Consider a dynamic (two-period) macroeconomic model with a representative household, a representative firm, and a government. The representative household makes consumption-saving and labor supply decisions. The representative firm makes labor demand and investment decisions.

(a) Clearly write down the representative consumer's problem and the necessary assumptions.

(b) Clearly write down the representative firm's problem and the necessary assumptions.

(c) Clearly define the competitive equilibrium for this economy.

(d) Derive (graphically) the output demand curve. State the necessary assumption(s).