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Problem set 3 49.5 total points Chapter 6 PROBLEMS 1. Use Figure 6.4 to determine: a. How many baskets of fish should be harvested at market prices of i. $17 ii. $13 iii. $9 b. How much total revenue is collected at each price? c. How much profit does the farmer make at each of these prices? (a) (b) (c) (d) 4. 1 pt (i) (ii) (iii) (i) (ii) (iii) (i) (ii) (iii) 5 baskets of fish. 1 pt 4 baskets of fish. 1 pt 3 baskets of fish. 1 pt Total revenue = P x Q = $17 x 5 = $85. 1 pt Total revenue = P x Q = $13 x 4 = $52. 1 pt Total revenue = P x Q = $9 x 3 = $27. 1 pt Total profit = Total revenue – Total cost = $85 - $61 = $24. Total profit = Total revenue – Total cost = $52 - $44 = $8. Total profit = Total revenue – Total cost = $27 - $39 = -$12. Graph the market behavior described in the Headline on p. 144. Price per Laptop S1 S2 P1 P2 D Q1 Q2 Q of Laptops 1 pt 1 pt 1 pt 5. Suppose that the monthly market demand schedule for Frisbees is: Price Quantity Demanded $8 1,000 $7 2,000 $6 4,000 $5 8,000 $4 16,000 $3 32,000 $2 64,000 $1 150,000 Suppose further that the marginal and average costs of Frisbee production for every competitive firm are Rate of Output 100 200 300 400 500 600 Marginal Cost $2.00 $3.00 $4.00 $5.00 $6.00 $7.00 Average Cost 2.00 2.50 3.00 3.50 4.00 4.50 Finally, assume that the equilibrium market price is $6 per Frisbee. a. Draw the cost curves of the typical firm and identify its profit maximizing rate of output and its total profits. b. Draw the market demand curve and identify market equilibrium. c. How many Frisbees are being sold in equilibrium? d. How many (identical) firms are initially producing Frisbees? e. How much profit is the typical firm making? f. In view of the profits being made, more firms will want to get into Frisbee production. In the long run, these new firms will shift the market supply curve to the right and push the price down to average total cost, thereby eliminating profits. At what equilibrium price are all profits eliminated? How many firms will be producing Frisbees at this price? (a) Cost Curves 8 Cost Per Unit 7 MC 6 5 ATC 4 3 2 1 0 0 100 200 300 400 Quantity 1 pt 500 600 700 If the market price is $6, then each individual profit maximizing firm would produce an output of 500 units (1 pt)where MC= MR=P. Total profits are $1,000: ($6 - $4) x 500. (1 pt) b. Price per Unit Market Demand 9 8 7 6 5 4 3 2 1 0 A 0 20000 40000 60000 80000 100000 120000 140000 160000 Quantity 1 pt. c. d. e. f. At $6 per Frisbee, market equilibrium is 4,000 units. 1 pt Since there is an equilibrium quantity sold of 4,000, there is room for eight firms. 1 pt Profits of a typical firm are $1,000. 1 pt The long run price equals the minimum ATC, $2 in this case 1 pt, at which point economic profits will equal zero. At this price, 64,000 units are demanded and individual firms will produce only 100 units. Thus there will be 640 firms in the industry in the long run. 1 pt Chapter 7 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? a. b. c. d. e. 2. Use Figure 7.2 to answer the following questions: a. b. c. What rate of output maximizes total profit? What is MR at that rate of output? What is price? If output is increased beyond that point, what is the relationship of MC to MR? How will this affect total profits? a. b. Profit is maximized where MR=MC which occurs at the output level of 4. 1 pt The MR is equal to $7 at 4 units of output. 1 pt Price, the maximum price consumers are willing and able to pay, at 4 units of output is $10. 1 pt If output is increased beyond 4 units of output, MC>MR. 1 pt This will cause total profits to fall because the additional costs incurred exceed the additional revenue received for each unit of output produced. c. 3. The highest price firms can charge and still sell fish is $13 as shown on the demand curve (corresponding to a quantity of 1). 1 pt At a price of $13, the firm could sell 1 basket of fish for total revenue of $13. 1 pt As shown in the table in Figure 7.1, as price is reduced from its maximum level, the total revenue increases. 1 pt Marginal revenue is still positive as price declines but is decreasing in value. 1 pt Total revenue is maximized at a price of $7 1 pt 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. e. 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? Graph the demand and MR curves. a. Price (per unit) Quantity demanded (Units per day) Total Revenue Marginal Revenue $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 ½ pt each above (9.5 total) b. c. d. e. Total revenue, P x Q, is maximized at 15 units of output. 1 pt Marginal revenue is less than price at all levels of output. 1 pt Marginal revenue becomes negative at 16 units of output. 1 pt 1 pt Market for Catfish $25 Price per unit $20 $15 Demand $10 $5 $0 ($5) 0 5 10 15 20 Marginal Revenue ($10) Quantity (Units per Day) 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. 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? If the market were perfectly competitive, what price would prevail? How much output would be produced? c. d. e. 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 Quantity (Units per day) 1 pt 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 20 c & d. The monopolist produces where MC=MR at 12 units of output 1 pt and charges a price of $18. 1 pt e. 5. If the market were competitive, price would equal $15 1 pt and quantity would also equal 15. 1 pt 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 Marginal revenue Price per unit Units demanded Total Revenue Marginal Revenue* ½ pt each (3 total) $40 $36 $32 $25 $2o $12 $4 10 12 14 17 25 50 150 $40 10 $400 ---- $36 12 $432 16 $32 14 $448 8 $25 17 $425 -7.667 $2o 25 $500 9.375 $12 50 $600 4 $4 150 $600 0