Chapter 11 Perfect Competition

Transcription

1 Chapter 11 erfect Competition Answers to Chapter 11 roblems (Text, pp ) 1. ee assignment. 2. etting price = equal to marginal cost (MC) = 2 + 4, solve for quantity: = 2 + 4, or 8 = 4 or = 2 units. The fixed cost that leads to zero economic profit is calculated by solving π = ( AVC) FC = 0 or ( 6)(2) FC = 0 for FC = $8. 3. hort run supply = horizontal MCi. We have MC i = 4 + i, and hence i = MC i 4. i = = MCi 4000, or = 00 MC For profit maximization, MC =, and so = , which means that industry supply is given by = Hence short run equilibrium occurs where = With = 6, we have = 2000 units, and = $6/unit. 6 4 Consumer surplus roducer surplus 2000 Consumer surplus = area of upper triangle = ( 6)(2000)/2 = $4000. roducer surplus = area of lower triangle = (6 4)(2000)/2 = $2000. Total loss of surplus = $ In the long run, if the aflatoxin problem persists, we would expect both demand and supply to become more elastic, as consumers found substitutes for peanut butter and peanut farmers shifted into other crops. Hence the long run loss of both consumer and producer surplus should be lower. 5. ince = MC > AVC, we know that the firm should continue at its current level of output (call it 0 ) in the short run. Is the firm making economic profits? ince LMC = 12 > min LAC =, we know that the firm is producing to the right of its long run cost-minimizing level, that LAC is rising, and therefore that < LAC( 0 ) < 12. ince MC LMC, LAC( 0 ) < AC( 0 ), and hence = MC < AC. Therefore the firm is incurring losses in the short run, and in the long run it should shift to a smaller size of plant (in fact, the size that minimizes LAC at *), as shown in the following diagram McGraw-Hill Ryerson Limited. 11-1

2 $/ 12 LAC AC AVC 8 LMC MC * 0 6. Long-run equilibrium price for this industry will occur at the minimum value of LAC. LAC = LTC/ = Minimum LAC occurs with dlac/d = 2 = 0, which solves for = 5 units per firm. At = 5, LAC = = $11/unit. 7. The LAC curve for firms in this industry is given by LTC/ = + 4. The minimum value of LAC now occurs at an output level of 0, where LAC takes the value 4. As a practical matter, the notion of an infinitesimally small firm has no meaning. Because of indivisibilities, a firm's LAC will rise, below some level of output, as approaches zero. 8. The taxi industry supply curve for Metropolis is a horizontal line at = $0.20/kilometre. The demand schedule intersects it at = 80,000 km/yr, which means 8 taxis. The equilibrium fare will be $0.20/km AC=MC (,000s) 9. If the total number of taxis is reduced from 8 to 6, the equilibrium fare will rise to $0.40/km. Ignoring the opportunity cost of the medallion, each medallion owner will earn a profit of $( ),000= $2000/yr. If the annual interest rate is %, a person would need $20,000 in order to earn as much interest as a medallion holder earns each year in profit. o medallions will sell in the market for $20,000 each. A person who buys a medallion at this price will earn zero economic profit McGraw-Hill Ryerson Limited.

