A competitive firm produces output y using two inputs, labour L and capital K, The production function is given by F(K,L)=K1/31/3L1/31/3

The production function is given by F(K,L)=K1/31/3L1/31/3

Price of output is , p=12

Price of Labour, w=2

Price of Capital, r=2

Profit=Revenue - Cost

Revenue= p* K1/31/3L1/31/3

Cost=w*L+r*K

Differentiating profit w.r.t K

d(Profit)/dK=d(Revenue)/dK-d(Cost)/dK

=4K^(-2/3)L^(1/3)-2

Using F.O.C

4K^(-2/3)L^(1/3)=2 --------------------------------------------(i)

Similarly, differentiating profit w.r.t L

4L^(-2/3)K^(1/3)=2 --------------------------------------------(ii)

(i)/(ii)

K/L=1

K=L

Putting the value in equation (i)

L=8

K=8

The profit is maximum when labour and capital are 8 units each.

The profit is 16 units