1. Suppose a cattle ranch is located next to a corn farm and each both as competitive firms. Let the amount of beef produced be measured by b and the amount of corn produced be measured by k. The cost functions of the two enterprises are

c_b(b) = b²/10 - k and c_k(k) = k²/100 + 2b.

Note MC_b = b/5 and MC_k = k/50

If firms operated together, C(b, k) = b²/10+ 2b - k + k²/100.

Then MC_b = b/5 + 2 and MC_k = k/50 - 1.)

The impact of one firm's production on the other firm isn't surprising because the cattle tend to stray into the corn fields whenever they can, making the cattle cheaper to produce and the corn more expensive to produce (depending on how many cattle are being raised). The price of beef is 8 and the price of corn is 6.

a. If the firms each operate independently,

the equilibrium amount of beef produced will be ____ and the equilibrium amount of corn produced will be ____

b. What would be the socially efficient amount of beef produced? ____

What would be the socially efficient amount of corn produced? ____

c. If the firms each operate independently, if you wanted to each to operate at efficient production levels, corn production will have

to be _____ [subsidized/taxed] by _____ per unit of corn produced to get the socially efficient amount of production.

d. If the firms each operate independently, beef production will have to be ____ [subsidized/taxed] by _____ per unit of beef produced to get the socially efficient amount of production.