3 AC=MC (,000s). The short-run MC curve for firms in the industry is dtc/d = + 2w. The equilibrium output is found by equating and MC: + 2w* = 28, which yields *=9/w. For firms with normal managers, w = 2, so * = 9/2 = 4.5 units/day. rofit of normal firms = 28(4.5) 2 (4.5) 2 45 M = 40.5 M. For the firm that hires Merlin, w = 1, so * = 9. rofit of firm with Merlin as manager = 28(9) M m = 81 M m, where M m is Merlin's salary. The premium paid to Merlin in equilibrium will be exactly the amount required to equate his firm's profits with those of other firms. rofits will be equal when (81 M m ) = (40.5 M), and so Marvin will be paid = $40.50/day more than the other managers. 11. a) With the new process, your costs, excluding your payment for use of the patent, will be TC' = To find your profit maximizing output level, we equate your new marginal cost, MC' = 1 + 2, to the industry price, which, as before, will be the minimum value of the average cost curve associated with the prevailing technology: LAC = 8/ => dlac/d = 2 8/ 2 = 0 => * = 2 => LAC = = *. If we use ' to denote the patentholding firm's profit-maximizing output level, we have MC'= = 1 + 2' => ' = 4.5. The patent holder's economic profit will thus be TR TC = 45 [ (4.5) 2 ] = $ o the most you would be willing to pay for the patent is $ b) Because the patented process can reduce the costs of each of the 01 firms by half, it is worth considerably more than $16.25; hence the inventor would not be willing to sell exclusive rights to its use to one firm at that price. For example, he could sell the patent to two firms for about $16.24 each, and so on. At some point, of course, attention would have to be given to the elasticity of market demand. For example, if all 01 firms produced 4.5 units instead of 2 units, industry supply would increase from 2002 to units, and the price would have to fall to eliminate excess supply at the original price. 12. a) MC = VC/ = w L/ = w/m L. imilarly, AVC = wl/ = w/a L. o when M L = A L, it follows that MC = AVC. b) ince the firm is perfectly competitive, its output price is equal to marginal cost, which here is equal to AVC. Hence all of the firm's revenue is paid out to workers, leaving nothing to cover its fixed costs. If the firm stays open in the short run, its loss will be equal to its fixed capital costs of $40/day, which is the same loss it would suffer if it were to shut down. o the firm will be indifferent between shutting down and remaining open in the short run. 13. TC = MC = dtc/d = In equilibrium, MC =, which implies = 6, which solves for = 27.5 units McGraw-Hill Ryerson Limited. 11-3

4 rofit = TR TC = 6(27.5) [0.2(27.5) 2 5(27.5) + 30] = $ ince the firm earns positive profit, it should stay open. 14. emand is given by = , and supply is given by = In equilibrium, sale and purchase prices are equal. Thus, we get = , which solves for = 800 litres and = $3.40/litre. With the tax, the supply curve facing buyers shifts upward by $1.20/litre, which makes it: = When we solve = , we get = 600 litres and = $3.80/litre. This is the price paid by consumers. uppliers get = = $2.60/litre. The incidence of tax on suppliers is 2/3, and on consumers it is 1/3. The consumer surplus before tax is [(5 3.4)(800)]/2 = $640. The producer surplus before tax is [( )(800)]/2 = $1280. The consumer surplus after tax is [(5 3.80)(600)]/2 = $360. The producer surplus after tax is [( )(600)]/2 = $720. Lost consumer surplus is $280, lost producer surplus is $560, tax revenue = $720, and eadweight loss = ( )( )/2 = $ McGraw-Hill Ryerson Limited.

5 15. a) With a perfectly competitive constant cost industry, the advertisement (which shifts the demand curve out) will increase long run quantity sold from to, but will leave price unchanged. ' ' 15. b) The result will be an upward shift in the long-run supply curve. rice will increase from to and quantity sold will decrease from to. ' ' ' 16. a) LAC = TC/ = /. The minimum point on LAC is found either by graphing the LAC curve or by taking the first derivative and setting it equal to zero: dlac/d = 4 0/ 2 = 0, which yields = 5 units. In the long run, = LAC = $140/unit. b) If demand is = 00, then at = 140, we get = 860 units. o in long run equilibrium, there will be 860/5 = 172 firms. c) Now LAC = (TC 36)/ = /. Again, the minimum point on LAC is found either by graphing the LAC curve or by taking the first derivative and setting it equal to zero. dlac/d = 4 64/ 2 = 0, which yields = 4 units. In the long run, = LAC = $132/unit. At this price, = 868 units, and the number of firms rises to 868/4 = McGraw-Hill Ryerson Limited. 11-5

