Question

In: Economics

1. The production function for the shoe producing company is Q=KL 2, with the price of...

1. The production function for the shoe producing company is Q=KL 2, with the price of capital and labor fixed at $10 and $15 respectively. what combination of capital and labor minimizes the cost of producing 100 shoes?

Solutions

Expert Solution

The production function,

Cost of capital = $ 10, Cost of labour = $ 15

Output = 100

The firm will be optimally utilizing its available resources at the point where the following relationship

Differentiate Q wrt L, we get

Now, differentiating Q wrt K, we get

Plug in the values we get

When Q = 100,

Therefore, K ≈ 4 units

L = (4×3.83)/3 = 5.10 units

Number of labour units = 5 (approximately)

Number of capital units = 4 (approximately)

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