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Unformatted text preview: Problem Set 4: General Equilibrium and Economic Welfare With Two Markets Econ 100B James Rauch Solutions 1. Set- MRS = p x /p y , yielding 2 y/x = p x /p y . Since p y = 1, this can be rewritten as x = 2 y/p x . Income is given by I = p x x + p y y . Since x = 10 and y = 15, we have I = 10 p x + 15. The budget constraint is p x x + p y y = I , but again since p y = 1, this becomes p x x + p y = I . Equating the budget constraint and the equation determining income, 10 p x + 15 = p x x + y . Thus, y = (10- x ) p x + 15. Substituting this expression into x = 2 y/p x and solving for x gives x D = 20 / 3 + 10 /p x . The market clears when x D = x S . Since x S = x = 10, this occurs precisely when 10 = 20 / 3 + 10 /p x . Solving for p x , we find that p x = 3. 2. Income is given by I = p x x + p y y , but since p y = 1, x = 10, and y = 15, I = 45. 3. From question 1, we know that setting- MRS = p x /p y gives x = 2 y/p x ....
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- Fall '07