Question

6. Suppose a certain contractor wants to maximize profit from building one bridge. The contractor uses both labor and capital and efficient combinations of Labor and capital that are sufficient to make a bridge is given by the function 0.25 L0.5 K0.5. If the prices of labor and capital are birr 5 and birr 10 respectively. Find the least cost combination of L and K and the minimum cost.

Answer 1

MRTS = $\frac{K}{L}$

$\frac{K}{L} = \frac{w}{r}$

$\frac{K}{L} = \frac{6}{16}$

$\frac{K}{L} = 0.375$

K = 0.375L

The least cost combination of L and K is where: K = 0.375L