1.Consider a price-taking firm operating in a market with price,p. The production function for the firm is F(K, L)=K^alpha L^beta. Where K is units of Capital and Lis units of Labour. If the cost of each unit of capital is rand the cost of each unit of labour is w.

a.Is the production function homogenous? If so, what is the degree of homogeneity?

b.Under what conditions does the production function exhibit increasing, constant or decreasing returns to scale?

c.Write out the Cost Function C(K,L). Is the cost function homogenous? If so, what is the degree of homogeneity?

d.Write out the profit function pie(K,L). Is the profit function homogenous? If so, what is the degree of homogeneity?

e.Find the critical values for the profit function, L*and K*.

f.Under what conditions are the values in part e. profit maximizing?

g.Find the maximum profit under the condition specified in part f.

What can you say about the case where the conditions in part f. are violated