Best answer up for grabs! A short past exam paper question that I can't work out! PLEASE HELP!?

Question

Consider a firm that has a production function Q = L.K where L represents labour and K
represents capital
a. Suppose that the wage rate, W, = €1 and the rental rate of capital, r, = €1. Suppose
that the firm wants to produce 100 units of output. What combination of capital and
labour should the firm choose? What is the total cost of producing 100 units of
output?


b. Suppose that the wage rate, W, increases to €4 and the rental rate of capital, r, = €1.
Suppose that the firm still wants to produce 100 units of output. What combination of
capital and labour should the firm choose? What is the total cost of producing 100
units of output?

Faz · Accepted Answer

Part (a)
MRTS = MPL / MPK = (∂Q/∂L) / (∂Q/∂K) = K/L......Eq1

Since we want 100 units of output:
100 = LK, then L = 100/K
Substitute in Eq1

MRTS = K/(100/K) = K²/100

Optimal levels of K and L is where MRTS = w/r
K²/100 = 1, therefore K = 10 units, L = 10 units.
TC: = wL + rK = 10+10 = $20

Part(b)
K²/100 = 4/1, then K=20 units, L = 100/20 = 5 units
TC = 4(5) + (1)(20) = $40

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Best answer up for grabs! A short past exam paper question that I can't work out! PLEASE HELP!?

1 Answer