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PROBLEMS 1. In Figure 7.1, a. What is the highest price the monopolist could charge and still sell fish? b. What is total revenue at that highest price? c. What happens to total revenue as price is reduced from its maximum? d. Is marginal revenue positive or negative as price declines? e. At what price is total revenue maximized? LO: 2 AACSB: Analytic a. b. c. d. e. 2. The highest price firms can charge and still sell fish is $13 as shown on the demand curve (corresponding to a quantity of 1). At a price of $13, the firm could sell 1 basket of fish for total revenue of $13. As shown in the table in Figure 7.1, as price is reduced from its maximum level, the total revenue increases. Marginal revenue is still positive as price declines but is decreasing in value. Total revenue is maximized at a price of $7 for total revenue of $49. If price is dropped to $6, total revenue will begin to decline as MR becomes negative. Use Figure 7.2 to answer the following questions: a. What rate of output maximizes total profit? b. What is MR at that rate of output? What is price? c. If output is increased beyond that point, what is the relationship of MC to MR? How will this affect total profits? LO: 2,3 a. b. c. 3. BT: Application AACSB: Analytic BT: Application Profit is maximized where MR=MC which occurs at the output level of 4. The MR is equal to $7 at 4 units of output. Price, the maximum price consumers are willing and able to pay, at 4 units of output is $10. If output is increased beyond 4 units of output, MC>MR. This will cause total profits to fall because the additional costs incurred exceed the additional revenue received for each unit of output produced. Suppose the following data represent the market demand for catfish. Price (per unit) $20 19 18 17 16 15 14 13 12 11 Quantity demanded 10 11 12 13 14 15 16 17 18 19 (Units per day) Total Revenue Marginal Revenue a. b. c. d. Compute total and marginal revenue to complete the table above. At what rate of output is total revenue maximized? At what rate of output is MR less than price? At what rate of output does MR become negative? e. Graph the demand and MR curves. LO: 2 AACSB: Analytic BT: Application a. Price (per unit) Quantity demanded (Units per day) Total Revenue Marginal Revenue b. c. d. e. $20 19 10 11 18 12 17 13 16 14 15 15 14 16 13 17 12 18 11 19 200 209 216 221 224 225 224 221 216 209 ---- 9 7 5 3 1 -1 -3 -5 -7 Total revenue, P x Q, is maximized at 15 units of output. Marginal revenue is less than price at all levels of output. Marginal revenue becomes negative at 16 units of output. Market for Catfish $25 $20 Price per unit $15 $10 Demand $5 $0 ($5) 0 5 10 15 ($10) Quantity (Units per Day) 20 Marginal Revenue 4. Assume that the following marginal costs exist in catfish production: Quantity produced 10 11 12 13 14 15 16 17 18 19 (Units per day) Marginal cost $3 5 7 9 12 15 18 21 25 29 (per unit) a. b. c. d. Graph the MC curve. Use the data on market demand from problem 3 to graph the demand and MR curves on the same graph. At what rate of output is MR=MC? What price will a monopolist charge for that much output? e. If the market were perfectly competitive, what price would prevail? How much output would be produced? LO: 4 AACSB: Analytic BT: Application a and b: $ per unit Market for Catfish $35 $30 $25 $20 $15 $10 $5 $0 ($5) 0 ($10) MC D MR 5 10 15 20 Quantity (Units per day) This chart of numbers helps answer the rest of the question P 20 19 18 17 16 15 14 13 12 11 Q 10 11 12 13 14 15 16 17 18 19 TR 200 209 216 221 224 225 224 221 216 209 MR 9 7 5 3 1 -1 -3 -5 -7 MC 3 5 7 9 12 15 18 21 29 33 c & d. The monopolist produces where MC=MR at 12 units of output and charges a price of $18. e. 5. If the market were competitive, price would equal $15 and quantity would also equal 15. This is the output and price that exist where MC = P=MR. Compute marginal revenues from the following data on market demand: Price per unit Units demanded $50 $46 $42 $35 $3o $22 $14 10 12 14 17 25 50 150 Marginal revenue LO: 2 AACSB: Analytic Price per unit Units demanded Total Revenue Marginal Revenue* $50 10 $500 ---- BT: Application $46 12 $552 26 $42 14 $588 18 $35 17 $595 15.4 $3o 25 $750 14.17 $22 50 $1100 14 $14 150 $2100 10 *Remember that Marginal Revenue is calculated as: (Change in Total Revenue)/(Change in Output) 6. If the price elasticity of demand for oil were 0.1, by how much would the quantity of oil demanded have fallen when OPEC raised the price of oil in 2006? (See Headline, p. 157) LO: 3 AACSB: Analytic BT: Application If the output cut results in a price increase of 1.9% with a price elasticity of 0.1, the quantity demanded would change by 0.19 %. %QD %QD 0.1 %P 1.9% %QD 0.19% Solving for %ΔQd yields the answer of 0.19%. 7. If the on-campus demand for soda is as follows: Price (per can) $0.25 0.50 0.75 1.00 1.25 1.50 1.75 2.00 Quantity demanded 100 90 80 70 60 50 40 30 (per day) and the marginal cost of supplying a soda is 50 cents, what price will students end up paying in. a. A perfectly competitive market? b. A monopolized market? LO: 4 AACSB: Analytic BT: Application The answer to this question is best illustrated using a graph. Market for Soda 2.5 2 Price (per can) 1.5 1 MC 0.5 D 0 -0.5 0 20 40 60 80 100 120 -1 -1.5 MR -2 -2.5 Quantity (per day) In a competitive market, students would pay $0.50 per Pepsi. Remember that in a competitive market, the price equals the MC of the last item sold. In a monopoly market, the monopolist produces at the point where MC=MR. In this case, MC = MR at 50 cans per day, thus students would pay $1.50 per can. 8. LO: 4 According to the Headline on p. 167, how much profit per year might the producers of Cardizem have been making if their average total costs were equal to that of the generic substitute. AACSB: Analytic Known: BT: Application PCardizem: PC=$73/month PGeneric: PG=$32/month Under competition P=ATC (in long run), so let's assume ATC=$32/month (generic price) for the manufacturing of Cardizem. AR-AC=A π $73-$32=$41 for 12 months=$492π over one year. The firm would earn $492/yr. on every individual purchasing Cardizem during this period of time. Total sales/Price per unit = $700,000,000/$73 = 9,589,041 units sold. $492(9.6 million) = $4.7 billion