Question

1. Suppose a firm faces a fixed price of output, ? = 1200. The firm hires workers from a union at a daily wage, ?, to produce output according to the production function ? = 2?^1/2. There are 225 workers in the union. Any union worker who does not work for this firm is guaranteed to find nonunion employment at a wage of $96 per day.

a. What is the firm’s labor demand function?

b. If the firm is allowed to choose ?, but then the union decides how many workers to provide (up to 225) at that wage, what wage will the firm set? How many workers will the union provide? What is the firm’s output and profit? What is the total income of the 225 union workers?

c. Now suppose that the union sets the wage, but the firm decides how many workers to hire at that wage (up to 225). What wage will the union set to maximize the total income of all 225 workers? How many workers will the firm hire? What is the firm’s output and profit? What is the total income of the 225 union workers? [Hint: To maximize total income of union, take the first order condition with respect to w and set equal to 0.]

Answer 1

ANSWER:

Given that

Wage = $ 96 per day

Fixed price of out put (P) =1200

Production function (q) = 2E^1/2

• Firms Labor demand Function
• The Definition of Labour Demand Function is marginal reserve production of labou.
• (MRP_E ) = MR x MP_E = 1200 x 1/E^1/2 =1200/ E^1/2

The firm offer wage rate (w) is less than 96

• No - workers will be provided
• This would leave the function with no out and no profit.
• If the workers receive = $ 96 / day.

Their fore the total daily income of 225 members

= 225 x 96

= $ 21,600

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