Question

1. Consider the last problem of Homework 2: Perfect Competition - consider a perfectly competitive market that has 4 firms in it (assume it is perfectly competitive despite their being only 4 firms). Two of the firms use technology A and two of the firms use technology B. The respective costs of producing using technology A and B are given by the cost functions: CA9A) = 40 + 29A +37A2 CB(9B) = 30 + 398 +298? Demand is given by Q” (P) = 20 - P. a) Determine short run equilibria, i.e. optimal outputs for each type of firm, equilibrium quantity for the market as a whole, and the equilibrium price, and then calculate equilibrium profits for each type of firm. b) If solved correctly, we would have found that firms using technology A (i.e. having a type A cost function) were making negative profits while firms with technology B were making positive profits. Given this, what will you expect to happen in the long run? Will other firms enter? Will price stay the same? How will this impact the two types of firms differently? Will both technologies be used in the long run? Explain.

Answer 1

For a competitive firm , the portion of MC curve that lies above the minimum point of AVC curve , is the supply curve of that firm .

Cost EACAA ) = 40+29A +39A2 -(1) functions ó CB (2B) = 30 + 348 +2965 - (2) Demand & GO(P) = 20-75 l To find equilibrium output, we have to equate market demand and food market Supply me curve that lies above the minimum is the supply curve for a competitive The portion of point of Ave form. (4o-TFE) o Tue = 290 +3902

2+620 orom equation (1) Me [Med(29A +390) - Edfonlan) for a perfectly competitive from Po MC P=2+69A = GIAP-2 - an - P/6-1/3 2 of the forms use this technology, so, QA = 2.94 = 2(P/6-1/3) - Plz-2/3 Again, forom equation (2), me = 3+ 4AB P = 3 +423 =2428 = P-3 => a3 - P/4-3/4 2 forms use this technology, so . Q = 2.98 = 2(P/4-3/4) - P/2 - 3/2

Market Supply curve -> QA + QB - = P/3-2/3 + Pla - 3/2 - 2P-4+3p_9 - 5P-13 Now, if we equate os and a 5p - 18 - 20-115 p 5 P + + P = 20 + 18 77 2506 P120713 -> T S p= 133.5 = 665 equili bocium quantity = (665. ) - 13 3325 - 403 - 186 133.5 06 y equilibrium price 11 31 1461 2922 +8 693 1461 93 497 31

= P/6-1/3 = 665 - 16 316 = 665 - 112 - 665-62 603 62 A = P/4-3/4 = 665 - 314 665 3/ 4 572 665 124 665 93 12,4 286 - 143 31 143 So, equilibrium Output for the forms using technology A-201 and those who use technology B 31

Tuilibodum porofit foor type TR = P.RA = 665. 201 A flooms-> TR - TO = 69.5447450572 = 70 62 TC = 40 + 2(20! ) + 3 (282 ) 03 ) + 3 ( 201 ) = 78.0143080125 =78.01 So, for technology A, te> TR , (TR-te) co =71088 =(70-78.01) porofit for type Bö TR - Te 72 = p.28 - 665. 143-98.9543143599 - 99 TC = 30 + 3(143)+2 (43)” = 86.3964620197 = 86-3 TR) Te, porofit= (99-86.3) = 12.7 31 31

B: In the long run, frons using technology A will lo ther Switch to technology B or will shut down production due to loss. From8 wing technology B earn positive profit and therefore, other forms will enter the market who will be willing to poroduce under technology B

Thus, price will fall and forms will enter as long as all frowns wing technology B earn Zeers profitYechnology A Rolll no longer be peracticed in the long oun and no entering from will produce using it. The existing a firms under technology A would try to produce under technology B and in case of failure, will exit from the market.