A firm has a choice of 2 production technologies. One allows the firm to produce using production function F (K,L) = 10K^(1/3)L^1/3. The other production function is G (K,L) = min (3K,3L), the firm wants to produce 100 per units per month in each of two countries. It must produce in each country because tariff restrictions would encumber its imports. The firms costs of capital is $500 per unit of capital per month in either country (so r=500). Assume fixed costs are ZERO for production in either country.
a) In country alpha w=$4000 per month. Find the firms cost minimizing quantities of capital and labor required to produce 100 units. Note that it can choose its production technology as well as its K* and L*.
b) In country Omega w=$500 per month. Find the firms cost minimizing quantities of capital and labor. Again, it can choose between F and G as well as choosing its optimal mix of K and L
c) Do F() and G() and exhibit increasing returns to scale, decreasing returns to scale or constant returns to scale (answer for each function)
d) Considering only the firms costs for labor and capital, would the firm gain from removal of all tariff barriers so that it could ship production from one country to the other? Would it consolidate production in one country? Explain your answer
e) Assuming the tariff barriers are eliminated, briefly explain why the firm would not consolidate production in one factory.