General Equilibrium in a Pure Exchange Economy.

Consider a pure exchange economy with two consumers, Harry and Meghan, who consume two commodities, pudding, and salmon. Harry's initial endowment is 16 puddings and 2 salmons. Meghan's endowment is 8 salmons and 4 puddings. Their utility functions areU_h=P^1/2_h S_h andU_m=P_mS^1/2_m

respectively.

1. Draw the Edgeworth box to illustrate the initial endowment, putting puddings on the horizontal axis and measuring goods for Harry from the lower-left corner. Label the initial allocation W. What is the utility level associated with the initial allocation for each consumer? Find the algebraic expression of the indifference curve passing through the initial endowment for each individual and draw both of them in the Edgeworth box.
2. Is the initial allocation Pareto-efficient? Can it be a general economic equilibrium? Explain
3. If you have concluded that W is not Pareto-efficient, what would the direction of trade be? Would Harry demand salmons in exchange for puddings or vice-versa? Explain.
4. Write down an equation that satisfies the condition for Pareto efficiency in terms of the goods consumed by both agents. What is the name of such Pareto-efficient locus of points? Draw it in the Edgeworth box (hint: obtain some points of such curve through its algebraic expression, plot them in the Edgeworth box and connect them).