Consider the closed-economy one-period macroeconomic model with a representative consumer and firm and competitive markets. The...

 

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Consider the closed-economy one-period macroeconomic model with a representative consumer and firm and competitive markets. The representative consumer chooses C and I to maximize utility U(C, 1), subject to the budget constraint: C=w(h-1) + − T, where C is consumption, leisure, w the real wage rate for labour, h is the hours available to the consumer for work or leisure, are firm profits and T is a lump-sum tax. (a) Write down the representative consumer's problem. (b) Use the Lagrangian method to solve the consumer's problem and to show that MRS,e = w holds in equilibrium (hint: MRS1,c U₁(C.D.). Uc = The representative firm produces output according to the production function Y = zF(K, Nd), where z is total factor productivity, K is capital inputs and Nd labour inputs. Assume K is a fixed input of production, and Nd as the only variable factor of production. Workers are paid a real wage w. (c) Write down the representative firm's profit maximization problem. (d) Derive the representative firm's profit maximizing condition (hint: MPN = d). Consider the closed-economy one-period macroeconomic model with a representative consumer and firm and competitive markets. The representative consumer chooses C and I to maximize utility U(C, 1), subject to the budget constraint: C=w(h-1) + − T, where C is consumption, leisure, w the real wage rate for labour, h is the hours available to the consumer for work or leisure, are firm profits and T is a lump-sum tax. (a) Write down the representative consumer's problem. (b) Use the Lagrangian method to solve the consumer's problem and to show that MRS,e = w holds in equilibrium (hint: MRS1,c U₁(C.D.). Uc = The representative firm produces output according to the production function Y = zF(K, Nd), where z is total factor productivity, K is capital inputs and Nd labour inputs. Assume K is a fixed input of production, and Nd as the only variable factor of production. Workers are paid a real wage w. (c) Write down the representative firm's profit maximization problem. (d) Derive the representative firm's profit maximizing condition (hint: MPN = d).