Question: Consider an exchange economy with two prominent leaders: Romney and Bernanke. Each get utility from destroying jobs, J; and from power, P. Their utility functions are: URomney = ln(P) + 2 ln(J) UBernanke = 2ln(P) + ln(J) Their initial endowments are as follows: Power and Jobs respectively; Romney: 40 power 20 Jobs Bernanke: 40 power 10 Jobs. Assume that both power and jobs to destroy are tradeable.
a. What are the market supply functions for power and jobs?
b. What is the income of both, expressed as a function of prices?
c. What are the Marshallian demand functions for power and jobs (this should be J* and P*, expressed as functions of prices)?
d. What is the market demand for power and jobs?
e. Using what you have done for a-d, what are the equilibrium prices and allocations?
f. Do any exchanges occur in the economy?
g. Show your results in an Edgeworth box (please use Romney as bottom left origin).
h. Use another Edgeworth box to show how your answers might change if both Romney and Bernanke had utility functions of U = ln(P) + ln(J). Would there be any trades? You may want to do the math again to verify your intuition.
i. Use another Edgeworth box to show how your original answers (with the original utility functions) might change if the original endowments changed to: Power Jobs Romney 30 15 Bernanke 30 15
j. What does the above suggest about the conditions under which exchange is most beneficial?