Problem Set 1 Answers

# Problem Set 1 Answers - Chapter 2, Exercises 2.1, 2.2, 2.3....

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Chapter 2 , Exercises 2.1, 2.2, 2.3. 2.1. General equilibrium consists of a wage rate w so that supply and demand are equated in each of the active markets, oysters and labor/leisure. Household behavior is described as choosing c, R to maximize u(c, R) subject to (2.29, 2.30) for given w and (treated parametrically). The first order condition is equation (2.19) of the text. u R w u c . Firm behavior is described as choosing L and q to maximize given w (treated parametrically). The first order condition is (2.14) in the text, F'(L) = w. w achieves a general equilibrium when these separate decisions are consistent with one another, that is, when q = c , and R + L = 168. 2.2. (a) Walras Law holds both in and out of equilibrium. It reflects merely the budget constraint and the inclusion of firm profits in household budgets, both of which occur both in and out of equilibrium. (b) The household budget is defined in terms of projected firm profits, not in terms of realized profits. Hence the budget in this model is unaffected by the disequilibrium. (c) Starting from an excess demand for labor/leisure, we would expect the wage rate to increase. 2.3. (a) The first order conditions for the solution to 2.3(a) are characterized in equation (2.7) as R q u F u . But this follows directly from (2.14) and (2.19) of problem 1. Hence (with the addition of second order conditions) the solutions are equivalent. (b) The result above in section (a) says that the solution of the general equilibrium and the efficient allocation problem are the same. Hence the general equilibrium solution is efficient. (c)

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## Problem Set 1 Answers - Chapter 2, Exercises 2.1, 2.2, 2.3....

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