Business, 17.07.2021 01:10 jeniferfayzieva2018

A little exchange economy has just two consumers, named Ken and Barbie, and two commodities, quiche and wine. Ken’s initial endowment is 3 units of quiche and 2 units of wine. Barbie’s initial endowment is 1 unit of quiche and 6 units of wine. Ken and Barbie have identical utility functions. We write Ken’s utility function as U(XK, YK) = XKYK and Barbie’s utility function as U(XB, YB) = XBYB, where XK and YK are amounts of quiche and wine for Ken and XB and YB are amounts of quiche and wine for Barbie. Ken’s marginal rate of substitution is |MRSXY | = YK and Barbie’s marginal rate of substitution is |MRSXY | = YB . XK XB(a) Draw an Edgeworth box to illustrate the situation. Put quiche on the horizontal axis and wine on the vertical axis. Measure goods for Ken from the lower left corner of the box and the goods for Barbie from the upper right corner of the box. (Be sure that make the length of the box equal to the market supply of quiche and the height equal to the market supply of wine.) Locate the initial allocation in your box, and label it E. On the sides of the box, label the quantities of quiche and wine for each of the two consumers and the initial endowment.(b) Use blue ink to draw the indifference curve for Ken that goes through the initial endow- ment. Use red ink to draw the indifference curve for Barbie that goes through the initial endowment.(c) Draw in the contract curve. HINT: You can use the tangency condition of Ken’s MRS equals Barbie’s MRS, the fact that market demand for good X = XK + XB must equal market supply of good X, and the fact that market demand for good Y = YK +YB must equal market supply of good Y to solve three equations and obtain the ratio YK/XK to draw the contract curve.(d) Solve for the final allocations and the competitive (market) prices. What is Ken’s con- sumption bundle? What is Barbie’s consumption bundle? What are the prices of the goods? HINT: Use the contract curve equation from above to obtain the price ratio.(e) On the Edgeworth box for Ken and Barbie, draw and label the competitive equilibrium allocation. Are both consumers better off having traded?

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A little exchange economy has just two consumers, named Ken and Barbie, and two commodities, quiche...

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