2. $ CHAPTER 10 - MONOPOLY. Answers to select-numbered problems: MC ATC P * Quantity

Transcription

1 CHAPTER 10 - MONOPOLY Answers to select-numbered problems: 2. $ P * MC ATC MR D Q* Quantity The monopolist produces where marginal cost equals marginal revenue and charges P* dollars per unit. It makes a profit of zero since the ATC associated with Q* equals P*. 4. If the airline charges all the students $40 per ticket, its marginal revenue from the last student ticket sold would be significantly lower than $40, i.e. it would be losing money. In particular, with the $40 dollar price, the airline would sell a quantity where the MC curve intersects the demand curve, and at that quantity, the MR curve would be very low (you can extend the MR curve to estimate what it would be). Instead the airline should use MR=MC rule to determine the price of the student ticket, which leads us to the price of $70 per ticket. 6. a. You will tutor two students, and will charge them each $35, for total weekly earnings of $70. b. You will tutor four students, charging each student the highest price they are willing to pay. That is, you will charge prices of $40, $35, $27, and $26. Your total weekly earnings will be $128. c. No, because your total revenue ($70) from two students will be less than your total cost ($75). Note that the total cost per week is a sum of $25*2 (the cost of your time and effort for tutoring 2 students per week) and $25 (the cost of the license per week), totaling $75. d. Yes, because your total revenue ($128) from these four students will be more than your total cost ($125). Note that the total cost per week is a sum of $25*4 (the cost of your time and effort) and $25 (the cost of the license), totaling $125.

2 8. a. Output Price Total Marginal Total Marginal Profit $5.50 $ $5.50 $5.50 $3.50 $2.00 $5.30 $ $5.40 $10.80 $5.45 $5.35 $5.10 $ $5.30 $15.90 $6.45 $9.45 $4.90 $ $5.20 $20.80 $6.90 $13.90 $4.70 $ $5.10 $25.50 $8.90 $16.60 $4.80 $ = Q* $5.05 $30.30 $13.40 $16.90 $4.00 $ $4.90 $34.30 $20.40 $13.90 b. The firm will produce 6 units of output and will earn a profit of $ Output Price Total Marginal Total Marginal Profit $5.50 $ $5.50 $5.50 $4.50 $1.00 $5.30 $ $5.40 $10.80 $7.45 $3.35 $5.10 $ $5.30 $15.90 $9.45 $6.45 $4.90 $ $5.20 $20.80 $10.90 $9.90 $4.70 $ = Q* $5.10 $25.50 $13.90 $11.60 $4.80 $ $5.05 $30.30 $19.40 $10.90 $4.00 $ $4.90 $34.30 $27.40 $6.90 The firm will produce 5 units of output and will earn a profit of $11.60.

3 c. Output Price Total Marginal Total Marginal Profit $5.50 $ $5.50 $5.50 $3.10 $2.40 $5.30 $ $5.40 $10.80 $4.65 $6.15 $5.10 $ $5.30 $15.90 $5.25 $10.65 $4.90 $ $5.20 $20.80 $5.30 $15.50 $4.70 $ $5.10 $25.50 $6.90 $18.60 $4.80 $ = Q* $5.05 $30.30 $11.00 $19.30 $4.00 $ $4.90 $34.30 $17.60 $16.70 The firm will produce 6 units of output, as in part a, but will earn a profit of $ a. As a monopolist, Patty will maximize her profit by producing the output at which MC = MR. We know that MC = $0.50 per swimmer. From Table 1, admitting the sixth swimmer has a MR = $2, so it makes sense to admit that person. What about the seventh? Again, from the table, we see that MR = $0. With a marginal cost of $0.50, Patty would suffer a decline in profit by admitting that person. So, Q = 6 is the profit-maximizing output level. At Q = 6, the admission fee would be $7 per swimmer. Table 1 indicates that TR = $42. TC = TFC + TVC = $25 + (6 x $0.50) = $28. So, profit = $42 $28 = $14. (Note that at Q = 7, TR = $42, TC = $25 + (7 x $0.50) = $ so profit would be be lower at $13.50). b. The excise tax would affect Patty s marginal cost raising it by $2 to $2.50 per swimmer. As in part (a), she maximizes profit by setting MC = MR. This would require an output of 5 swimmers per day (because a sixth would lower MR to $2, which is less than marginal cost with the excise tax). With Q = 5, she will charge $8 per swimmer, resulting in a total revenue of TR = $40 per day. Total cost is TC = TFC + TVC = $25 + (5 x $2.50) = $ Profit would be $ = $2.50 per day.

