Mr Barnes' Mine Has a Monopoly on Coal Production in the Local

question 47

Essay

Mr. Barnes' Mine has a monopoly on coal production in the local community. Also, Mr. Barnes' Mine is the sole employer in the local community. The market supply of labor is:
L^S(w) = 50w - 250
Or equivalently
w = 50 + 0.02L^S
Mr. Barnes' wage bill is:
WB = 50L + 0.02L²
The resulting marginal expenditure of labor function is:
ME(L) = 50 + 0.04L
The marginal product of coal as a function of labor is:
MP_L = 0.01.
The marginal revenue of coal sales as a function of labor is:
MR(L) = 100,000 - 28.57L
Determine Mr. Barnes' marginal revenue of the product of labor. What is Mr. Barnes' optimal employment of labor? What is the wage rate Mr. Barnes pays for a unit of labor?

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Definitions:

Variable Costs

Costs that vary directly with the level of production, such as materials and labor, in contrast to fixed costs which remain constant regardless of production level.

Homogeneous Products

Goods that are identical in quality and features, making them interchangeable in the eyes of consumers.

Indistinguishable

Incapable of being identified as different or distinct, often used in contexts where two or more items appear exactly alike.

MR

In economics, Marginal Revenue, referring to the increase in revenue that results from the sale of one additional unit of output.