Question

Patty and Ben operate a small company that produces bicycles. Their fixed cost is $ 4000
per month. They can hire workers for $ 4000 per month. Their monthly production function for
bicycles is as given in the following table:
Quantity of Labour Quantity of Bicycles
0 0
1 10
2 30
3 60
4 120
5 170
6 200
7 220
8 230
a.) For each quantity of labour calculate the following: total product (TP), marginal product (MP),
average productivity (AP), average variable cost (AVC), average fixed cost (AFC), average total
cost (ATC), and marginal cost (MC).
b.) On one diagram draw the MP and AP
c.) On one diagram draw the AVC, ATC, and MC
d.) At what point does Patty and Ben experience decreasing marginal productivity? At what level of are ATC minimized?

Answer 1

Total Product (TP) refers to the total number of products produced with the given number of inputs. So here, the quantity of bicycles produced can be considered as Total Product.

Labor	TP
0	0
1	10
2	30
3	60
4	120
5	170
6	200
7	220
8	230

Marginal Product is the difference between the outputs with a particualr number of input and out put with increased input

Labor	TP	MP
0	0	0
1	10	10 (10-0)
2	30	20 (30-10)
3	60	30 (60-30)
4	120	60 (120-60)
5	170	50 (170-120)
6	200	30 (200-170)
7	220	20 (220-200)
8	230	10 (230-220)

Average Productivity can be calculated by dividing Total output produced by total employees produced

Labor	TP	MP	AP
0	0	0	0
1	10	10	10 (10/1)
2	30	20	15 (30/2)
3	60	30	20 (60/3)
4	120	60	30 (120/4)
5	170	50	34 (170/5)
6	200	30	33.33 (200/6)
7	220	20	31.43 (220/7)
8	230	10	28.75 (230/8)

Average variable cost is calculated by dividing the Variable cost by the quantity produced. In this problem, the wages of the workers is the variable cost.

Labor	TP	MP	AP	Total Variable cost	Average Variable Cost
0	0	0	0	0	0
1	10	10	10	4000 (1*4000)	400 (4000/10)
2	30	20	15	8000 (2*4000)	266.67 (8000/30)
3	60	30	20	12000 (3*4000)	200 (12000/60)
4	120	60	30	16000 (4*4000)	133.33 (16000/120)
5	170	50	34	20000 (5*4000)	117.65 (20000/170)
6	200	30	33.33	24000 (6*4000)	120 (24000/200)
7	220	20	31.43	28000 (7*4000)	127.27 (28000/220)
8	230	10	28.75	32000 (8*4000)	139 (32000/230)

Average Fixed Cost can be calculated by Dividing the total fixed cost by the number of products produced.

Labor	TP	MP	AP	AVC	Total Fixed Cost	AFC
0	0	0	0	0	4000	0
1	10	10	10	400	4000	400 (4000/10)
2	30	20	15	266.67	4000	133.33 (4000/30)
3	60	30	20	200	4000	66.67 (4000/60)
4	120	60	30	133.33	4000	33.33 (4000/120)
5	170	50	34	117.65	4000	23.53 (4000/170)
6	200	30	33.33	120	4000	20 (4000/200)
7	220	20	31.43	127.27	4000	18.18 (4000/220)
8	230	10	28.75	139	4000	17.39 (4000/230)

Average Total Cost can be calculated by adding AVC and AFC

Labor	TP	MP	AP	AVC	AFC	ATC
0	0	0	0	0	0	0
1	10	10	10	400	400	800 (400+400)
2	30	20	15	266.67	133.33	400 (266.67+133.33)
3	60	30	20	200	66.67	266.67 (200+66.67)
4	120	60	30	133.33	33.33	166.66 (133.33+33.33)
5	170	50	34	117.65	23.53	141.18 (117.65+23.53)
6	200	30	33.33	120	20	140 (120+20)
7	220	20	31.43	127.27	18.18	145.45 (127.27+18.18)
8	230	10	28.75	139	17.39	156.39 (139+17.39)

Marginal Cost is calculated by Dividing the Change in the cost  by the Change in the units produced i.e., Margianl Quantity Produced. The total FC and total VC we have already calculated in the tables above

Labor	TP	MP	AP	AVC	AFC	ATC	Variable cost	Fixed Cost	TC	MC
0	0	0	0	0	0	0	0	4000	4000	0
1	10	10	10	400	400	800	4000	4000	8000	400 (8000-4000/10)
2	30	20	15	266.67	133.33	400	8000	4000	12000	200 (12000-8000/20)
3	60	30	20	200	66.67	266.67	12000	4000	16000	133.33 (16000-12000/30)
4	120	60	30	133.33	33.33	166.66	16000	4000	20000	66.67 (20000-16000/60)
5	170	50	34	117.65	23.53	141.18	20000	4000	24000	80 (24000-20000/50)
6	200	30	33.33	120	20	140	24000	4000	28000	133.33 (28000-24000/30)
7	220	20	31.43	127.27	18.18	145.45	28000	4000	32000	200 (32000-28000/20)
8	230	10	28.75	139	17.39	156.39	32000	4000	36000	400 (36000-32000/10)