Question

The following table represents a certain production function of what a certain facility can produce in one day. Assume the firm has a fixed amount of physical capital that they rent for $500 a day. We will use this example to review CH. 7.  [probably easiest to copy and paste the table and question parts into the submission box and then add your response. Make your text a different color for ease of viewing]

L	Q	MPL	FC	VC	TC	AFC	AVC	ATC	MC
0	0		$500	$0	$500
1	20			$100
2	50
3	100
4	120
5	130
6	135

1) Complete the table by filling in all the missing values. You can assume that each worker earns $100 per day

2) Do you see gains from specialization in the production function. In what range do you see these gains? (specify the workers)

3) For which worker does the marginal product start to decrease? Briefly explain why there is a diminishing marginal product of labor.

4) Why does marginal cost rise so quickly at the end? Explain by connecting to marginal product of labor.

5) At what quantity does average total cost start to rise? What causes it to rise?

Answer 1

1) TC=FC+VC

AFC=FC/Q

AVC=VC/Q

ATC=TC/Q

MC = change in TC/change in Q

L	Q	MP	FC	VC	TC	AFC	AVC	ATC	MC
0	0		500	0	500
1	20	20	500	100	600	25	5	30	5
2	50	30	500	200	700	10	4	14	3.33
3	100	50	500	300	800	5	3	8	2
4	120	20	500	400	900	4.17	3.33	7.5	5
5	130	10	500	500	1000	3.85	3.85	7.69	10
6	135	5	500	600	1100	3.70	4.44	8.15	20

2) Yes, the gains from specialization occurs from 1st worker up to the firm hires 3rd worker

3) MPL starts to decrease when the firm hires 4th worker

The diminishing marginal product occurs because the firm uses too much variable input to the constant fixed input which increases inefficiency and decreases productivity.

4) Marginal cost increases because the cost of hiring additional labor at the end is very high compared to the marginal product that the labor is bringing so the output increases at a very slow pace whereas the total cost increases at an increasing rate.

5) ATC starts to increase when the firm produces 130 units as the marginal product decreases, the inefficiency by hiring the more than required workers causes the average cost to increase and the firm experiences diseconomies of scale.