Question

Consider the following production​ function: q equals 100 Upper L Superscript 0.8 Baseline Upper K Superscript 0.4. Currently the wage rate​ (w) is ​$2.00 and the price of capital​ (r) is ​$2.00. If the firm is using 20 units of capital in​ production, how much labor should be employed to minimize costsLOADING...​? Labor inputequals nothing units. ​(Enter a numeric response using a real number rounded to two decimal​ places.)

Answer 1

Answer: Labor input ≈ 71

Explanation:

Production Function(q) = L superscript 0.8 Baseline upper K superscript 0.4

q = L^0.8 x K^0.4

plug in q = 100 units and K = 20 units into the Production Equation

q = L^0.8 x K^0.4

100 = L^0.8 x (20)^0.4

100 = L^0.8 x 3.3144540173

L^0.8 x 3.3144540173 = 100

L^0.8 = 100/3.3144540173

L^0.8 = $\sqrt[0.8]{30.170881683}$

L = 70.710678119

Labor inputs ≈ 71 units

Approximately 71 units of Labor should be employed to minimize total costs. Total Costs will be 71 x $2 + 20 x $2 = $124 + $40 = $162