1 ECON4415: International Economics Problem Set 4 - Solutions

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Beverly Garrison
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1 ECON445: Iteratioal Ecoomics Problem Set 4 - Solutios. I Moopolistic competitio. Moopolistic competitio is a market form where May rms producig di eret varieties. Each rm has moopoly power over its ow variety (=> each rm determies ow price). May cosumers with prefereces (usually CES) for each variety. The varieties are imperfect substitutes from the cosumers poit of view. This meas that eve if a rm charges a higher price tha others, it will have positive sales (i other words, each rm faces a dowward slopig demad curve). No barriers to etry => I the log ru, pro ts are zero i equilibrium. No strategic iteractio With moopolistic competitio ad ecoomies of scale, the uit cost curve caot lie above the demad curve D - free etry esures that pro ts are squeezed to zero (see g. ). A positive productivity shock will shift the uit cost curve dow, geeratig positive pure profts. This will cause etry of ew rms, which will capture a share of the market. Thus, the demad curve facig the existig rms will shift towards origo. The equilibrium price ad quatity is idetermiate, ad will i geeral deped o the elasticity of demad. p 3 2 uit cost Figure D x

2 2. We kow that pro t maximizatio implies p ( =") = k, where deotes elasticity of demad (absolute value) ad k deotes margial costs (costat). If is costat, the p must be costat as well. Thus, with costat elasticity, the aswer to excercise is that lower variable costs imply lower prices (ad higher productio). Ecoomic itegratio is equivalet to icreasig the size of the market. With costat elasticity, prices ad productio per rm will remai xed. There will be more varieties available to the cosumer, however. 3. We saw that pro t maximizatio implies p = k"= (" ) (*), i.e. a markup over variable costs. If the elasticity of demad is high for low levels of demad, the 0 < 0 (c cosumptio). If we di eretiate (*), we = " 0 = ( ) 2 > 0, meaig that a pro t maximizig rm will charge a higher price for higher levels of demad. Thus, we have derived the upward slopig PP curve i gure 2. Firm demad for labor is l = F + xk: Productio per rm x is equal to cosumptio per capital times the populatio x = c. Free etry esures that pro ts are zero at all times. Reveue equals costs: px = w(f + xk) () () p = wf + wk (2) x = wf + wk (3) c Thus, we have derived the dowward slopig ZZ curve i gure 2. 2

3 p, AC 2.0 PP ZZ Figure 2 Clearly, p is ot xed aymore. Ecoomic itegratio ca be modelled as a icrease i the labor force. " does ot chage the PP curve. " will shift the ZZ dowwards. A ew equilibrium must exist with lower prices ad lower cosumptio per variety per capita. Ituitio: A larger market ad more varieties will reduce the amout cosumed per variety per capita. People spread their cosumptio over more goods. This raises the elasticity of demad ad make the market more competitive, which will drive dow prices. We have a additioal source of gais from trade, compared to the Spece-Dixit-Stiglitz model, because prices fall (a scale e ect). The umber of rms per coutry: Free etry meas that price = uit cost. If prices fall, uit costs must fall as well. Icreasig returs imply that productio per rm has to icrease. The labor force i each coutry is immobile. Thus, the icreased demad for labor (because productio is up) must be o set by a fewer umber of rms. If ot, labor demad is higher tha labor supply. Aalytically, labor supply = labor demad: = P l = (F + xk) () = = (F + xk) (**): Hece, x " implies # : c The total umber of rms: 3

4 Writig (**) i terms of cosumptio istead, = = (F= + ck), we see that " ad c # gives " : All i all, trade icreases the total amout of varieties available to the cosumers, but the umber of varieties ( rms) per coutry falls..2 II (Krugma 980, Scale Ecoomies, Product Di eretiatio, ad the Patter of Trade). 2 coutries, a moopolistic competitio, icreasig returs sector i each coutry. abor is the oly iput. Utility is CES, u = P c i ; 0 < <. Utility maximizatio the yields for two varieties j ad k. cj c k = p j p k (4) abor demad is l i = + x i :We kow that pro t maximizatio ad free etry yields costat price ad productio i optimum (because the elasticity of demad is costat). There are iceberg type trasport costs g < : et = demad for a foreig variety k relative to a domestic variety j. From the utility max. coditio: cj gc k = c k c j = p j p k =g, (5) pj g (6) p k p k is here the producer price ad p k =g is the price icludig trade costs. The fact that producer prices are a costat markup over variable costs esures that p j = p k :Thus, = g : We see that the import share icrease with ecoomic itegratio (g "), ad that = whe g = : Equilibrium i the product market i the home coutry must satisfy: px = (x) px = c hh c hh + c fh w + c hf c hf + c ff w (7) + w + + w (8) 4

