Question

You manage Widgets USA, a small manufacturer of widgets in a perfectly competitive market. Below is your production function for widgets, showing the relationship between the number of workers you hire per hour and the hourly volume of widgets produced at different levels of labor. Your total fixed costs, regardless of production volume and hiring rate, are $100/hour, representing the rental contract rate per hour of your single production line.

Number of workers hired per hour	Widgets produced per hour
0	0
1	5
2	9
3	12
4	14
5	15

Part A and B have already been answered, REFER TO : https://www.chegg.com/homework-help/questions-and-answers/manage-widgets-usa-small-manufacturer-widgets-perfectly-competitive-market-production-func-q26914049

(c) If the going wage rate is $6 per hour per worker, how many widgets will maximize your hourly profit and how many workers should you hire?

(d) Given the above data, what is the wage elasticity of your labor demand?

(e) Suppose the going wage rate is $6 per hour but your labor productivity doubles (i.e. all the widget production figures double at each hiring level). Now how many widgets will maximize your hourly profit and how many workers should you hire?

Answer 1

c) Firm will hire labor upto the point where value of the marginal product is equal to the market wage. If wage rate is 6, there will be 4 workers hired because VMPL of 4th worker is 6

Number of workers hired per hour	Widgets produced per hour	MP	VMPL
0	0		0
1	5	5	15
2	9	4	12
3	12	3	9
4	14	2	6
5	15	1	3

Total widgets produced = 14.

d) When wage rate is $9, a total of 3 workers are hired. When wage falls to $6, 4 workers are hired. Hence wage elasticity = % change in labor demanded/% change in wage rate

= (4-3)*100/3 divided by (6 - 9)*100/9 = -1.

e) At this level we would hire 5 labors because the VMPL of 5th labor is 6. Total widgets = 30

Number of workers hired per hour	Widgets produced per hour	MP	VMPL
0	0		0
1	10	10	30
2	18	8	24
3	24	6	18
4	28	4	12
5	30	2	6