Question

If a firm has the production function f(L,K) =(L+1)K, and currently uses no units of labor, but K=3 units of capital, what is its marginal rate of substitution?Aretherevaluesofwandrsuchthatthischoiceoffactorinputs is optimal?

Answer 1

i)Give production function f(L,K) = (L+1)K

therefore, Marginal rate of labour or MR_L = f(L,K)/L = K

Also Marginal rate of capital or MR_K = f(L,K)/K = L+1

Therefore marginal rate of technical substitution is MR_K/ MR_L = (L+1)/K= (0+1)/3 = 1/3 ( since K=3 and L = 0)

ii) Putting the values of K and L in the production function, we get,

f(L,K) = (0+1).3 = 3 which is value of capital (K) used. Therefore, input values of labour and capital are optimal.