Homework Clinic

Social Science Clinic => Economics => Topic started by: shanell on Nov 23, 2022

Title: Value of the Marginal Product and the Demand For LaborThe table shows the number of workers (L) and ...
Post by: shanell on Nov 23, 2022

Value of the Marginal Product and the Demand For Labor

The table shows the number of workers (L) and the output of lightbulbs (Q) each week. The lightbulb maker is a price taker in both the product and labor markets.

Number of Workers (L)	Output of Lightbulbs (Q)
0	0
1	27​
2	70​
3	108​
4	140​
5	167​
6	185​

Assume the price of a lightbulb is $2.75. If the equilibrium wage is $88, how many workers should this firm hire? What if the equilibrium wage rises to $118.25?
◦ 4 workers, 1 worker
◦ 5 workers, 2 workers
◦ 5 workers, 1 worker
◦ 4 workers, 2 workers

Title: Value of the Marginal Product and the Demand For LaborThe table shows the number of workers (L) and ...
Post by: Hamad on Nov 23, 2022

4 workers, 2 workers

For the firm, profit is maximized when the value of the marginal product (VMP) from the last worker equals the wage.

First determine the marginal product of each worker (MP):

Number of Workers (L)	Marginal Product (MP)
0	-
1	27 - 0 = 27
2	70 - 27 = 43
3	108 - 70 = 38
4	140 - 108 = 32
5	167 - 140 = 27
6	185 - 167 = 18

VMP = MP*Price of product, $2.75

Number of Workers (L)	Value of Marginal Product (VMP)
0	-
1	27*2.75 = 74.25
2	43*2.75 = 118.25
3	38*2.75 = 104.5
4	32*2.75 = 88
5	27*2.75 = 74.25
6	18*2.75 = 27.5

So if the equilibrium wage is $88, the firm will hire 4 workers.
If the equilibrium wage rises to $118.25, the firm will hire 2 workers.