Question

C1 [19 marks] Suppose Malcolm and Barnaby are the only two people in a pure exchange economy. Food and clothing are the only two commodities. Malcolm is endowed with 30 units of food and 10 units of clothing, while Barnaby is endowed with 10 units of food and 30 units of clothing. Let F = units of food and C = units of clothing. Malcolm’s utility function is UM = 2 min(F, C) and Barnaby’s utility function is UB = min(F, C).

(a) In an appropriately dimensioned Edgeworth box diagram, illustrate the initial endowment allocation for this economy along with initial indifference curves for Malcolm and Barnaby. Draw your diagram with food on the horizontal axis and clothing on the vertical axis, and Malcolm at the “bottom” and Barnaby at the “top”. Label the indifference curves with the utility of each at the endowment point. (5 marks)

(b) What allocations of food and clothing to Malcolm and Barnaby are Pareto efficient? That is, show the contract curve on your Edgeworth box diagram from part (a) using these particular preferences for Malcolm and Barnaby. For at least two points on the contract curve show the indifference curves of the two people at that point. (2 marks)

(c) Represent the allocations on the contract curve in a carefully labelled and numbered utility possibility curve diagram. (4 marks)

(d) Suppose this economy uses the Rawlsian social welfare function.

i) Write down the social welfare function for this two-person economy. (1 mark)

ii) What point(s) on the utility possibility curve is (are) optimal if we use the Rawlsian social welfare function? (3 marks)

iii) Illustrate the optimal point you found in part ii) graphically by sketching some social indifference curves. (2 marks)

iv) What is social welfare at the optimal allocation that you computed in part ii)? (2 marks)

Answer 1

Hope my answer helps!
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