Question

4. Person A and Person B have been stranded on an island. They are the only two people on the island and there are only two goods: coconuts (C) and grapefruits (G). A found (is endowed with) 16 coconuts and 16 grapefruits. B found (is endowed with) 4 coconuts and 144 grapefruits. Therefore, the total endowment for this economy is 20 coconuts and 150 grapefruits. A's marginal rate of substitution between coconuts and grapefruitss MRS here Ca and Ga are A's consumption of coconuts and grapefruits. Likewise, B's marginal rate of substitution between coconuts and grapefruits is MRS here CB and GB are B's consumption of coconuts and grapefruits. (a) Draw the Edgeworth box depicting this economy (for consistency put coconuts on the x-axis and grapefruits on the y-axis). Label the initial endowment point and sketch the indifference curve through the endowment point for each person. (b) What area in the Edgeworth box in (a) represents all Pareto improvements to the initial endowment point. (c) A competitive equilibrium is a set of prices and an allocation ( Po PG, CA,CB, GA, G.) such that each person is maximizing his utility subject to his budget constraint and each market clears. Because the preferences of these two individuals are well-behaved, the conditions for the competitive equilibrium are satisfied if (i) the slopes of the two indifference curves are tangent to each other and to the budget constraints, (ii) supply equals demand in each market, and (iii) each person is consuming along his budget constraint. Write out these conditions for this economy (d) Normalize pG-I. Using your conditions in (c), solve for the competitive equilibrium of this economy

Answer 1

Page 0 160) E hital endocw ment bPrea enolosed by too sc shous the osetv n popveneut eca MRSA TCA 6 ch→ (800) endowmeut Income

4) ll Now Pg: 1, then MA= 16 Pct 16, MB24fct l44 at ce 그 CAM 144 16 2 GB = 88