Question

1. Let's say that you are looking at a table with output and cost data for a firm and you observe the following: At a quantity of 10 units, the firm's marginal cost and marginal revenue both equal $.75. At a quantity of 18 units, the firm's marginal cost reaches its lowest point at $.35. At a quantity of 26 units, the firm's average total cost reaches a minimum of $.50. At a quantity of 28 units, the firm's marginal cost and marginal revenue also both equal $.75. At a quantity of 30 units, the firm's marginal cost is $1.00 and its marginal revenue is $.65. If this firm wants to maximize its profits, which quantity should it produce?

2.

Consider the following table with a monopolist's cost and revenue data. The profit-maximizing output is _____, and the price which the monopolist will charge at this output is _____ (Hint: find the marginal revenue values):

Output	Price	TR	TC	MC
0	$8.00	$0	$150	-
50	7	350	350	4
100	6	600	530	3.6
150	5	750	675	2.9
200	4	800	800	2.5
250	3	750	950	3
300	2	600	1,125	3.5

3. Let's say that you are looking at a table with output and cost data for a firm and you observe the following: At a quantity of 12 units, the firm's marginal cost and marginal revenue both equal $.75. At a quantity of 30 units, the firm's marginal cost and marginal revenue also both equal $.75. At a quantity of 22 units, the firm's marginal cost reaches its lowest point at $.35. At a quantity of 28 units, the firm's average total cost reaches a minimum of $.50. If this firm wants to maximize its profits, which quantity should it produce?

4.

Output	Price	Marginal Cost
400	10	0.50
500	9	1.50
600	8	2.50
700	7	3.50
800	6	5.50
900	5	6.50

Please consider the above data for a monopolist. At which output level does the monopolist maximize its profits (or minimize its losses)?

Answer 1

Question no. 1.

At a quantity of 10 units, the firm's marginal cost and marginal revenue both equal $.75. At a quantity of 18 units, the firm's marginal cost reaches its lowest point at $.35. At a quantity of 26 units, the firm's average total cost reaches a minimum of $.50. At a quantity of 28 units, the firm's marginal cost and marginal revenue also both equal $.75. At a quantity of 30 units, the firm's marginal cost is $1.00 and its marginal revenue is $.65.

Q	MR	MC	AC
10	0.75	0.75
18		0.35
26			0.50
28	0.75	0.75
30	0.65	1.00

The firm should produce at a point where MR=MC and the MC is rising. Thus if this firm wants to maximize its profits it should produce 28 units of output.

Question no. 2.

Output	Price	TR	MR	TC	MC
0	8.0	0.0		$150	-
50	7.0	350.0	7.0	350.0	4.0
100	6.0	600.0	5.0	530.0	3.6
150	5.0	750.0	3.0	675.0	2.9
200	4.0	800.0	1.0	800.0	2.5
250	3.0	750.0	-1.0	950.0	3.0
300	2.0	600.0	-3.0	1125.0	3.5

The firm maximises output at MR=MC or MR being just greater than MC. The profit max output is 150 and Price charged by the monopolist is $5.

Total Revenue = Price*Quantity

MR = Change in TR/Change in Q (MR represents marginal revenue)

Question no. 3.

Q	MR	MC	AC
12.00	0.75	0.75
30.00	0.75	0.75
22.00		0.35	0.50
28.00			0.50

The firm should produce at a point where MR=MC and the MC is rising (note that at after Q=12, the marginal cost MC has fallen to minimum 0.35 so Q=12 cannot be the correct option. Thus if this firm wants to maximize its profits it should produce 30 units of output.

Question no. 4.

Output	Price	Marginal Cost	TR	MR
400	10	0.5	4000
500	9	1.5	4500	5
600	8	2.5	4800	3
700	7	3.5	4900	1
800	6	5.5	4800	-1
900	5	6.5	4500	-3

Total Revenue = Price*Quantity

MR = Change in TR/Change in Q (MR represents marginal revenue)

The firm maximises output at MR=MC or MR being just greater than MC. The profit max output is 600 and Price charged by the monopolist is $8.