Consider the two-period endowment economy described in class (or chapter 8 of th

Question

Consider the two-period endowment economy described in
class (or chapter 8 of the text)

(a) De?ne the competitive equilibrium.

(b) Characterize the competitive equilibrium.

(c) Suppose that N = 10, y = 14, y = 16.5, G = 20 and G = 65. Further, suppose that
the utility function is given by U (c, c ) = ln (c) + ? ln (c ), with ? = 0.8. Calculate the
equilibrium variables.

(d) Could you calculate all of the equilibrium variables in part c? Explain.

(e) Are the consumers borrowing and lending between themselves?

Explanation / Answer

General equilibrium theory is a branch of theoretical economics. It seeks to explain the behavior of supply, demand, and prices in a whole economy with several or many interacting markets, by seeking to prove that a set of prices exists that will result in an overall equilibrium, hence general equilibrium, in contrast to partial equilibrium, which only analyzes single markets. As with all models, this is an abstraction from a real economy; it is proposed as being a useful model, both by considering equilibrium prices as long-term prices and by considering actual prices as deviations from equilibrium. General equilibrium theory both studies economies using the model of equilibrium pricing and seeks to determine in which circumstances the assumptions of general equilibrium will hold. De…nition of Competitive Equilibrium Now we will de…ne a competitive equilibrium for this economy. Let us …rst lookat …rms. Without loss of generality assume that there is a single, representative…rm that behaves competitively (note: when making this assumption for …rms,this is a completely innocuous assumption as long as the technology featuresconstant returns to scale. We will come back to this point). The representative…rm’s problem is , given a sequence of prices Since in each period all inputs are rented (the …rm does not make the capitalaccumulation decision), there is nothing dynamic about the …rm’s problem and

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