Question III (30 points): Pareto optimality and productivity shocks
Consider a one-period closed economy model with production and no government (G=0). The representative consumer has the utility function U(C,l) that satisfies the three usual assumptions imposed on the preferences. C denotes consumption. The total number of hours his allocated between leisure land work N. The consumer receives the real wage wfor every hour worked. In addition, the consumer owns the firm and receives the real dividends π.The aggregate production function Y=zF(K,L) depends on the capital and labour inputs Kand as well as on the total factor productivity z. The production function satisfies the usual assumptions. 1.(5 points)Define a social planner’s problem for this economy. Make sure to state explicitly the planner’s objective and constraint(s), as well as to indicate the choicevariables of the planner. 2.(5 points)Which two mathematical conditions define the planner’s optimal choice of consumptionand leisure? Explain the economic meaning of these conditions. Show the optimal choice on a diagram that has leisure on the horizontal axis and consumption on the vertical axis. 3.(5 points)Is the competitive equilibrium of this model Pareto optimal? Explain your answer.In answering the parts (4) and (5) of this question, assume that the utility function and the production function are as follows U(C,l) = lnC + bln l, b>0Y =z KaL1-a, where 0 < a <4.(5 points)Find consumption, leisure, employment and output that solve the planner’s problem, as functions of exogenous variables and the parameters of the model. 5.Consider an increase in total factor productivity za.(5 points)How do consumption and leisure respond to this shock in the model? Use the expressions from the previous sub-question to find ∂C/∂z and ∂l/∂z. Illustrate the model response to an increase is zon a diagram that has leisure on the horizontal axis and consumption on the vertical axis. How does employment respond to an increase in zin the model? b.(5 points) List the stylized business cycle facts about the comovement of consumption and employment with output. Are the predictions of the model for the comovement between consumption and output, and employment and output consistent with these stylized business cycle facts? Explain.
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Question IV (15 points) Money demand
1.(5 points)What determines the demand for outside money(currency) in the monetary intertemporal model? Draw the nominal money demand curve. Does it have a positive or a negative slope? Why? 2.(5 points)Many different factors can change the preferences for nominal money holdings, and hence shift the money demand curve. Give one example of such a factor. Illustrate its effect graphically. 3.(5 points)Describe the empirical evidence on the stability of money demand in Canada. What impact did shifts in money demand in the 1980s have on the Canadian monetary policy?