Consider the specific factors model in which there are two industries: oil and manufactur-  ing. Examine a single country which takes prices as exogenous. There are three factors of production: oil fields O, manufacturing labor L, and capital K . Assume that oil fields are “specific” to oil production and cannot be used in manufacturing production. Manufactur-  ing labor is“specific” to manufacturing and cannot be used in oil production.  Capital is “mobile” in that it is perfectly mobile can be used in either sector. If Ko is the employment of capital in oil production and Km  is employment of capital in manufacturing, then full employment of capital implies Km + Ko = K .

Assume that oil fields receive a return (i.e. a“wage”) of wo , manufacturing workers receive a wage of wL , and capital receives a return of wK .  Assume that all agents are paid their marginal revenue product.

Production functions in the two industries are Cobb-Douglas as follows where Yo is produc- tion of oil and Ym  is manufacturing production:

Yo = O0.5 Ko(0) .5                               Ym = L0.5 Km(0.)5

Finally, let po  be the price of oil and pm  be the price of manufacturing output.  For the moment, assume that po  = pm  = 2 and that the economy has K=450 units of capital, O=225 units of oil fields, and L=225 manufacturing workers.

1. Derive an expression for the marginal revenue product of oil (MRPO) in terms of po , O, and Ko .

2. Derive an expression for the marginal revenue product of manufacturing labor (MRPL) in terms of pm , L, and Km .

3. Derive an expression for the marginal revenue product of capital in the oil industry (MRPKo) in terms of po , O, and Ko . On a graph with MRPKo  on the vertical axis, and Ko  on the horizontal axis, plot MRPKo .

4. Derive an expression for the marginal revenue product of capital in the manufacturing industry (MRPKm) in terms of pm , L, and Km . On a graph with MRPKm  on the vertical axis, and Km  on the horizontal axis, plot MRPKm .

5. If capital is mobile between the two industries, what relationship must hold between MRPKo  and MRPKm? Derive this in terms of po , pm , L, Km , Ko, and O .

6. Plot MRPKo  and MRPKm  on the same graph using the Scissors Graph as we did in class.  Graphically show the equilibrium wage of capital wK  and how much capital is allocated to the two industries:  Ko  and KM .  You do not need to calculate any numbers.

7. Using the numbers in the preamble, solve for Km , Ko , Yo, and Ym .