Question

A firm’s production can be described with the following production function q = 6L2 -L3 + 20L, the amount of capital is fixed at 3 units and the total revenues are given by TR = 5q. Labour supply that the firm faces is given by the function w = 100.

• Decide whether the company is a perfect or imperfect competitor in the output market.

• Decide whether the company is a perfect or imperfect competitor in the labour market.

• Express the function MRPL , ARPL , MFCL , and AFCL .

• Determine how employees the firm is willing to employ. Next, determine the wage rate that the firm will pay for each unit of labour.

Answer 1

Solution:

Production function (q) = 6L² – L³ + 20L

MPL = $\frac{\partial Q} {\partial L}$ = 12L – 3L² + 20

The company is an imperfect competitor in the output market since it is a monopoly.

 

The company is an imperfect competitor in the labor market.

 

MRPL = MR x MPL

MR = $\frac{\partial TR} {\partial Q} = 5$

MRPL = 5 $\times$ (12L – 3L² + 20) = 60L – 15L² + 100

 

ARPL = AR $\times$ APL

AR = $\frac{TR}{Q} = \frac{5Q}{Q} = 5$

APL = $\frac{Q}{L}$ = 6L² – L³ + $\frac{20L}{L}$ = 6L – L² + 20

ARPL = 5 x (6L – L² + 20) = 30L – 5L² + 100

 

MFCL = MFC x L

MFC = $\frac{\partial TFC} {\partial Q}$ = 12L – 3L² + 20

MFCL = 100 $\times$ (12L – 3L² + 20) = 1200L – 300L² + 2000

 

AFCL = AFC $\times$ L

AFC = $\frac{TFC}{Q}$ = 6L² – L³ + $\frac{20L}{L}$ = 6L – L² + 20

AFCL = 100. (6L – L² + 20) = 600L – 100L² + 2000

 

Number of employees to employ = $\frac{TFC}{Q}$

TFC = 6(3²) – 3³ + 20(3) = 87

= $\frac{87}{3}$ = 29

Number of employees to employ = 29 employees

Wage rate = $\frac{29}{3}$ = 9.6