Question

Suppose a firm's production function is given by Q = F(L,K) = 5LK, where L is the amount of labor and K is the amount of capital. The wage rate is $100 per unit of labor and the rental rate of capital is $25 per unit of capital. What is the lowest possible cost of producing 980 units of output?

Answer 1

$ 9800.

Step-by-step explanation:

First, we must know that the cost minimization of capital and labour is; MRTS = MPL/ MPK.

Where the marginal product of labour = dQ/dL which is equal to; 5K.

The marginal product of capital = dQ/dK = 5L.

Hence, the marginal rate of technical substitution = 5K/5L = 100/25.

K = 4L.

Next, we will substitute the value of K into Q= 5LK.

That is; Q = 5L × 4L. Where Q = 980 units.

Then, 980 = 20L.

L = 49.

If L = 49, then K = 4 × 49 = 196.

So, we will now use what we have gotten above to determine the lowest possible cost;

lowest possible cost= (100 × 49) + (25 × 196).

lowest possible cost = 4900 + 4900.

lowest possible cost= $ 9800