Question

A profit-maximizing firm in a perfectly competitive market operates in the short run with total fixed costs of D $2,250 and total variable costs (TVC) as is below. The firm can only produce integer amounts of output (Q):

Q (Output)	TVC (Total Variable Cost
0	0.00
1	2,500
2	4,000
3	5,000
4	6,200
5	7,600
6	9,360
7	11,500
8	13,860
9	16,450
10	19,200
11	22,310

3a. How much output should the firm produce if it can sell all the output it produces at a price of E $2,400 per unit? Show your work!

3b. What are firm profits (or losses) when price per unit is E $2,400? Show your work!

Answer 1

We know that Total Cost(TC) = Total Fixed Cost(TFC) + Total Variable Cost(TVC)

Marginal Cost(MCn) = TCn - TCn-1

Total Revenue(TR) = P x Q

Marginal Revenue(MRn) = TRn - TRn-1

Given: Price = $2400

3a)

Q(Output)	TVC(in Dollars)	TFC(in Dollars)	TC(in Dollars)	MC	TR	MR
0	0	2250	2250	-	0	-
1	2500	2250	4750	2500	2400	2400
2	4000	2250	6250	1500	4800	2400
3	5000	2250	7250	1000	7200	2400
4	6200	2250	8450	1200	9600	2400
5	7600	2250	9850	1400	12,000	2400
6	9360	2250	11,610	1760	14,400	2400
7	11,500	2250	13,750	2140	16,800	2400
8	13,860	2250	16,110	2360	19,200	2400
9	16,450	2250	18,700	2590	21,600	2400
10	19,200	2250	21,450	2750	24,000	2400
11	22,310	2250	24,560	3110	26,400	2400

For a perfectly competitive firm, the profit maximization condition is given by:

MR = MC

Although, in this case, MR doesn't equal MC at any point.

So, in order to maximize profit, the firm should produce 8 units of output because that is the point till which MR > MC. After this output, marginal cost becomes greater than marginal revenue.

3b)

Profit = Total Revenue(TR) - Total Cost(TC)

So, for each output, the firm's profits(losses) are as follows:

Q(Output)	TVC(in Dollars)	TFC(in Dollars)	TC(in Dollars)	MC	TR	MR	Profit
0	0	2250	2250	-	0	-	-2250
1	2500	2250	4750	2500	2400	2400	-2350
2	4000	2250	6250	1500	4800	2400	-1450
3	5000	2250	7250	1000	7200	2400	-50
4	6200	2250	8450	1200	9600	2400	1150
5	7600	2250	9850	1400	12,000	2400	2150
6	9360	2250	11,610	1760	14,400	2400	2790
7	11,500	2250	13,750	2140	16,800	2400	3050
8	13,860	2250	16,110	2360	19,200	2400	3090
9	16,450	2250	18,700	2590	21,600	2400	2900
10	19,200	2250	21,450	2750	24,000	2400	2550
11	22,310	2250	24,560	3110	26,400	2400	1840

From the above table also,we can see that the profit is maximized at Q = 8 and the profit is $3090.