Question

Consider the following cost minimization problem:

Minimization CT = wL + rK

Hold it: q= L^1/2 K^1/2

a) Obtain the long-run cost function

b) If K = 9 and w = 1, obtain the long-run cost function

Answer 1

$$\frac{\delta q}{\delta L}=\frac{1}{2}\times(\frac{K}{L})^{0.5}$$

$$\frac{\delta q}{\delta K}=\frac{1}{2}\times (\frac{L}{K})^{0.5}$$

$$r(\frac{K}{L})^{0.5}=w(\frac{L}{K})^{0.5}$$

$$K=\frac{wL}{r}$$

If K = 9 and w = 1

$$L=9r$$

$$CT=9r+9r=18r$$