Consider an exchange economy with two prominent leaders Romn

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:Romney: Power 40 Jobs 20. Bernanke Power 40 Jobs 10 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?

Solution

U Romney: lnP+2lnJ

U Bernanke: 2lnP+lnJ

MRS of Romney = MU(P)/MU(J) = 1/P / 2/J = Jr/2Pr

MRS Bernanke: MU(P)/MU(J) = 2/P / 1/J = 2Jb/Pb

a)

Romney: 40P and 20J

Bernanke: 40P and 10J

Market supply function of Power: P=40Pr+40Pb

Market supply function of Jobs: J=20Jr+10Jb

b)

Income constraint: I=xP+yJ

Where, x and y are the prices of power and jobs

Romney: I=40x+20y

Bernanke: I=40x+10y

c)

At the optimal point, the MRS of each consumer is equal to its price ratio

This gives the Marshallian demand function.

Thus,

Romney: MRS = Price of P/Price of J

Romney: Jr/2Pr = x/y or, Jr=2xPr/y

Similarly,

Bernanke: MRS = Price of P/Price of J

Bernanke: 2Jb/Pb = x/y or, Jb=xPb/2y

Also, Jr+Jb=80 and Pr+Pb=30

Substitute these equations into one another to get the demand curves.

d)

Market demand for power and Jobs is calculated above.

e)

Upon substitution of demand curves, the optimal allocation will be achieved.