lec101b_new

lec101b_new - 1. General Equilibrium An island community...

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1 1 1. General Equilibrium x An island community produces guns(X) and butter(Y) with only labor inputs » The production functions are X=(4L X ) .5 and Y=(L Y ) .5 where L X and L Y are the number of hours of labor devoted to X and Y, respectively » Labor supply on the island is fixed at 18,000 hours per week » Community preferences are represented by U=X .2 Y .8 2 General Equilibrium continued x a) Find the formulas for the island’s rate of product transformation (RPT) and its marginal rate of substitution (MRS) » L X =.25X 2 and L Y =Y 2 . L X +L Y = 18000, so the PPF is .25X 2 +Y 2 =18000 » Take total differential of PPF to get RPT. We have .5X dX + 2Y dY = 0, so RPT=-dY/dX=X/(4Y) » MRS=MU X /MU Y =Y/(4X)
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2 3 General Equilibrium continued x b) Suppose that the island does not trade with the rest of the world. What are the optimal levels of X and Y? What is U*? » The island must consume and produce the same quantities, so we should find tangency between PPF and U for representative consumer » RPT=MRS, so X/(4Y)=Y/(4X) or Y=X » Substituting in the PPF, we have .25X 2 +X 2 =18000 » X*=Y*=U*=120 4 General Equilibrium continued x c) Now suppose that the island changes government and enacts a “free trade” policy with the rest of the world and that the ratio P X /P Y =1. What are the new production and consumption choices? What is U**? x The country should produce along the PPF where RPT equals the price ratio of 1 » From before, RPT= X/(4Y), X/(4Y)=1 and X=4Y at production equilibrium. PPF is .25X 2 +Y 2 =18000, so .25(4Y) 2 +Y 2 =18000 and country should produce Y=60 and X=240
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3 5 General Equilibrium continued x The country should consume where MRS equals the price ratio of 1 » MRS=Y/4X, so Y=4X at equilibrium consumption » Budget is determined by monetary value of production: 1(240) + 1(60) = 300, so budget constraint is X + Y = 300 » Substitution of equilibrium condition (Y=4X) into the budget constaint yields X + 4X = 300. » U with trade is 181.89 6 General Equilibrium continued x d) Explain under what circumstances the country will gain from trading with the rest of the world. Are there any circumstances where trade will not be beneficial to this island country? » The country always gains if the world price vector is different than the implicit price vector associated with optimality in the pre-trade regime
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4 7 2. Diversification A stock market speculator is considering two investment opportunities x An investment in the first company would yield an income of 50,000 in a strong economy and an income of 10,000 in a recession. x The second company is much more recession proof and yield 30,000 in a strong economy, but 20,000 in a recession. x
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This note was uploaded on 05/26/2008 for the course ECON 101 taught by Professor Buddin during the Winter '08 term at UCLA.

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lec101b_new - 1. General Equilibrium An island community...

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