Selective Promotion of Industries and PickingWinnersAmy Jocelyn GLASSTexas A&M [email protected] LITERATURE Brander and Spencer (1985) show export subsidiescan increase national welfare by shifting pro…ts fromforeign to domestic …rms in Cournot oligopolies. Dixit and Grossman (1986) demonstrate that a uni-form subsidy to all industries promotes none andmerely bids the price of the common …xed factorhigher by the amount of the subsidy. To raise domestic welfare, the government must tar-get the industries with the greatest pro…t-shifting po-tential per unit of the common …xed factor. Governments may experience di¢ culty in identifyingwhich industries to target due to lack of information. Grossman and Helpman (1994) s tudy the role ofcontingent contributions in in‡uencing the choice oftrade policy under perfect competition, where freetrade is optimal. Can lobbying contributions reveal pro…t-shifting po-tential and thus permit the government to tailor ex-port s ubsidies across industries despite lack of knowl-edge of relevant parameters? Each industry o¤ers an implicit contribution sched-ule, o¤ering donations contingent on the govern-ment’s c hosen allocation of export subsidies. Industry lobbying permits the government to prop-erly s elect the subsidy leve l for ea ch industry thatmaximizes overall domestic welf are. The lobbying equilibrium implements the allocationof targeted subsidies described by Dixit and Gross-man (1986) that maximizes domestic welfare.2 SETUP Similar to Dixit and Grossman but with cost of for-eign rival the only di¤erence across industries for s im-plicity. Continuum of high-tech industries i 2[0; 1] thatare Cournot duopolies (Dixit and Grossman have dis-creet number of industries n). Output of a domestic …rm yiand output of a f oreign…rm Yi. A numeraire industry that is perfectly competitive. Two factors, scientists and workers, available in …xedsupplies k and l. No factor constraints abroad. High-tech goods use one scientist and ai= a unitsof workers (Dixit a nd Grossman allow industries todi¤er in the number of workers needed per scientist). Numeraire good uses one unit of workers. Output ofnumeraire good based on labor not used to producehigh-tech goods x = l  aR10yidi. Normalize the price of the numeraire good to be one. Scienti…c wage z, workers wage 1. These wages aretaken as given by …rms. Marginal cost of domestic production c = a+z (costof domestic …rms varies in Dixit and Grossman dueto di¤erences in number of workers used). Marginal cost of foreign production Ci, with averageeC R10Cidi. Speci…c domestic export subsidy si, with a veragees R10sidi. Foreign government is not policy active. No domestic consumption of high-tech goods.3 MODEL OF INDUSTRIES Domestic pro…ts = (price plus subsidy minus cost)times outputi= [pi+ si a  z] yi Domestic inverse demand function linear with do-mestic and foreign products imperfect substitutes( > 0;  > 0)pi= b   yi Yi Domestic …rst order condition (pick domestic outputyito maximize domestic pro…ts itaking foreignoutput Yias given)@i@yi= b  2 yi Yi+ si a  z = 0 Domestic rea ction function (solve FOC for domesticoutput yiin terms of foreign output Yi)yi=b + si a  z  Yi2 Subsidy shifts out domestic reaction function so thatdomestic …rm produces higher output yifor any givenlevel of Yi. Foreign pro…tsi= [Pi Ci]Yi Foreign inverse demand ( > 0;T  2> 0)Pi= b  T Yi yi Foreign …rst order condition@i@Yi= b  2T Yi yi Ci= 0 Foreign reac tion functionYi=b  Ci yi2T Equilibrium outputs (found by solving two FOCs, in-tersection of two reaction functions)yi=2T(b + si a  z)   (b  Ci)4T  2Yi=2 (b  C)   (b + si a  z)4T  2 Subsidy causes domestic output to expand and for-eign output to contract. Substitute equilibrium outputs into domestic pro…tsto …nd equilibrium pro…ts. Pro…t shifting e¤ect@i@si=4T (b + si a  z)   (b  Ci)4T  22> 0bigger when foreign …rm’s costs bigger@2i@si@Ci=4T4T  22> 0 Figure 1 show s how equilibrium domestic pro…ts variesby amount of subsidy. A larger subsidy generates alarger increase in domestic pro…ts. The increase inpro…ts is largest for the …rm with the highest c ost for-eign rival (the biggest winner) and smallest for the…rm with the lowest cost foreign rival (the biggestloser). Domestic resource constraint (plug equilibrium do-mestic output intoR10yidi = k)2T(b +es  a  z)  b eC= k4T  2_Increase in ProfitSubsidy to SectorFigure 1: Increase in Profitof Domestic Firm due to Subsidy)B)B)B)B_ Equilibrium scienti…c wage (level of z that makesdemand for scientists equal the …xed supply k)z = b +es  a b eC+ k4T  22T Domestic welfare with no domestic consumption (fac-tor income plus total industry pro…ts net of subsidypayments)w = l + zk +Z10(i siyi) di Optimal subsidies (solve @w=@si= 0 for si) arelarger f or industries with higher cost foreign rivalssies =34T  2CieC> 0 () Ci>eC Unlike ly government would know how CieC variesby industry (or the parameters of demand); however,each …rm may have a solid se nse of how its pro…tsimight be a¤ected by various subsidy levels si.4 LOBBYING IMPLEMENTATION Use lobbying framework similat to Grossman andHelpman (1994) ”Protection for Sale”to implementexport subsidy scheme – Promotion for Sale here. Total s ubsidy paymentst =Z10siyidi Lobby welfare (lobby owns one high tech …rm an arepresentative share fiof fa ctor income with subsidypayments taxed lump sum)Wi= fi(l + zk  t) + i Net of c ontributionsVi(si) = Wi(si)  i(si)  0 E¤ect on lobby welfare@Wi@si= fi k@z@si+@t@si!+@i@si Contributions truthfully reveal gains@i@si=@Wi@si Government’s FOC to maximize total contributions(solves @=@si= 0 where  =R10idi andR10fidi =1)Z10@i@sjdi = k@z@sj+@t@sj8j 2 [0; 1]has same solution as condition for maximizing do-mestic welfare w so the optimal subsidies are chosen.5 POSSIBLE EXTENSIONS Under Bertrand competition, will the industries w ithgreatest pro…t shifting