Problem:

Suppose a monopoly's demand schedule is given by the first two columns of the following table. Its total cost of production is given in the next column.

1. Fill in the Total Revenue column by computing the firm's total revenue associated with each output level.
2. By comparing total cost and total revenue, find the output level that maximizes the firm's profit.
3. What price should the firm set to achieve maximum profit?
4. Complete the final two columns to verify that the same conclusions are reached using the MR = MC rule.

Answer:

1. Total revenue is the product of output and price. For example, if the firm wishes to sell two units, it sets a price of $18 and its total revenue is 2 x $18 = $36. The completed table is shown below.

   Output	Price	Total Cost	Total Revenue	MC	MR
   0	$24	$10	$ 0
   1	21	14	21	$ 4	$21
   2	18	20	36	6	15
   3	15	28	45	8	9
   4	12	38	48	10	3
   5	9	50	45	12	–3



2. At one unit of output, profit is the difference between total revenue and total cost: $21 – $14 = $7. As output is increased from 2 to 5, profit becomes $16, $17, $10, and –$5. Profit is greatest at an output level of 3 units.
3. According to the demand schedule, price must be set at $15 to sell three units.
4. Comparing MR to MC, output should be expanded to produce the third unit, but not the fourth. The marginal revenue of the fourth unit is $7 less than its marginal cost, and will cause profit to decrease.

Problem:

Suppose a price-discriminating monopoly has segregated its market into two submarkets and can prevent resale between the two. Assume that its marginal cost is constant and equal to its average total cost of $8. The firm's demand schedule for the first group is given by the first two columns of the following table.

1. Find the firm's total revenue schedule for this submarket, entering the data into the table where indicated. Use these data to determine the marginal revenue schedule in this submarket.
2. What output level and price will maximize the firm's profit in this submarket?
3. The firm's demand schedule for the second group is given by the first two columns of the following table.

   Output	Price	Total Revenue	MR
   0	$33
   1	30
   2	27
   3	24
   4	21
   5	18
   6	15		>nbsp;
   7	12
   8	9

   Find the firm's total and marginal revenue schedules in this second submarket. What output level and price will maximize the firm's profit in this submarket?
4. Based on these prices, which submarket has the more elastic demand?
5. What is this firm's total economic profit?

Answer:

1. The completed table is shown below.

   Output	Price	Total Revenue	MR
   0	$24	$ 0
   1	22	22	$22
   2	20	40	18
   3	18	54	14
   4	16	64	10
   5	14	70	6
   6	12	72	2
   7	10	70	–2
   8	8	64	–6

2. Using the MR = MC rule, profit is maximized at 4 units of output, implying a price of $16.
3. The completed table is shown below.

   Output	Price	Total Revenue	MR
   0	$33	$ 0
   1	30	30	$ 30
   2	27	54	24
   3	24	72	18
   4	21	84	12
   5	18	90	6
   6	15	90	0
   7	12	84	–6
   8	9	72	–12

   Comparing MR and MC, maximum profits are achieved by selling 4 units in this submarket as well, but at a price of $21 as shown in the demand schedule.
4. Since the price is higher in the second submarket, demand is more elastic in the first submarket.
5. The firm earns revenue of 4x$16 = $64 in the first submarket and revenue of 4x$21 = $84 in the second. Its total revenue is then $64 + $84 = $148. Its total cost is 8x$8 = $64, so its total economic profit is $148 – $64 = $84.