Chapter 7: Answers to Questions and Problems

Transcription

1 19. Based on the nformaton contaned n Table 7-3 of the text, the food and apparel ndustres are most compettve and therefore probably represent the best match for the expertse of these managers. Chapter 7: Answers to Questons and Problems Answerkey ProblemSet3 1. The four-frm concentraton rato s, $175, 000 $150, 000 $15, 000 $100, 000 C4 " " $1,000,000 Chapter7. a. The HHI s " # $00, 000 $ # $400, 000 $ # $500, 000 $ HHI " 10, 000 %' =3,719 ( ' & ( ' (. % + ) * ) * ) * &, b. The four-frm concentraton rato s 100 percent. c. If the frms wth sales of $00,000 and $400,000 were allowed to merge, the resultng HHI would ncrease by 1,3 to 5,041. Snce the pre-merger HHI exceeds that under the Gudelnes (1,800) and the HHI ncreases by more than that permtted under the Gudelnes (100), the merger s lkely to be challenged. 3. The elastcty of demand for a representatve frm n the ndustry s 1.5, snce # 0.9 # " - EF " " # E F a. $100. To see ths, solve the Lerner ndex formula for P to obtan 1 1 P " # ' $ ( MC " # ' $ ( $35 " $100. ) 1 # L * ) 1 # 0.65 * # 1 $ # 1 $ b. Snce P " ' ( MC, t follows that the markup factor s ' ( ".86. ) 1 # L * ) 1 # 0.65 * That s, the prce charged by the frm s.86 tmes the margnal cost of producng the product. c. The above calculatons suggest prce competton s not very rgorous and that the frm enjoys market power. 5. Managers should not specalze n learnng to manage a partcular type of market 17. structure. Market structure generally evolves over tme, and managers must adapt to See Table 7-1. these changes. Own Prce Elastcty 6. To the extent that the HHIs are based on too narrow a defnton of the product (or of Demand for geographc) market or the Own mpact Prce Elastcty of foregn of competton, Representatve Frm's the merger mght be allowed. It mght also be allowed Market Demand f one of the frms Product s n fnancal Rothschld trouble, Index or f sgnfcant economes of scale exst n the ndustry. Agrculture Constructon Durable manufacturng Nondurable manufacturng Transportaton Communcaton and utltes Manageral Economcs and Busness Strategy, 7e Page 1 Wholesale trade Retal trade Fnance Servces Table 7-1 Based on the Rothschld ndces n Table 7-1, wholesale trade most closely resembles a monopoly, whle fnance most closely resembles perfect competton. P MC $3 $ The Lerner ndex s L " " " 0.9, whch ndcates the frm has P $3 consderable market power. Ths makes sense because the product that the frm sells s currently under patent protecton, whch essentally makes the frm a legal monopoly.

