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PS11 Q1 tips - B ’s origin is in the upper-right corner...

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Problem Set No. 11 Q1: Helpful Tips In this question, we will build on our knowledge of preferences, utility functions, indifference curves and the marginal rate of substitution to consider an exchange economy that consists of two con- sumers, A and B . The total endowment e of the exchange economy determines the size of the Edgeworth Box that we will draw, and the point labeled e will represent the distribution of this total endowment between A and B . The preferences of A and B , together with their endowments, will determine the scope for mutually beneficial trades. Since every type of preference we have considered has a utility function representation and corresponding indifference curves, every type of preference also has a curve in the Edgeworth Box. Recall also that the MRS gives the slope of an indifference curve, so evaluating the MRS at the endowment will help us to draw the indifference curves through the endowment and determine the direction of trade (fortunately, the MRS also gives the slope of B ’s indifference curves, even though
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Unformatted text preview: B ’s origin is in the upper-right corner of the Edgeworth Box). Solving the problem for each pair of utility functions and endowment is easy to do, just follow these steps: Step 1: First you draw the Edgeworth Box. Make sure the box has the correct dimensions, so that the q 1 axis has length e A 1 + e B 1 and the q 2 axis has length e A 2 + e B 2 . Step 2: Next you find the endowment in the box. The point labeled e should reflect the endowments e A = ( e A 1 ,e A 2 ) and e B = ( e B 1 ,e B 2 ) of A and B , respectively. Step 3: Then you draw the indifference curves in the box. Again, their slopes will be equal to the MRS of each consumer. We are particularly interested in the indifference curves through the endowment, so we must evaluate the MRS at the endowment. If MRS A 6 = MRS B at e , then there is scope for mutually beneficial trades. And that’s the way you do it! Remember, every type of preference has indifference curves in the box. 1...
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