Question

Table refer to a monopolist demand and cost schedules.

Quantity Demanded

0

1

3

4

5

6

Demand Price

20

18

16

14

12

10

8

Quantity Supplied

0

1

2

3

4

5

6

Total Cost

10

14

20

30

42

56

72

NB. Whole table

Derive the marginal revenue and marginal Cost Schedules.

Determine the monopolists profit maximizing price, quantity and economic profits.

Why is this position an equilibrium position for the monopolist.

Answer 1

Solution:

Marginal revenue is the additional revenue earned by increasing quantity sold by a single unit. Similarly, marginal cost is the additional cost incurred when increased production by a single unit. Then, the required schedules can be derived using the given information as follows:

Quantity, Q	Price, P	Total cost, TC	Total revenue, TR = P*Q	Marginal revenue, MR	Marginal cost, MC	Profit = TR - TC
0	20	10	0*20 = 0	-	-	0 - 10 = -10
1	18	14	1*18 = 18	18 - 0 = 18	14 - 10 = 4	18 - 14 = 4
2	16	20	2*16 = 32	32 - 18 = 14	20 - 14 = 6	32 - 20 = 12
3	14	30	3*14 = 42	42 - 32 = 10	30 - 20 = 10	42 - 30 = 12
4	12	42	4*12 = 48	48 - 42 = 6	42 - 30 = 12	48 - 42 = 6
5	10	56	5*10 = 50	50 - 48 = 2	56 - 42 = 14	50 - 56 = -6
6	8	72	6*8 = 48	48 - 50 = -2	72 - 56 = 16	48 - 72 = -24

For the monopolists, we can clearly see from the above table that maximum profit is $12, which is generated at price of $14 per unit and quantity of 3 units.

For a monopolist, the optimal equilibrium position occurs where it's marginal cost equals the marginal benefit. Using the above table, we can see that this occurs at quantity level of 3 units (where MC = MR = 10). So, this position is the equilibrium position for the monopolist (notice how below this point there is a possibility to gain a higher profit, and beyond this level, the profits are reduced).