Question

Consider a firm that daily rents machinery for the cost of $1000 and employs workers at the cost of $100 for a full day of work. The following table describes the production function of the firm. Fill the table such that you can make some production decisions for this firm.

Units of Labor	Units of Production	Fixed Costs	Variable Costs	Total Costs	Average Variable Costs	Average Total Costs	Marginal Cost
1	11.00
2	16.24
3	19.89
4	22.48
5	24.48
6	26.13
7	27.51
8	28.71
9	29.78
10	30.72
11	31.58
12	32.36
13	33.08
14	33.75
15	34.37

1. What is the average variable cost of production when 10 units of labor are employed?

2. What is the average total cost of production when 10 units of labor are employed?

3. What is the marginal cost of production when 10 units of labor are employed?

Answer 1

Give,

Fixed costs = Daily rent for machinery = $1,000

The daily wage of a worker = $100

Units of Labor	Units of Production	Fixed Costs ($)	Variable Costs ($)	Total Costs ($)	Average Variable Costs ($)	Average Total Costs ($)	Marginal Product of Labor (Units)	Marginal Cost ($)
1	11	1000	100	1100	9.09	100.00	11.00	100.00
2	16.24	1000	200	1200	12.32	73.89	5.24	19.08
3	19.89	1000	300	1300	15.08	65.36	3.65	27.40
4	22.48	1000	400	1400	17.79	62.28	2.59	38.61
5	24.48	1000	500	1500	20.42	61.27	2.00	50.00
6	26.13	1000	600	1600	22.96	61.23	1.65	60.61
7	27.51	1000	700	1700	25.45	61.80	1.38	72.46
8	28.71	1000	800	1800	27.86	62.70	1.20	83.33
9	29.78	1000	900	1900	30.22	63.80	1.07	93.46
10	30.72	1000	1000	2000	32.55	65.10	0.94	106.38
11	31.58	1000	1100	2100	34.83	66.50	0.86	116.28
12	32.36	1000	1200	2200	37.08	67.99	0.78	128.21
13	33.08	1000	1300	2300	39.30	69.53	0.72	138.89
14	33.75	1000	1400	2400	41.48	71.11	0.67	149.25
15	34.37	1000	1500	2500	43.64	72.74	0.62	161.29

Formulae used:

Fixed Cost = Daily rent for machiner = $1000

Variable Costs = Units of labor * Daily wage of labor

Total Costs = Fixed Cost + Variable Costs

Average Variable Cost = Variable Cost/Units of production

Average Total Cost = Total Cost/Units of production

Marginal Product of Nth worker = Units of production of N workers - Units of production of (N-1) workers

Marginal Cost at Nth worker = Daily wage of worker/Marginal product of Nth worker = $100/Marginal product of Nth worker

Q1.

When 10 units of labor are employed, Average variable cost = $32.55

Q2.

When 10 units of labor are employed, Average Total cost = $65.10

Q3.

When 10 units of labor are employed, the marginal cost of production = $106.38