The bauble industry is competitive with free entry.There is a fixed-coefficient technology.One unit of labor and one unit of plastic are required for each bauble.Workers in the bauble industry must all belong to the Bauble-Makers Union.The union sets the wage that will be paid to all bauble makers.The price of plastic is 10 dollars per unit and the demand function for baubles is 1,000 - 10p.Long-run equilibrium requires that the price of baubles equals the cost of production.The wage per unit of labor that maximizes total revenue of workers is
A)100 dollars.
B)10 dollars.
C)45 dollars.
D)20 dollars.
E)infinity.

Question

Quizplus · Accepted Answer

In the long run equilibrium, the price of baubles will equal the cost of production, which is the wage rate plus the cost of plastic. Thus,
p = w + 10
The Bauble-Makers Union will set the wage to maximize the total revenue of workers, which is given by the product of the wage rate and the number of workers. Since there is free entry, the number of workers is determined by the demand for baubles. Thus,
TR = wF1F1F1S1F1F1F10 10
Taking the derivative of TR with respect to w, we get
dTR/dw = F1F1F1S1F1F1F10 10 > 0
Therefore, TR is increasing in w. Since we want to maximize TR, we should set w as high as possible. However, we also need to ensure that p = w + 10 in order to achieve long-run equilibrium. Therefore,
w = p – 10
Substituting this expression into the TR equation, we get
TR = (p – 10)F1F1F1S1F1F1F10 10
Taking the derivative of TR with respect to p, we get
dTR/dp = F1F1F1S1F1F1F10 10 – F1F1F1S1F1F1F10 10 = 0
At the maximum, the derivative of TR with respect to p is zero. Therefore, we have
p – 10 = 100
p = 110
Thus, the wage per unit of labor that maximizes total revenue of workers is
w = p – 10 = 100
Therefore, the answer is C) 45 dollars.

The Bauble Industry Is Competitive with Free Entry