Question

Use the following information to answer questions 1-7

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. At what approximate level of production is the marginal cost of production equal to the average total cost?

2. What would be the firm’s level of production if the price of the good was $60?

3. What would be the firm’s profits at equilibrium if the price of the good was $60?

4. What would be the price of the good if the firm is employing 8 workers at equilibrium?

5. What would be the profit of the firm if the firm is employing 8 workers at equilibrium?

6. What would be the price of the good if the firm is employing 9 workers at equilibrium?

7. What would be the profit of the firm if the firm is employing 9 workers at equilibrium?

Answer 1

L	Q	FC= rK= $1000	VC= wL= (100)(L)	TC= FC+VC	AVC= VC/Q	ATC=TC/Q	MC=(Change in TC/ Change in Q)
1	11	1000	100	1100	9.09	100	-
2	16.24	1000	200	1200	12.32	73.89	19.08
3	19.89	1000	300	1300	15.08	65.36	27.4
4	22.48	1000	400	1400	17.79	62.28	38.61
5	24.48	1000	500	1500	20.42	61.27	50
6	26.13	1000	600	1600	22.96	61.23	60.61
7	27.51	1000	700	1700	25.45	61.8	72.46
8	28.71	1000	800	1800	27.86	62.7	83.3
9	29.78	1000	900	1900	30.22	63.80	93.46
10	30.72	1000	1000	2000	32.55	65.10	106.38
11	31.58	1000	1100	2100	34.83	66.5	116.28
12	32.36	1000	1200	2200	37.08	67.99	128.20
13	33.08	1000	1300	2300	39.3	69.53	138.89
14	33.75	1000	1400	2400	41.48	71.11	149.25
15	34.37	1000	1500	2500	43.64	72.74	161.3

1. We know that MC = ATC , when ATC is at its minimum level. So, approximate Q=26.13 units, marginal cost of production equal to the average total cost.

2. Profit maximizing condition is P=MC. If P=$60 , then the firm's optimal level of production is 24.48 units.

3. Firm's profit = TR-TC =(P)(Q)- (TC)= $(60)(24.48)-1500 = -$31.2 (i.e loss).

4. If L=8 , then price of the good is $83.3 i.e equal to MC.

5. If L=8 , then optimal output is 28.71 units . Therefore,Profit = TR-TC = (83.3)(28.71)- (1800)= $591.54.

6. If L=9 , then price of the good is $93.46 which is equal to MC .

7. If L=9 , then optimal output is 29.78 units. Therefore, profit = TR-TC= (93.46)(29.78)-1900 = $883.23.