The company has the following production function Q 20K 4L

The company has the following production function Q = 20K + 4L, where K denotes capital, while L denotes labour. The price of capital is 15 euros per unit, while the price of labour is 5 euros per unit. The company wants to produce 400 units of output with minimum cost. choose the correct answer

a) The company should employ 100 units of labour. b) The company should employ 25 units of labour. c) The company should employ 20 units of labour. d) The company should employ only capital. e) None of the above.

Solution

Option (d).

Q = 400 = 20K + 4L, or

100 = 5K + L

Total cost (Euro) = wL + rK = 5L + 15K

A linear production function means that L and K are substitutes, and only one of them would be employed.

When L = 0, K = 100/5 = 20 and Total cost (Euro) = 5 x 0 + 15 x 20 = 300

When K = 0, L = 100 and Total cost (Euro) = 5 x 100 + 0 = 500

Since total cost is lower when L = 0 and K = 20, this is optimal input combination. So firm should employ only capital (20 units).