1. Answer this question using calculus. Consider a version of the two period general equilibrium model with pro- duction, as seen in the notII. Extend the model to allow for three periods instead of two. Assume that the household has an additive utility function with discounting. (a) Formally define a competitive equilibrium in this economy. [3 points] (b) Write down the household's problem, and generate rst order conditions. Explain why the rational expectations assumption is needed in order to solve household's problem. [3 points] (c) Write down the representative rm's problem. Generate and interpret the rst order conditions for the firm. [3 points] ((1) Generate equations that characterize the equilibrium allocation and prices. [3 points]