5 , total reveue for domestic rms= expediture o domestic goods. I the rst lie, I have deoted c ij as the cosumptio per variety of goods from i i coutry j: The rst term o the right had side measures home expediture of domestic goods. a) The omiator is the umber of h-goods cosumed, b) the deomiator is the total umber of goods cosumed, c) the fractio is thus the share of h-goods cosumed. The secod term measures foreig expediture of domestic goods. Wages are equal i home ad foreig (w = w ), more or less by assumptio (see KHs lecture otes). If = ad =, we see that px simpli es to w=2 + w =2, i.e. cosumers divide their icome evely betwee imports ad domestic goods. Equilibrium i the foreig product market is symmetric, (xx) px = + w + + w (9) ( rst term is expediture by h, secod term is expediture by foreig). Questio: What is the equilibrium umber of rms i each coutry? Dividig (x) ad (xx) by ad respectively ad the solvig them by elimiatig px yields = + +, (0) = where b = = : This is also equal to () = b b (xxx) (2) b = =b b (3) We see immediately that if b > ; the (= ) = b >, meaig that a larger home coutry will geerate disproportioally more rms i the home coutry. This is the home market e ect (HME). The, home must be a et exporter. Ituitio: Ecoomies of scale meas that cocetratio of productio facilities is pro table. Trade costs meas that rms choose to locate close to large markets. 2. 5

6 a) Di eretiatig = c2 b 2 > 0 (4) if b > :ower trade costs is equivalet to g " :We previously foud that the import share is = g : If g", the " ad " : I words, HME is ampli ed with lower trade costs. Ituitio: ower trade costs will ted to make it more pro table to locate i the larger market ad export to other locatios. However, we could argue that lower trade costs should dampe HME: With low trade costs, rms may choose to locate i regios where costs are low (ad demad low). This e ect is ot captured i the HME model however, because of factor price equalizatio (equal wages). b) It is possible to show (see appedix) that = ( ) is equal to the ratio betwee margial ad xed costs (i equilibrium), which is a commoly used measure of ecoomies of scale (EoS). If EoS#! = ( ) "! #! HME # : This seems plausible because less EoS would dampe the icetive to cocetrate productio. c) The elasticity of demad is " = = ( ) (see appedix). If cosumers become more price sesitive, " ", the = ( ) "! #! HME # : Ituitio: Cosumers will buy less foreig goods, because they are more expesive tha domestic goods. Thus, rms would rather locate i every market, istead of exportig. 3. HME should operate i markets where there are may rms ad they have some degree of market power. the goods are uique but are close substitutes to other varieties. there is free etry there are ecoomies of scale (large xed costs ad low variable costs) Some cadidates may be. the automotive idustry (BMW vs Mercedes vs..) 2. pharmaceuticals (Paracet vs Ibux vs..) 3. the software idustry These markets ted to be characterized by large R&D costs ad low variable costs (at least 2 ad 3). It seems that most rms i these idustries locate i large markets as well. Also look at the Davis & Weistei papers where may HME idustries are ideti ed. 6

7 .3 Appedix Why is " = = ( )? Utility is de ed u = P c i : The FOC is cj p j = 0 () p j = c j = x. arge group assumptio: is costat. This meas that each rm s pricig policy will have a egligible e ect o the margial utility of icome. The, di eretiatig the FOC, p = (5) () " = (6) What is optimum price i the HME model? Pro t maximizatio implies p = w () p = " w w = " " (7) What is optimum productio per variety x i the HME model? Free etry implies px = wl = w( + x) () x = p (8) w = (isertig optimal p) = () (9) ( ) Why is = ( ) a measure of ecoomies of scale? From (*), = x The omiator is variable costs, the deomiator xed costs. (20) 7

EC426 Class 5, Question 3: Is there a case for eliminating commodity taxation? Bianca Mulaney November 3, 2016

EC426 Class 5, Question 3: Is there a case for eliminating commodity taxation? Bianca Mulaney November 3, 2016 EC426 Class 5, Questio 3: Is there a case for elimiatig commodity taxatio? Biaca Mulaey November 3, 2016 Aswer: YES Why? Atkiso & Stiglitz: differetial commodity taxatio is ot optimal i the presece of