4 The data below is for a firm in a perfectly competitive ma

4. The data below is for a firm in a perfectly competitive market. Complete the following table by calculating Average Cost (AC) and Marginal Cost (MC) for the various levels of output. (5 marks) Output (Q Total Marginal Cost (MC) Total Cost Average Cost (AC) (AR-MR) Revenue (TR) $45 72 87 $30 30 60 120 150 180 210 240 270 94.50 105 135 180 240 330 4 30 (a) At what levels of output will the firm break even? (2 marks) (b) What level of output should this firm operate in order to maximize their profits? (I mark)

Solution

Working notes:

(1) AC = TC/Q

(2) MC = Change in TC / Change in Q

(a) In breakeven, TR = TC, which holds true when Q = 3 and TR = TC = $90

(b) Profit is maximized when P = AR = MC, which holds true when Q = 6 and P = AR = MC = $30

Q	AR	TR	TC	AC	MC
0	30	0	45
1	30	30	72	72	27
2	30	60	87	43.5	15
3	30	90	90	30	3
4	30	120	94.5	23.625	4.5
5	30	150	105	21	10.5
6	30	180	135	22.5	30
7	30	210	10	1.43	-125
8	30	240	240	30	230
9	30	270	330	36.67	90