Question

Given Q=4LK +L^2 , Labour cost is 2 and cost is 1, find the maximum out put and the level k and L at which it is achieve when total input cost are fixed at $105

B. Verify that the ratio of marginal product to price is the same for both input at the optimiub

Answer 1

$$\frac {\delta Q}{\delta K}=4L$$

$$\frac{\delta Q}{\delta L}=4K+2L$$

$$2L+K=105$$

$$L=30$$

$$K=45$$ $$\frac{4L}{4K+2L}=\frac{120}{180+60}=0.5$$