhibits positive and diminishing marginal product and (iii) has constant return to scale: Y = F(K, L) (1) Given the capital rental price R and the wage to, and the good price P is normalized to 1, the rm can choose K and L to maximize its prot: 1}1{acF(K, L) RK 10L (2) "'""" " '\"'\""""' ---...........- I." \"""'" ""1 Consider a Diamond model, where we set the productivity factor A; to unity (1) in all periods. The working population, Lg, grows at rate R, i. e., Li\": (1 + n)L. Lower-case letters denote perworker terms, e.g. k, = K,/L,. Agents live for tam periods. Income earned (from labor) in the rst period of life (10,) is spent on saving (3,) and rstperiod consumption (Cu). The rst-period budget constraint can thus be written 011 = to: ' 31. In retirement, the same agent consumes 02,\Firms in the perfectly competitive constant cost widget industry have access to technology that allows them to produce widgets at a cost of C(q) = 300 + 10q + 3q2, with sunk costs of 225. Demand for widgets is Q = 1300 - 10P. a) The industry is currently in a long-run competitive equilibrium. What is the market price and quantity that each firm produces? How many firms are there currently operating in the industry. b) Illustrate the current state of the industry on carefully drawn and labeled graphs of the typical firm's marginal and average costs and the market. c) What is the short-run market supply curve for the industry? d) Suppose that demand for widgets changes to Q = 1540 - 10P. What will happen to the price in the short-run? What will happen to the price in the long-run?[IS-LM-AD-AE model; 25 points] Consider a closed economy described by a simple Keynesian model that consists of the following equations: Consumption function : C(Y .. T, r] = or (Y T] [tor Investment function : Hr] = "HE?" + 5, Real money demand function : L[Y, r) = Y * 1' Taxes : T = I] where U {I or f. 1 is the marginal propensity to consume (MPG). This model is slightly different from the textbook model, as consumption now depends on the real interest rate as well as disposable income. Regarding the exogenous variables, we x taxes (T) at l} as given above, while the value of government purchases (G), the money supply [M], and the price level (P) are unspecied to consider different values. (a) [3 points] 1Why might consumption depend negatively on the interest rate? Briey discuss. (b) [3 points] Derive the equation for the LM curve. (Note: To receive a credit, you need to express Y as a function of v, M and P oniy]. Discuss how expansionary monetary policy [i.e. an increase in M] shifts the LM curve. (c) [3 points) Derive the equation for the IS cun'e. (Note: To receive a cmdit, you need to express Y as a mction of r, G, or and constant only). Discuss how expansionary scal policy (Le. an increase in G] shifts the IS curve. (d) [3 points] Based on the IS equation in [c], how does the extent of such a shift in the IS curve depend on o? 'Wby? Explain intuitively. (e) {3 points) Fi'om the IS and LM curves you obtained above, derive the AD curve (Note: As above, you need to solve for Y to receive a. credit). Do P and Y have an inverse relationship? Discuss how output in the short run depends on government purchases and the central bank's money supply. (f) [4 points) How does the effect of monetary policy on output depend on the MP0 [or]? Why? Explain intuitively. (g) [3 points] Suppose M = 5, P = 1, and CI! = E. Draw the ISLM diagram for this case. He sure to label the curves, axes, and horizontal and vertical intercepts [which may depend on G]. (h) [3 points) lGiven the values in part (g), nd the equilibrium level of output, Y, and the real interest rate, r, in the short run (hint: they depend on G]. Does expansionary scal policy increase 1
