1. Analyze the baseline economy consisting of two goods, two periods, and two representative consumers with...

 

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1. Analyze the baseline economy consisting of two goods, two periods, and two representative consumers with endowments. • Xavier has Cobb-Douglas preferences over consumption today and tomorrow. U*(C, C2) = .51 log(C,) + 49 log(C,). • He begins with an endowment of 1000 pounds for consumption today and 1000 pounds for consumption tomorrow (E=E=1000). Note that people consume three to five pounds of food per day so 1,000 per year is a reasonable value. Well, at least it is a nice round number. Yuri also has Cobb-Douglas preferences but is slightly more impatient than Xavier is. U' (C,, C) = .52 log(C,) + 48 log(C,). He starts with the identical endowment of 1000 pounds for consumption today and 1000 pounds for consumption tomorrow (E:=E2-1000). A. Solve for the general equilibrium. What prices and interest rates underlie the equilibrium? Pi = S_ P2 = $ B. State the amount each person consumes in each period. Xavier: C = C2 = Yuri: C = C2 = C. Demonstrate numerically that the goods markets in period 1 and in period 2 clear. (market clearing) D. Demonstrate numerically that both Xavier and Yuri are better off at the new consumption levels than at their respective endowments. (utility maximizing) E. Demonstrate numerically that both Xavier and Yuri can afford their new consumption levels. (budget constraint) F. Explain who bought, who sold, and why? 1. Analyze the baseline economy consisting of two goods, two periods, and two representative consumers with endowments. • Xavier has Cobb-Douglas preferences over consumption today and tomorrow. U*(C, C2) = .51 log(C,) + 49 log(C,). • He begins with an endowment of 1000 pounds for consumption today and 1000 pounds for consumption tomorrow (E=E=1000). Note that people consume three to five pounds of food per day so 1,000 per year is a reasonable value. Well, at least it is a nice round number. Yuri also has Cobb-Douglas preferences but is slightly more impatient than Xavier is. U' (C,, C) = .52 log(C,) + 48 log(C,). He starts with the identical endowment of 1000 pounds for consumption today and 1000 pounds for consumption tomorrow (E:=E2-1000). A. Solve for the general equilibrium. What prices and interest rates underlie the equilibrium? Pi = S_ P2 = $ B. State the amount each person consumes in each period. Xavier: C = C2 = Yuri: C = C2 = C. Demonstrate numerically that the goods markets in period 1 and in period 2 clear. (market clearing) D. Demonstrate numerically that both Xavier and Yuri are better off at the new consumption levels than at their respective endowments. (utility maximizing) E. Demonstrate numerically that both Xavier and Yuri can afford their new consumption levels. (budget constraint) F. Explain who bought, who sold, and why?

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