In: Economics
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?
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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