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Solutions to Problems
Chapter 12
1a. Minnie's total revenue schedule is listed in table 1.
1b. Minnie's marginal revenue schedule lists the change in revenue that results from increasing the quantity sold by 1 bottle. The
marginal revenue schedule is shown in table 1.
1c. The price elasticity of demand for Minnie's Mineral Springs is equal to 1 when the price is $5 a bottle and marginal revenue
equals 0. When marginal revenue equals 0, a change in price does not change total revenue because the % change in price
equals the % change in quantity demanded and price elasticity of demand equals one. This is the mid-point of the demand
curve (see figure 1).
Table 1  Problems 1&3 Minnie’s Mineral Springs
Price
$
10
Quantity
Demanded
Total
Revenue
PxQ
0
Marginal
Revenue
TR/Q
$0
Total
Cost
$1
$8
8
1
8
2
3
7
12
4
5
6
13
-4
2
5
4
0
4
8
8
21
-8
TR  TC
$1
3
12
Profit
$2
4
6
Marginal
Cost
TC/Q
1
13
10
0
5
0
31
31
3a. The marginal cost of increasing the quantity from 1 bottle to 2 bottles is $4 a bottle ($7 minus $3). That is, the marginal cost
of the 1.5 bottles is $4 a bottle. The marginal revenue of increasing the quantity sold from 1 bottle to 2 bottles is $4 ($12
minus $8). So the marginal revenue from 1.5 bottles is $4 a bottle. Profit is maximized when the quantity produced makes
the marginal cost equal to marginal revenue (see table 1).
(i)
Minnie's profit-maximizing output is 1.5 bottles.
(ii). Minnie's profit-maximizing price is $7 a bottle.
The profit-maximizing price is the highest price that Minnie's can sell the profit-maximizing output of 1.5 bottles.
Minnie's can sell 1 bottle for $8 and 2 bottles for $6, so it can sell 1.5 bottles for $7 a bottle.
(iii) Minnie's marginal cost is $4 a bottle.
(iv). Minnie's marginal revenue is $4 a bottle.
(v) Minnie's economic profit is $5.50 (see figure 1).
Economic profit equals total revenue minus total cost. Total revenue equals price ($7 a bottle) multiplied by quantity
(1.5 bottles), which is $10.50. Total cost of producing 1 bottle is $3 and the total cost of producing 2 bottles is $7, so
the total cost of producing 1.5 bottles is $5. Profit equals $10.50 minus $5, which is $5.50 (see table 1).
3b. Minnie's is inefficient. Minnie's charges a price of $7 a bottle, so consumers get a marginal benefit of $7 a bottle. Minnie's
marginal cost is $4 a bottle. That is, the marginal benefit of $7 a bottle exceeds Minnie's marginal cost. There is a DWL
shown in figure 1.
Figure 1
5a. The profit-maximizing output is 150 newspapers a day.
Profit is maximized when the firm produces the output at which marginal cost equals marginal revenue which is at 150
newspapers a day in figure 3.
5b. The price charged is 70 cents a paper.
The highest price that the publisher can sell 150 newspapers a day is read from the demand curve in figure 3.
5c. The daily total revenue is $105 (150 papers at 70 cents each).
5d. Demand is elastic.
Along a straight-line demand curve, demand is elastic at all prices above the midpoint of the demand curve. The price at the
midpoint is 50 cents. So at 70 cents a paper, demand is elastic.
7a. The efficient quantity is 250 newspapers—the quantity that makes marginal benefit (price) equal to marginal cost. With 250
newspapers available, people are willing to pay 50 cents for a paper. To produce 250 newspapers, the publisher incurs a
marginal cost of 50 cents a paper.
7b. The consumer surplus is $22.50 a day.
Consumer surplus is the area under the demand curve above the price. The price is 70 cents, so consumer surplus equals
(100 cents minus 70 cents) multiplied by 150/2 papers a day, which is $22.50 a day (see figure 3).
7c. The deadweight loss is $15 a day.
Deadweight loss arises because the publisher does not produce the efficient quantity. Output is restricted to 150, and the
price is increased to 70 cents. The deadweight loss equals (70 cents minus 40 cents) multiplied by 100/2 (see figure 3).
9.
The maximum that will be spent on rent seeking is $5.50 a day—an amount equal to Minnie's economic profit. The total
social cost equals the deadweight loss plus the amount spent on rent seeking. In figure 1 the efficient output is 2.25 bottles.
The deadweight loss is:
($7$4) x (2.25 1.5) = $1.125.
The loss to society is:
$5.50 + $1.125 = $6.625.
11a. The firm will produce 2 cubic feet a day and sell it for 6 cents a cubic foot. Deadweight loss will be 4 cents a day.
The profit- maximizing output is 2 cubic metres at which marginal revenue equals marginal cost. The price charged is the
highest that people will pay for 2 cubic metres a day, which is 6 cents a cubic metre.
The efficient output is 4 cubic metres, at which marginal cost equals price (marginal benefit). So the deadweight loss is
(42) x (6c2c)/2 = 4 cents a day (see figure 5).
11b. The firm will produce 3 cubic feet a day and charge 4 cents a cubic foot. Deadweight loss is 1 cent a day.
If the firm is regulated to earn only normal profit, it produces the output at which price equals average total cost—at the
intersection of the demand curve and the ATC curve (see figure 5).
11c. The firm will produce 4 cubic metres a day and charge 2 cents a cubic metre. There is no deadweight loss.
If the firm is regulated to be efficient, it will produce the quantity at which price (marginal benefit) equals marginal cost—at
the intersection of the demand curve and the marginal cost curve (see figure 5).
Figure 5
Figure 6