Question

Output	Price	Marginal Cost
100	7.50	0.50
200	7	1.50
300	6.50	2.50
400	6	3.50
500	5.50	5.50
600	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)?

  

At an output of 500

   

At an output of 400

   

At an output of 300

   

At an output of 200

   

At an output of 600

Part b:

Output	Price	TR	MR	TC	MC
0	$18	$0	-	$400	-
100	17	1,700	$17	1,900	$15
200	16	3,200	15	2,900	10
300	15	4,500	13	3,500	6
400	14	5,600	11	4,000	5
500	13	6,500	9	4,600	6
600	12	7,200	7	5,350	7.50
700	11	7,700	5	6,150	8
800	10	8,000	3	7,300	13
900	9	8,100	1	9,300	20

Please consider the above table with cost and revenue data for a monopoly firm. The above monopolist will maximize profits at output:

  

500

   

200

   

400

   

600

   

700

Answer 1

The monopolist would maximize the profit where the MR is equal to MC. The MR will be in the table as below.

Q	P	TR=P.Q	MR=$\dpi{80} \frac{\Delta TR}{\Delta Q}$	MC
100	7.5	750	-	0.5
200	7	1400	6.5	1.5
300	6.5	1950	5.5	2.5
400	6	2400	4.5	3.5
500	5.5	2750	3.5	4.5
600	5	3000	2.5	5.5

Here, the profit maximization would be where Q=400. At 500 production level, the marginal cost to produce is greater than MR (meaning profit would decrease), and before Q=400, the MR is less than MC (meaning scope for profit exist if output is increased). At Q=400, the profit is maximum.

The correct option is hence

• At an output of 400

The table is as below.

Output	Price	TR	MR	TC	MC	Profit
0	$18	$0	-	$400	-	-$400
100	17	1,700	$17	1,900	$15	-$200
200	16	3,200	15	2,900	10	$300
300	15	4,500	13	3,500	6	$1000
400	14	5,600	11	4,000	5	$1600
500	13	6,500	9	4,600	6	$1900
600	12	7,200	7	5,350	7.50	$1850
700	11	7,700	5	6,150	8	$1550
800	10	8,000	3	7,300	13	$700
900	9	8,100	1	9,300	20	-$1200

The profit would be maximized at Q=500. Before that, the MR is greater than MC (meaning there is scope for profit by increasing output). After Q=500, MR is less than MC (meaning that profit would start to decrease).

The correct option is hence

• 500

Note : If the MR isn't exactly equal to the MC, then the profit maximizing output would be for which the lowest MR that is greater than the MC.