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

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?