Question

Suppose the production function is given Q(L,K)=L3/4K1/4 assuming capital is fixed find APL and MPL

Answer 1

Answer:

Explanation:

To determine the optimal capital-labor ratio set the marginal rate of technical substitution equal to the ratio of the wage rate to the rental rate of capital: K L = 30 120 , or L = 4K. Substitute for L in the production function and solve where K yields an output of 1,000 units: 1,000 = (100)(K)(4K), or K = 1.58.

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Answer 2

Answer:

• How to calculate the ideal capital-labor ratio Set the wage rate to capital rental rate ratio as the marginal rate of technical substitution:
• L = 4K if K L = 30 120.
• L should be substituted for in the production function to address the problem when K produces 1,000 units of output:
• 1,000 = (100)(K)(4K), or K = 1.58
• While Marginal Product of Labor (MPL) is the additional output obtained by hiring one additional unit of labour, Average Product of Labor (APL) equals Q/L. The rule of diminishing returns is what causes the curves to be to the right and to appear as they do.
• The average product will tend to increase when the MPL curve is higher than the APL curve, or when MPL APL, because if you take a higher number, add it to the average, and then take a new average, the new average must be higher. The MPL curve will eventually cease rising and start lowering until it collides with the APL curve. Thus, the AP curve won't start to fall until the MPL APL since the new average must be lower because now a smaller quantity is being added. Therefore, the MPL's greatest point must be where the APL curve and it meet.

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