Question

The following table provides incomplete information on the costs of producing diagnostic imaging tests. It uses two inputs to produce its outputs: capital and labour. The fixed capital costs reflect the monthly leasing cost for the diagnostic imaging machine and the variable labour costs reflects the wages and hours worked by staff.

Assume that the firm is operating in a perfectly competitive market. Also assume that its fixed costs are sunk costs (i.e. it cannot recuperate these costs even if it decides to leave the market.

Quantity produced	Fixed cost	Variable cost	Total cost	Average total cost	Average variable costs	Marginal cost
0	25	0
1	25	35
2	25	60
3	25	80
4	25	95
5	25	105
6	25	125
7	25	155
8	25	186
9	25	225
10	25	280

1. Complete all empty cells in the table above

2. Provide a brief explanation of why the marginal costs could exhibit the pattern you observe in part (a).

3. Add three columns to the table above headed: (i) marginal revenue; (ii) total revenue; and (iii) profit. If the market price was $40, complete all new columns in the table over the output range of 0 to 10

4. If the market price was $40, what would be the optimum level of production for the firm? Why?

Answer 1

a.Ans:

Quantity produced	Fixed cost	Variable cost	Total cost	Average total cost	Average variable costs	Marginal cost
0	25	0	25	--	--	--
1	25	35	60	60	35	35
2	25	60	85	42.5	30	25
3	25	80	105	35	26.67	20
4	25	95	120	30	23.75	15
5	25	105	130	26	21	10
6	25	125	150	25	20.83	20
7	25	155	180	25.71	22.14	30
8	25	186	211	26.38	23.25	31
9	25	225	250	27.78	25	39
10	25	280	305	30.5	28	55

Explanation:

Total Cost = Fixed Cost + Variable Cost

Average Total Cost = Total cost / Quantity of output

Average Variable Cost = Total Variable cost / Quantity of output

Marginal cost = Change in total cost / Change in Quantity of output

b. Ans: Initially , marginal cost decreases due to economies of scale and then increases due to diseconomies of scale in the production process.

c. Ans:

Quantity produced	Fixed cost	Variable cost	Total cost	Average total cost	Average variable costs	Marginal cost	Marginal Revenue	Total Revenue	Profit
0	25	0	25	--	--	--	--	0	-25
1	25	35	60	60	35	35	40	40	-20
2	25	60	85	42.5	30	25	40	80	-5
3	25	80	105	35	26.67	20	40	120	15
4	25	95	120	30	23.75	15	40	160	40
5	25	105	130	26	21	10	40	200	70
6	25	125	150	25	20.83	20	40	240	90
7	25	155	180	25.71	22.14	30	40	280	100
8	25	186	211	26.38	23.25	31	40	320	109
9	25	225	250	27.78	25	39	40	360	110
10	25	280	305	30.5	28	55	40	400	95

Explanation:

Total Revenue = Price * Quantity of output

Marginal Revenue = Change in total revenue / Change in Quantity of output

Profit = Total Revenue - Total Cost

d. Ans: The optimum level of production for the firm would be 9 units. Because at this level of output, price is greater than marginal cos. After this production level , marginal cost becomes greater than the price.

Explanation:

Under perfect competition , the profit maximization condition is where price equals marginal cost ( P = MC) or price is greater than marginal cost ( P > MC).