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3. An Application of the Production Model and the Consumption Leisure Model. In this question, you will solve a general equilibrium model that contains the production sector and the household. (a) Suppose the production function is Y = AL, where Y denotes total output in the economy, A denotes productivity, and L denotes labor. Write down the prot function of the rm. Derive the labor demand equation of this economy. (b) Plot the labor demand curve in the (w, L) space (with w on the yaxis and L on the xaxis). (0) Suppose each household's utility function is H2 1 C 0g 2 9 where C denotes consumption, and H denotes labor hours. Each household's budget constraint is C = (1 T)'wH + T where '1' denotes the labor income tax in this economy and T denotes a lump sum transfer from the government to the household. Households treat both T and T as exogenous. Derive the labor supply equation. (Don't need to express H" as a function of exogenous variables and parameters, just write down the rst order condition that H\" need to satisfy.) (d) Suppose that T = (1 T)2 2 1, and there are N = 1 households in the economy (thus L = H). Plot the labor supply curve in (w, L) space of question (b). Clearly label the supply curve, the demand curve. (e) Thus, this general equilibrium model contains two markets, goods and labor. State the endogenous variables of this general equilibrium model. With T = (1 \"022122 1, drive the equilibrium