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 byband the amount of corn produced be measured byk. The cost functions of the two enterprisesare

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

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

(Note, 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 thecorn fieldswhenever 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 is8and the price of corn is 6.

a.Ifthe firms each operate independently,

theequilibrium 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, cornproduction will have to be _____ [subsidized/taxed] by_____ per unit of corn produced to get the socially efficient amount ofproduction.

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