Question

Suppose that a firms out put is given by: q = αLK2 Where α is a productivity factor.

i. Specify the marginal products of labour and capital.

ii. If the cost function is C = wL + rK. Specify the quanitites of capital and Labour that minimize costs?

Answer 1

i.

The marginal product of capital $\frac{∂Q }{∂L }= αK^2$

The marginal product of labor $\frac{∂Q }{∂K }= 2αLK$

ii

$C = wL + rK\\$

When plotted with capital on the vertical axis and has intercepted at K =r and L = w.

The cost-minimizing point is a corner solution.