Question

26.5 The bauble industry is competitive with free entry. There is a fixed-coeffiient 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 1000-10p. 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.
(b) 10.
(c) 45.
(d) 20.
(e) in finity.
The correct answer is c, why?

Answer 1

Solution :-

Production Function is given by:

Q = min{L,P}

where Q = number of bubbles

L = Labor

P = Plastic

As it is a leontief function A producer will always higher labor and Plastic such That L = P = Q

Hence Cost = wL + 10P = (w + 10)Q, Hence MC = Marginal Cost = dC/dQ = w + 10 , where w = wage rate

Hence company will maximize Profit under perfect competition when p = MC

=> p = w + 10

Hence L = Q = 1000 - 10p = 1000 - 10(w + 10)

Total revenue of Workers (TR) = wL = w(1000 - 10(w + 10))

FOC:

dTR/dw = 0

=> 900 - 20w = 0

=> w = $45

So the Correct answer is (C)