Econ 211
Problem Set 3 Answers
1. We did this one in class.
2. The relevant hiring criterion should be a comparison of the marginal benefits of adding a worker versus the marginal costs of adding a worker. If the MB > MC, then it makes sense to hire the worker. Diminishing returns has nothing to do with this. Diminishing returns simply means that the additional worker is not generating as many marginal benefits as the previous worker.
3. What is the rule for determining the profit maximizing number of cars to sell? Does fixed costs enter into that equation?
4. I'll let you ponder this one.
5. Sunk costs should be ignored. As long as the MB > MC, the project should continue. In this case, the MB of completing the project are the (still) unrealized gains of $15 billion. The MC of completing the project are X and unknown. Thus, as long as the X < $15 billion, the project should continue.
6. Here are the calculations:
b) and c) Average product and marginal product
| Labor | Average Product | Marginal Product |
| 1 | 1 | 1 |
| 2 | 1.5 | 2 |
| 3 | 2 | 3 |
| 4 | 2.5 | 4 |
| 5 | 3 | 5 |
| 6 | 3.5 | 6 |
| 7 | 3.7 | 5 |
| 8 | 3.75 | 4 |
| 9 | 3.67 | 3 |
| 10 | 3.5 | 2 |
d) For output rates just below 30 boats, which is equivalent
to a little less than 8 workers per week, the MP > AP, and the
AP rises.
e) For output rates just above 30 boats, which is equivalent to a
little more than 8 workers per week, the MP < AP, and the AP
falls.
7. Cost figures based on previous question.
| Output | TC | VC | FC | ATC | AFC | AVC | MC |
| 1 | 1400 | 400 | 1000 | 1400 | 1000 | 400 | 400 |
| 3 | 1800 | 800 | 1000 | 600 | 333 | 267 | 200 |
| 6 | 2200 | 1200 | 1000 | 367 | 167 | 200 | 133 |
| 10 | 2600 | 1600 | 1000 | 260 | 100 | 160 | 100 |
| 15 | 3000 | 2000 | 1000 | 200 | 67 | 133 | 80 |
| 21 | 3400 | 2400 | 1000 | 162 | 48 | 114 | 67 |
| 26 | 3800 | 2800 | 1000 | 146 | 38 | 108 | 80 |
| 30 | 4200 | 3200 | 1000 | 140 | 33 | 107 | 100 |
| 33 | 4600 | 3600 | 1000 | 140 | 30 | 109 | 133 |
| 35 | 5000 | 4000 | 1000 | 143 | 28 | 114 | 200 |
I'll leave it to you to recalculate the costs after FC increase to 1100. You should note, however, that MC will be unaffected by this change.
8. American Production Company.
| Output | TC | ATC | MC |
| 50 | $50,000 | $1000 | -- |
| 51 | $52,000 | $1019 | $2000 |
| 52 | $53,976 | $1038 | $1976 |
| 53 | $58,976 | $1112 | $5000 |
9. Think Ross Perot and diminishing returns.
10. We did this one in class.
11. No diagrams here--you're on your own.
12. We did this one in class.
13. We did this one in class.
14. We did this one in class.
15. We did this one in class.
16. Short run curves get their shapes from the productivity curves (which are governed by the concept of diminishing returns in the short run). The long run average cost curve gets its shape from the concept of economies of scale (which involves a proportionate change in all resources).
17. Think about the following string of equalities: P = MR = MC = ATC.
18. This is similar to #23 below except that it refers to an decreasing cost industry.
19. a) The firm will produce where P = MC. Since P = 10 cents, MC is 10 cents at approximately 80 pages per hour. (b) TR is $8 per hour. TC is about $5.6 per hour. Profits are about $2.40 per hour.
20. a) profit maximizing output is 4 pizzas per hour.
b) The shutdown price is equal to the minimum AVC which, in this
case, is $10.
c) The firm's supply curve is that part of their MC which lies
above the shutdown point. In this case, Pat's supply curve
consists of the following price/quantity pairs: P= 11, Q =3;
P=13, Q=4; P=15, Q=5.
d) Pat leaves the pizza industry if P < ATC. Thus Pat will not
operate if P is lower than the lowest ATC which, in this case, is
$13.50.
e) Entry occurs if P > ATC. Thus, any price above $13.50 will
attract entry.
f) The long run equilibrium price is $13.50.