6 17. At a world price of $30/LHB, domestic demand is 35 LHBs per year. omestic producers supply 20 of this total, foreign producers the remaining 15 (left panel). With a tariff of $20/LHB, the import price becomes $50/LHB. Because the domestic market clears at $40/LHB (centre panel), this means that no LHBs will be imported. ince no LHBs are imported, the tariff raises no revenue. Consumer surplus and producer surplus with the tariff is the area of triangle ABC (centre panel), which equals $1350/yr, $450 in producer surplus and $900 in consumer surplus. Consumer surplus and producer surplus before the tariff -- the shaded area in the right panel -- was $1425/yr ($200 in producer surplus and $1225 in consumer surplus), which means that the tariff has reduced the sum of consumer and producer surplus by $75/yr. 0 0 A B C (i) Costs will fall for all existing firms. At existing prices the firms will make positive economic profits and increase output, as shown in the following diagram. ($/unit of output) rofit MC MC' 0 ATC ATC' 0 1 (ii) New firms will enter the industry, attracted by the economic profits McGraw-Hill Ryerson Limited.

7 (iii) The industry supply curve will shift out until profits are again driven down to zero. The final result is that prices fall, quantity increases, and there are more firms than before. In the long run, consumers reap the benefit of the innovation. 19. As the following figure shows, (a) in the case of a proportional decrease in all input prices with an increase in industry output, the minimum LAC point for a representative firm does not alter as industry output expands. (b) If input prices do not decline proportionally, however, it is quite possible that the level of output at which a firm reaches its minimum LAC point will change as industry output expands, in which case, among other consequences, there may be more volatility in the number of firms in the industry with an expansion in industry output. 20. (a) LAC i = i + ( i.) 2, and LMC i = i + 3( i.) 2. (b) Minimum LAC i is found where dlac i /d i = i = 0, or where i = 18. Minimum LMC i is found where dlmc i /d i = i = 0, or where i = 12. LMC i reaches its minimum to the left of the point at which LAC i reaches its minimum. (c) Minimum LAC i (which occurs at i = 18 rings) = (18) + (18) 2 = $180/ring, which determines the price of rings in long-run equilibrium. At this price, with demand given by = , then long-run equilibrium = 9000 rings, and the equilibrium number of firms is 9000/18 = 500 firms. (d) If market demand becomes = , then long-run equilibrium = 6300 rings, and the equilibrium number of firms is 6300/18 = 350 firms. The transition path from the initial equilibrium to the new equilibrium is as follows: when demand falls, there is an excess supply of rings at the original equilibrium price, and so the market price falls, and firms contract output along their short-run MC curves. At the lower market price, however, firms are experiencing economic losses, which will induce the exit of some firms, leading to a leftward shift in supply and a resultant return of the market price to its long-run equilibrium level, at the lower equilibrium level of output of 6300 rings. 21. enoting the price-elasticity of supply as E and the slope as m, we have E = /m = ( )/2. When =15, E = 0/30 = 0; when = 30, E = 30/2(30) = 1/2. More generally, since E = /m = ( )/2 = 1 15/, as tends to infinity (increases indefinitely), 15/ tends towards zero, and hence E tends towards unity. 22. (a) E = /m, where m = d/d, the slope of the demand curve at a given point. With = , d/d =.02, and E = /.02 2 = 1 when.01 2 = 16, or when = 40. Below = 40, demand is price-elastic, and above = 40, demand is inelastic McGraw-Hill Ryerson Limited. 11-7

8 (b) With = 4 + 1/2, we have d/d =.5 1/2, and E = 4 + 1/2 /.5 1/2 = 1 when 1/2 = 8, or when = 64. Below = 64, demand is price-inelastic, and above = 64, demand is elastic. (c) With = 6, we have m = d/d = 6, and E = /m = 6/6 = 1 at every point on the supply curve. Any supply curve that is a ray from the origin ( = 6, or =, or =.25) has a unitary price-elasticity of supply at every point! McGraw-Hill Ryerson Limited.