Question

Use the following data for a firm's output at various levels of employment and the profit-maximizing input rule to identify how many workers the firm will choose to employ: The firm can sell all it wants at the fixed product price of $10. The firm can hire all the labor it wants at the fixed wage of $40 per worker.

      Number of         

     Workers (L)      Output (Q)        

         0                       0

         1                      20

         2                      52

         3                      72

         4                      88

         5                    100

         6                    108

         7                    112

Answer 1

In order to maximize profit a firm produces that quantity at which Marginal Productivity of that input is equal to real cost of hiring that input. In this case input is Labor and hence we have to find Labor(L) at which Marginal Productivity of Labor(MPL) = Real wage(w/P)

Here w = nominal wage = 40

P = Product Price = 10

Hence We have to Find L such that MPL = w/P = 40/10 = 4

MPL(L) is the additional output produced by hiring one more unit of Labor and we can write mathematically MPL as :

MPL(L) = Q(L) - Q(L - 1) , where Q(L) represents Output when L units of Labor are hired and MPL(L) represents MPL of Lth Labor

We can see from above table that MPL(7) = Q(7) - Q(6) - 112 - 108 = 4

Hence MPL = w/P = 4 when L = 7

Hence He should hire 7 units of Labor(or worker) in order to maximize its profit.

Hence He should hire 7 workers.