Question

In a competitive labor market, market labor demand and supply functions are given as follows: LS = -2500 + 1000W; LD = 10500 - 625W, where LD = labor demand, LS = labor supply and W = hourly wage. The production function Q = 88.8L - 0.5L² of a firm operating in this market where skiing vehicles are produced, where Q = refers to production (output in units / hour) and L = number of workers employed per hour. This company sells the product it produces as 10 dollars / piece.
  a) Find the market balance wages and employment levels. Calculate the economic rent obtained by the employees.
b) Find out how many workers this firm should employ at this wage level determined in the market. The total production of this firm should be how many?

Answer 1

A) At the market equilibrium, we will have LS = LD. Hence, equating the two, we will find market balancing wages and employment level.

LS= LD ==> -2500 + 1000W = 10500 - 625W

==> 1000W + 625 W = 10500+2500

==> 1625 W = 13000 ===>. W = 8

This will give us LS = LD = L = 10500-625(8)

= 10500 - 5000 = 5,500

Economic Rent is the income received by a factor of production over and above what they need to be in operation.

From the graph plot below we can see that the labour supply line gives us the minimum the labour would want as wages. So the area below the wage line and above supply curve will give us the economic rent to employees.

the shaded area gives economic rent to the employee =

0.5(8-2.5)(5500) = 0.5(5500)(5.5) = 15125

B) The firm will employ up to the level at which Marginal Product of Labor becomes equal to the wage rate.

MPL = 88.8 - L and W = 8

==> 88.8 -8 =L ==> L = 80.8

Hence , the Q = total production of the firm = 88.8(80.8) - 0.5(80.8)2 = 3910.72