Analyze the following economy (two goods,two periods,two representative consumers with endowments).
• Xavier has Cobb-Douglas preferences over consumption today (A1 for apples today) and tomorrow (A2) of the form UX=.51 log(A1 ) + .49 log(A2 ). He begins with an endowment of 10 units for consumption today and 10 units for consumption tomorrow.
• Yuri also has Cobb-Douglas preferences but is slightly more impatient than Xavier UY=.52 log(A1 ) + .48 log(A2 ). He starts with the same endowment of goods as Xavier.
• Solve for the general equilibrium.? State the amount each person consumes in each period, the prices of both goods, and the real interest rate. Verify that all markets clear. Verify that neither party has an incentive to trade further (marginal condition).
• Hint: Remember to use natural logs.
• Hint: Do not round intermediate calculations.
• Hint: It is suggested that you solve this once with pencil & paper to understand the model and a 143 second time in excel for accuracy and repeatability. We will do this calculation repeatedly to consider the “comparative statics” of the model.