2 mnmum % E of & ts AVC curve. % ".5 Here, & MC 50 " 8q # 3q and 3. your frm can ncrease profts by reducng prce n order to sell more plls. 3 50q " 4q # q a. AVC 7 unts. 50 " 4q # q. Snce MC and AVC are equal at the 15. Notce b. $130. that MR = 1,000 q 10Q, MC 1 = 10Q 1 and MC = 4Q. In order to maxmze profts c. mnmum $140, (or snce mnmze pont ($130 of ts AVC, 110) losses), set x 7 MC the = $140. frm = AVC equates to get MR 50= " MC 8q 1 # and 3q MR 50=MC " 4q.# Snce q, Q = d. Q 1 Ths frm s demand wll decrease over tme as new frms enter the market. In the Chapter8 or + q Q, ths. Thus, gves AVC us s mnmzed at an output of unts, and the correspondng long-run, economc profts 1000 wll shrnk " 10$ Qto zero. AVC s $ % $ % 1 Q % # 10Q1 AVC 50 " 4 # 46. Thus the frm s. supply curve s descrbed " 10$ Q1 Q % # 4Q by the equaton MC 50 " 8q # 3q f P & $46 ; otherwse, the frm produces a. MR = 00 4Q and MC = 6Q. Settng MR = MC yelds 00 4Q = 6Q. Solvng Solvng zero yelds yelds unts. Q = 0 Q unts. # 00 1 The. proft-maxmzng prce s obtaned by pluggng ths nto b. A the monopolst demand equaton produces 9 & unts and Q # 500 & unts. The optmal prce to where get P = MR 00 = - MC (0) and = $160. thus 9 does not have a supply curve. c. b. A Revenues monopolstcally are R = ($160)(0) compettve = $300 frm produces and costs where 00 are C MR 500 = 000 = MC (0) and thus = $300, does not s the amount consumers wll pay for the Q1 Q # # & unts, have so the a frm s supply profts curve. are zero and c. s Elastc. determned by the nverse demand curve: 6. d. TR s maxmzed 700 " when $5, 500 MR = 0. Settng MR = 0 yelds 00 4Q = 0. Solvng for a. P # Q 1, Q = 000 yelds 3 unts; " 5 Q # = P 50 = $70. $ unts. # The prce & $ at ths. output At ths s prce P = 00 and output, (50) = revenues $100. are R = b. e. Q Usng = 4 unts; % the results P 9 = $60. & 9 from part d, the frm s maxmum revenues are R = ($100)(50) = ($611.11)(77.78) c. DWL $5, = $47,53.14, whle costs are $ $70 " $40 % $ 1 % $15. Cf. 1 Unt C # elastc. $ 10, 050 5$.% % $ 5, 000 $ % % # $3, The frm thus 7. earns profts of $3, a. The nverse lnear demand functon s P = 10.5Q. 16. College b. MR = Computers 10 Q and s MC a monopolstcally = 14 + Q. Settng compettve MR = MC frm yelds and 10 faces Q a = downward 14 + Q. slopng Solvng demand for Q for yelds ts product. Q = 8 unts. Thus, The you optmal should prce equate s P MR = 10 = MC.5(8) to = maxmze $6. profts. c. Revenues Here, are MR R = 1000 ($6)(8) Q = $48. and Costs MC = are Q. C Settng = (8) + Q (8) = = Q $56. mples Thus that the your frm optmal earns output a loss of s $8. 50 However, unts per the week. frm Your should optmal contnue prce operatng s P = 1000 snce t 50 s = Manageral $750. Economcs and Busness Strategy, 7e Page 1 coverng Your weekly varable revenues costs. are R = ($750)(50) = $187,500 and your weekly costs are d. In C = the 000 long + run (50) ext = wll $64,500. occur and Your the weekly demand profts for ths are frm s thus product $13,000. wll You ncrease should Chapter expect untl other t 9: earns frms Answers zero to economc enter the to market; profts. Questons Otherwse, your profts the wll frm and declne should Problems over ext tme the busness and you wll n lose the market long run. share to other frms "# Your average varable cost of producng the 10,000 unts s $600 (deprecaton s a fxed A EQA, 0.1 a. $# The %&# cost). Snce the prce you have been offered ($650) exceeds your average varable optmal cost ($600), advertsng you should to sales accept rato the s gven offer; by dong R so " Eadds $50 QP, per unt (for a '# %"# total of $500,000) to your frm s bottom lne. (# A EQA, A 0.1 b. A $.05% $ $50, 000 % $, 500. R)# *&+# " EQP, $50, 000 ))# +,-)./# Chapter9 )))# *&+.0*1+# &# a# c" " "++ #"& " $# Q" $ # Q& $ # Q& $ && # +#1Q& $- & b & & & & " a # c& " "++ # &+ " Q & $ # Q" $ # Q" $ &+ # +# 1Q" # & b & &&" & Page Mchael R. Baye '# 3 " 4"563 & 4"&# Page 4 (# 74"++8&9&:;4*<<# Mchael R. Baye # " 4*1"&6 & 4*&::# =# $# "&1,-)./# '# "++,-)./>$(?# # "1+,-)./# ># )# F1,-)./# ))# G'0,.""&#1,-)./#

3 '# "++,-)./>$(?# # "1+,-)./# ># )# F1,-)./# ))# G'0,.""&#1,-)./# <# a# cf " &+H +++ # <H +++ " $# QF $ # QL $ # QL $ "H 5++ # +#1QL # & b & & 1 & '# 3 I 4":++63 J 4F++# (# 74&+H+++819&1++;4*FH1++# # I 4*:#"K)AA)0-6 J 4*&#<1K)AA)0-# 1# $# L>.74MN.0O>.1++8&34*"++#L0AP)-OQ)>A/34&++,-)./# '# 74MN4*"++# (# R$(?D)BK>$B-/S>B0>(0-0K)(CB0D)./# " Part. Problem1. Manageral Economcs and Busness Strategy, 7e Page 1 Seepage41 43ofthetextbook.

4 1 Part II 1.1 Problem Margnal revenues MR = 100 Q Margnal cost San Jose MC SJ =4q sj Margnal cost Santa Cruz MC SC =6q sc We know that a suffcent condton to produce n both plants s MR = MC SJ = MC SC workng out the algebra, we get q sj =3/q sc and 100 q sj q sc = 6q sc 100 3q sc q sc = 6q sc 100/11 = q sc Therefore, q sj = 150/11 For completeness we need to check f jont profts s hgher than profts producng usng one plant. π BOT H = / (150/11) 3(100/11) Notce that q 1 SJ = 100/6 and q1 SC = 100/8 π SJ = /6 75 (100/6) π SC = /8 5 3 (100/8) comparng profts, we can check that t s optmal to produce ONLY n Santa Cruz 1. Problem 3 - from the game n class let s work out a general case and then use the varables gven n the problem set, assume a lnear nverse demand P = A b( N =1 q )=A bq and a lner cost functon C = cq where q represents the quantty produced by frm,n s the total number of frms n the market and Q the total quantty produced n the market. the profts for the frm j s gven by π j = Pq j cq j the FOC s N A b( q ) bq j c =0 =1 then addng the FOC for each frm n the market N A N b Q bq Nc =0 1

5 then solvng for Q Q = N(A c) b(n + 1) Now, let s check the parameters gven n the problem set. We know that A = 100, N =4, c =4, b =1 therefore, the total quantty n the market s Q = then each frm produces q = 96/5 19 Note: Notce that game n class, groups are choosng quanttes smultaneously. Therefore, the appropate model to study the game played s the COURNOT model. Cournot was one of the poneers n mcro-theory.