4 c. The swimming tax would raise Patty s fixed costs to FC = $25 + $2 = $27 per day. It would not affect marginal cost, and therefore would not affect her optimal choice of output. Her profit-maximizing output level would be Q = 5 and the corresponding admission fee would be $8/swimmer. What about profit? TR would still be $40 per day. But now, TC = TFC + TVC = $27 + (5 x $2.50) = $ Her profit would now fall to $0.50 per day. d. As in part (c), marginal cost would not be affected, but fixed cost would increase to $25 + $5 = $30 per day. If she chose the profit-maximizing output level, she would admit 5 swimmers per day and charge them $8 each for admission. Profit would now be determined by comparing TR = $40 with TC = TFC + TVC = $30 + (5 x $2.50) = $ She would suffer a loss of $2.50 per day. e. In the short run, Patty will continue to operate because her TR of $40 per day exceeds her TVC of $30 per day. Also, from a profit perspective, It is better for her to lose $2.50 per day than to shut down and suffer a daily loss equal to her TFC of $30 per day. In the long run, however, she will be better off leaving this industry. f. The first statement is true. The excise tax was $2 per swimmer, but it resulted in Patty raising her admission fee from $7 to $8 per person. The tax of $2 was shared between consumers (who paid $1 more per admission) and the producer (whose marginal revenue net of the tax fell from $7 to $6). The second statement is not true as stated. A fixed tax has no effect on monopoly unless it is so large as to create a loss which causes the firm to shut down in the short run or exit in the long run. MORE CHALLENGING QUESTIONS 12. a. With MC = $5, Patty will determine her profit-maximizing output rate by setting MC = MR. From the table in the chapter, we can see that she will admit Q = 4 swimmers per day, charging each of them a $9 admission fee. Her profit would be TR TFC TVC = $9*4 $24 (4 x $5) = $36 $44 = a loss of $8 per day. To determine whether she should shut down, we can use the shutdown rule, comparing her TR = $36 to her TVC = $20. Because TR > TVC, she will continue to operate in the short run, because she would be covering all her variable cost and part of her fixed cost. Shutting down would entail a larger loss equal to her fixed cost of $24 per day. In the long run, however, she will leave this industry. b. The demand curve provides information about potential swimmers willingness to pay for admission. Specifically, we can see that one swimmer is willing to pay as much as $12 to swim. A second swimmer is willing to pay $11, a third is willing to pay $10 down to eight persons willing to pay $5, but no more.

5 Using this information, and assuming that Patty can determine which swimmers are willing to pay at least $9 per day and which are willing to pay $5 per day (but not $9), she can adjust her pricing accordingly. She can charge $9 to the first 4 swimmers and $5 per day to the next 4 swimmers. In this case, she would admit Q = 8 swimmers. Under this pricing scheme, her TR = (4 x $9) + (4 x $5) = $ = $56. TC = TFC + TVC = $24 + (8 x $5) = $64. Her loss would be $8 per day, the same as in part (a). Now we see that Patty would be indifferent between admitting 8 swimmers, with price discrimination into two groups of $9 and $5, and admitting 4 swimmers with a single price of $9. Assuming that she chooses the higher output level, her profit-maximizing output is Q=8 swimmers. As in part (a) she will continue to operate in the short run, but leave the industry as soon as she can. c. By analogy to the reasoning in part (b), Patty would charge a price of $10 to the first 3 swimmers, $9 to the next customer, and $5 to another 4 swimmers. She would admit a total of 8 swimmers per day, thereby generating TR = (3 x $10) + (1 x $9) + (4 x $5) = $30 + $9 + $20 = $59. TC would still be $64, so Patty would now lose $5 per day. She will continue to operate in the short run, but leave the industry in the long run. d. Under perfect price discrimination, Patty will charge each swimmer the maximum amount he or she would be willing to pay. To determine how many swimmers to admit, she would look for the quantity at which a horizontal MC = $5 curve crosses the demand curve, i.e. where MR=MC. That would be Q = 8 swimmers per day. At Q =8, Patty s total daily cost would still be $64 per day. But now, her TR = $12 + $11 + $10 + $9 + $8 + $7 + $6 + $5 = $68 per day, and her profit is $4 per day. You may notice Patty is actually indifferent between choosing Q = 7 or Q = 8. If she chooses Q = 7, her TR = $12 + $11 + $10 + $9 + $8 + $7 + $6 = $63, her TC = $24 + 7*$5 = $59 and her profit is again $4 per day. The question previously asked us to assume that, if indifferent, Patty would choose the higher output level, so the final answer is Q=8 If Patty can practice perfect price discrimination, she can earn a profit of $4 per day and she will be happy to continue operating in both the short run and the long run.