21. a) The market price of a cassette is determined by the intersection of the market demand and the market supply curves. The market demand is given in the problem. The market supply curve equals the sum of the individual supply curves for the 1000 firms in the industry. Each firm's supply curve is its MC curve above the AVC curve. From the cost structure of the firms in the market, the firm and market supply curves are as follows:
| Price (equals MC) | Firm Supply Curve | Market Supply Curve (1000 x firm supply curve) |
| 7.00 | 250 | 250,000 |
| 7.65 | 300 | 300,000 |
| 8.40 | 350 | 350,000 |
| 10.00 | 400 | 400,000 |
| 12.40 | 450 | 450,000 |
| 12.70 | 500 | 500,000 |
The market supply curve equals 1000 times the individual
supply curve. Combining the market supply curve with the market
demand curve, the equilibrium price is $8.40.
b) Equilibrium industry output is 350,000 cassettes per week.
c) Each firm produces 350 cassettes per week.
d) The firm's economic profit is calculated as (P-ATC)(q), which
in this case is (8.40-10.06)(350) = -$581. Each firm is making an
economic loss of $581.
e) The shutdown point is a price of $7 per cassette.
f) Long run equilibrium price is $10.
g) At a price of $10 per cassette, 300,000 cassettes are
demanded, and at $10 per cassette each firm produces 400
cassettes. Hence 750 firms remain in the industry.
22. Think about the difference between accountants and economists in terms of defining profits.
23. We did this one in class (although I didn't exactly refer to the situation as the beer market)..
24. I'll leave this one for you to ponder..
25. Price discrimination could be beneficial to the economy in the sense that it encourages the monopolist to eliminate dead weight loss by selling to more customers. The three conditions are in your notes.
26. Price discrimination:
a) those who do not own a boat
b) adults
c) business travelers
d) rich
27. I'll leave this one for you to ponder.
28. If you treat the Mafia as a crime monopolist, then we would predict that the Mafia has incentives to restrict the amount of crime in order secure greater profits. In other words, the Mafia may be able to erect entry barriers to prevent small-time hoods from engaging in too much criminal behavior.
29. 10 units at a price of $8 for $30 in profit.
30. Two words: Entry barriers.
31. We will do this one in class.
32. Since MC > MR, the monopolist should cut output (and thereby raise its price).
33. The profit maximizing output (where MR = MC) is Q = 50 and the price is P = 55. The firm earns profits of $1450 at this output/price combination. The lowest price the firm would be willing to operate at is $17.50.
34. Miata.
| Q | P | TR | MR | MC | FC | VC | TC | PROFIT |
| 1 | 50000 | 50000 | 50000 | 10000 | 50000 | 10000 | 60000 | -10000 |
| 2 | 40000 | 80000 | 30000 | 10000 | 50000 | 20000 | 70000 | 10000 |
| 3 | 30000 | 90000 | 10000 | 10000 | 50000 | 30000 | 80000 | 10000 |
| 4 | 20000 | 80000 | -10000 | 10000 | 50000 | 40000 | 90000 | -10000 |
| 5 | 10000 | 50000 | -30000 | 10000 | 50000 | 50000 | 100000 | -50000 |
b) A single-price monopolist maximizes profit by selling Q = 3
(where MR = MC) at a P = $30,000. Profits are $10,000.
c) A price discriminating monopolist has an incentive to sell to
all those who are willing to pay above the MC. Thus, the firm
will sell to all 5 buyers (that last buyer will be indifferent)
at the maximum price each is willing to pay. Thus TR=$150,000 and
profits will be $50,000.
35. Parkin #1:
a) Q = 150 newspapers per day.
b) P = 70 cents
c) TR = $105
d) Demand is price elastic. Only when the demand is price elastic
is the MR > 0. Because MC is always greater than zero, in
order for MC to equal MR, the demand must be elastic.
Parkin #2:
a) Q=250
b) CS = $22.50
c) DWL = $10
36. Parkin #5:
a) Q = 2 and P = 6
b) MC = 4
c) MR = 4
d) Profit = 5
e) Minnie's is not efficient since they are producing at a point
where P > MC. This means that society would be better off if
output is expanded to a point where P = MC (in which case the DWL
is eliminated).
Parkin #6:
a) Q = 2
b) TR = 14
c) Profit = 7
d) Yes.