DO NOT ROUND UNTIL YOUR FINAL ANSWERS ! I suggest you use Excel, but you can use a calculator if you prefer. Round prices to the nearest penny ($1.23), quantities to the nearest integer (123.) , and interest rates in percent to one decimal place (12.3%). Only round a s you write down your answer . Use the full value in all subsequent calculations. 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 X ( C 1 , C 2 ) = . 51 ln ( C 1 ) + . 49 ln ( C 2 ) . He begins with an endowment of 1000 pounds for consumption today and 1000 pounds for tomorrow ( E 1 =E 2 =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 (less patient) than Xavier is. U Y ( C 1 , C 2 ) = . 52 ln ( C 1 ) + . 48 ln ( C 2 ) . He starts with the identical endowment of 1000 pounds for consumption today and 1000 pounds for tomorrow ( E 1 =E 2 =1000). A. Solve for the general equilibrium. What prices and interest rates underlie the equilibrium? P 1 = $ __ __ . __ __ P 2 = $ __ __ . __ __ r = __ __ .__ %

B.State the amount eachperson consumes in each period, verify that each market clears, andexplain who bought each good and who soldit.What was bought?C1C2What wassold?

Xavieroptimal consumption____________________________________________

Yurioptimalconsumption____________________________________________

Marketconsumption____________________________________________(Xavier + Yuri)

C.Demonstrate numerically that both Xavier and Yuri are better off at the new consumptionlevels thantheir respective endowments. (Hint: comparetheutility oftheendowment andtheoptimalconsumption)

D.Demonstrate numerically that both Xavier and Yuri can afford their new consumption levels.(Hint:calculate the wealthof each person based on their endowment. Thenshow theconsumption basket for each personsatisfiestheirbudget constraint.)

E.Demonstrate numerically that both Xavier and Yuri have no incentive to trade further at thecurrent prices. Hint:Calculate the MRS for each person and show it equals the ratio of theprices