Download ECNS 251 Spring 2013 Homework 6 Answer Key 1. a. Figure 5

ECNS 251
Spring 2013
Homework 6 Answer Key
1. a. Figure 5 shows the typical firm in the industry, with average total cost ATC1, marginal
cost MC1, and price P1.
b. The new process reduces Hi-Tech’s marginal cost to MC2 and its average total cost to
ATC2, but the price remains at P1 because other firms cannot use the new process. Thus
Hi-Tech earns positive profits.
c.
When the patent expires and other firms are free to use the technology, all firms’
average-total-cost curves decline to ATC2, so the market price falls to P3 and firms earn
zero profit.
2. a. Profit is equal to (P – ATC) × Q. Price is equal to AR. Therefore, profit is ($10 – $8) ×
100 = $200.
b. For firms in perfect competition, marginal revenue and average revenue are equal. Since
profit maximization also implies that marginal revenue is equal to marginal cost, marginal
cost must be $10.
c.
Average fixed cost is equal to AFC /Q which is $200/100 = $2. Since average variable
cost is equal to average total cost minus average fixed cost, AVC = $8 − $2 = $6.
d. Since average total cost is less than marginal cost, average total cost must be rising.
Therefore, the efficient scale must occur at an output level less than 100.
ECNS 251
Spring 2013
3. a. The table below shows TC and ATC for a typical firm:
Q
TC
ATC
1
2
3
4
5
6
11
15
21
29
39
51
11
7.5
7
7.25
7.8
8.5
b. At a price of $11, quantity demanded is 200. Since marginal revenue is $11, each firm
will choose to produce 5 pies. Therefore, there will be 40 firms (= 200/5). Each producer
will earn total revenue of $55 ($11  5), total cost is $39, so profit is $16.
c.
The market is not in long-run equilibrium because firms are earning positive economic
profit. Firms will want to enter the market.
d. With free entry and exit, long-run equilibrium will occur when price is equal to minimum
average total cost ($7). At that price, 600 pies are demanded. Each firm will only
produce 3 pies, meaning that there will be 200 firms in the market.
4. a. Figure 9 shows the current equilibrium in the market for pretzels. The supply curve, S1,
intersects the demand curve at price P1. Each stand produces quantity q1 of pretzels, so
the total number of pretzels produced is 1,000 × q1. Stands earn zero profit, because
price is equal to average total cost.
ECNS 251
Spring 2013
b. If the city government restricts the number of pretzel stands to 800, the market supply
curve shifts to S2. The market price rises to P2, and individual firms produce output q2.
Market output is now 800 × q2. Now the price exceeds average total cost, so each firm is
making a positive profit. Without restrictions on the market, this would induce other firms
to enter the market, but they cannot because the government has limited the number of
licenses.
c.
If the city charges a license fee for the licenses, it will have no effect on marginal cost,
so it will not affect the firm's output. It will, however, reduce the firm's profits. As long as
the firm is left with a zero or positive profit, it will continue to operate. Thus, as long as
the market supply curve is unaffected, the price of pretzels will not change.
d. The license fee that brings the most money to the city is equal to (P2 − ATC2) × q2,
which is the amount of each firm's profit.
5. a. The following table shows total revenue and marginal revenue for each price and
quantity sold:
Price
Quantity
24
22
20
18
16
14
10,000
20,000
30,000
40,000
50,000
60,000
Total
Revenue
$240,000
440,000
600,000
720,000
800,000
840,000
Marginal
Revenue
---$20
16
12
8
4
Total
Cost
$50,000
100,000
150,000
200,000
250,000
300,000
Profit
$190,000
340,000
450,000
520,000
550,000
540,000
b. Profits are maximized at a price of $16 and quantity of 50,000. At that point, profit is
$550,000.
c.
As Johnny's agent, you should recommend that he demand $550,000 from them, so he
receives all of the profit (rather than the record company).
6. Larry wants to sell as many drinks as possible without losing money, so he wants to set
quantity where price (demand) equals average total cost, which occurs at quantity QL and
price PL in Figure 6. Curly wants to bring in as much revenue as possible, which occurs where
marginal revenue equals zero, at quantity QC and price PC. Moe wants to maximize profits,
which occurs where marginal cost equals marginal revenue, at quantity QM and price PM.
ECNS 251
Spring 2013
7. a. A monopolist always produces a quantity at which demand is elastic. If the firm produced
a quantity for which demand was inelastic, then if the firm raised its price, quantity
would fall by a smaller percentage than the rise in price, so revenue would increase.
Because costs would decrease at a lower quantity, the firm would have higher revenue
and lower costs, so profit would be higher. Thus the firm should keep raising its price
until profits are maximized, which must happen on an elastic portion of the demand
curve.
b. As Figure 10 shows, another way to see this is to note that on an inelastic portion of the
demand curve, marginal revenue is negative. Increasing quantity requires a greater
percentage reduction in price, so revenue declines. Because a firm maximizes profit
where marginal cost equals marginal revenue, and marginal cost is never negative, the
profit-maximizing quantity can never occur where marginal revenue is negative. Thus, it
can never be on the inelastic portion of the demand curve.
c.
8
Total revenue is maximized where marginal revenue is equal to zero ( QTR on Figure 10).
a. The monopolist would set marginal revenue equal to marginal cost and then plug the profit-
ECNS 251
Spring 2013
maximizing quantity into the demand curve:
10 – 2Q = 1 + Q
9 = 3Q
Q=3
P = 10 – Q = $7
Total revenue = P  Q = ($7)(3) = $21
Total cost = 3 + 3 + 0.5(9) = $10.5
Profit = $21 – $10.5 = $10.5
b. The firm becomes a price taker at a price of $6 and no longer has monopoly power. The
firm will export soccer balls because the world price is greater than the domestic price (in
the absence of monopoly power). As Figure 11 shows, domestic production will rise to 5
soccer balls, domestic consumption will rise to 4, and exports will be 1.
c.
The price actually falls even though Wickham will now export soccer balls. Once trade
begins, the firm no longer has monopoly power and must become a price taker.
However, the world price of $6 is greater than the competitive equilibrium price ($5.50)
so the country exports soccer balls.
d. Yes. The country would still export balls at a world price of $7. The firm is a price taker
and no longer is facing a downward-sloping demand curve. Thus, it is now possible to
sell more without reducing price.