International Monopoly under Uncertainty

Transcription

1 Interntionl Monopoly under Uncertinty Henry Ary University of Grnd Astrct A domestic monopolistic firm hs the option to service foreign mrket through export or y setting up plnt in the host country under exchnge rte uncertinty. We nlyze the effect of the prmeters of the demnd nd cost functions on hysteresis. We lso show results on the effect of txtion nd lor cost in ttrcting or voiding reloction. We find tht when the firm is multintionl it pys more txes. Much more importntly, tx rte reduction is effective in ttrcting investment nd voiding reloction. When the firm is multintionl it lso incurs lower lor costs. However, lor cost is not determinnt in the loction of production. Keywords: Exchnge rte uncertinty, rel option, txtion, lor cost. JEL Code: F3, F3. I would like to thnk Jvier Grdezl for vlule comments. Correspondence to: University of Grnd, Deprtmento de Teorí e Histori Económic, Cmpus de l Crtu s/n,87, Grnd, pin. Phone: Fx: e-mil: hry@ugr.es.

2 Introduction The decision of where to locte the production of trdle good is n investment decision mde under uncertinty nd is costly to reverse. An exporting firm hs the option of setting up plnt in host country t ny time. In the sme wy, multintionl firm hs the option t ny time of ndoning the host country nd serving it through exports. In ny cse, the firm finds it convenient to wit for etter conditions. A firm fcing this prolem cn e understood s hving finncil option. Dixit (989) developed model for the decision whether to enter nd exit mrket sed on finncil option theory. The rgument is simple: "n opportunity to mke rel investment is cll option on stock tht consists of the cpitl in plce". Accordingly, the option vlue of n investment proect is evluted to represent the vlue of witing. The investment decision entils sunk costs, which cn e understood s the strike price. In this rticle we consider tht the uncertinty comes from the exchnge rte. Theoreticl models such s Golderg nd Kolstd (995), ung nd Lpn () nd Ary nd Grdezl (6) show tht exchnge rte movements influence the loction decisions of firms. The empiricl evidence ville on the reltionship etween exchnge rte fluctutions nd FDI includes Blonigen (997), who rgues tht the exchnge rte my ffect FDI ecuse cquisitions involve firm-specific ssets which cn generte returns in domestic currency, nd Cmp (993), who finds negtive effect of exchnge rte voltility on the numer of foreign firms entering the U.. mrket. In this pper we use the methodology of Dixit (989) nd Dixit nd Pyndick (994) s well s the model of Ary nd Grdezl (6) to study monopolist's loction decision in n uncertin environment. We nlyze the effect of chnges in the

3 prmeters of the demnd nd cost functions, locl nd foreign txtion nd the role of lor costs in deciding where to locte production. The model. Generl Frmework Bsed on Dixit's model, Ary nd Grdezl (6) developed model of the entry nd exit decisions of domestic oligopolistic firm competing à l Cournot with n foreign firms in host country where ll the firms hve liner demnd nd cost functions. We follow their model to explin the cse of monopolist fcing nonliner demnd nd cost functions. Assume tht the exchnge rte,, chnges over time s Brownin motion, nd hence ll uncertinty rises from the exchnge rte. d µ dt σdz () where dz is the increment of stndrd Wiener process, normlly distriuted with zero men nd vrince dt, µ is the trend rte of growth of the exchnge rte or the devition of the exchnge rte from its equilirium pth t ech point in time, nd σ is mesure of its potentil voltility. According to the Dixit's model, the firm's decision prolem is reduced to the prolem of exercising n option. The pproch hs two stte vriles: the current exchnge rte,, nd discrete vrile,,, tht indictes whether the firm is n exporter () or multintionl (). In stte (,) the firm decides whether to produce only in the domestic mrket nd to export or to egin to produce (nd sell) in the foreign mrket, which mens exercising the option of going multintionl. In stte (,) it decides to 3

4 4 continue producing (nd selling) in the host county or to go domestic gin, which mens exercising the option of eing n exporter. The current profit of firm in stte s function of the exchnge rte is π () nd the expected discounted vlue of the firm given n initil exchnge rte nd stte cn e expressed s V (). A firm fcing such prolem nd le to chnge flexily from one stte to nother hs to price oth options simultneously. Under non-ritrge opportunities the following must e stisfied ( ) ( ) ( ) ( ) () V dt dv E ρ π where ρ is discount rte nd E is the expecttion opertor. By Ito's Lemm, we hve ( ) ( ) ( ) ( ) V V V π ρ µ σ The generl solution of (3) cn e written s ( ) ( ) ( ) (3) dt e t E B A V t ρ η η π where > < σ ρ σ σ η σ ρ σ σ η µ µ - µ - µ - It cn e considered tht exporting is profitle when the domestic currency is deprecited nd setting up plnt rod is profitle when the domestic currency is pprecited. This simple resoning introduces the restrictions A B. Eliminting the su-index we write

5 β V η η ρt ( ) ( ) A B E π ( ( t) ) e dt (4) Let ( ) e the level of exchnge rte low enough to induce the firm to invest in the host country, tht is, the exchnge rte t which the firm exercises the option to go multintionl (ndon the host country). Thus, the firm retins its option to go multintionl over the intervl (, ). However, multintionl firm will continue operting in the host country over the intervl (, ). Notice tht >. Let I nd D e the sunk costs in foreign currency of undertking the proects of going multintionl nd exporting respectively. The vlue mtching nd the smooth psting conditions will e given y V V V V ( ) V ( ) ( ) V ( ) I I ( ) V ( ) ( ) V ( ) D D (5) The equtions in (5) form nonliner system tht hs to e solved for A, B, nd.. The cse of nonliner demnd nd cost functions Let the foreign currency mrket price e given y the following inverse nonliner demnd function P αq with α >, - > β > (6) The totl cost is ssumed to e lso nonliner C ( Q ) γ Q with γ >, > β (7) The firm solves the following prolem whtever the stte mx ( t ) ( ) [ ] ] β τ αq γ Q (8) 5

6 6 where τ [,]. Positive vlues of τ cn e interpreted s iceerg-type trnsport costs rther thn s n d-vlorem triff ecuse trde restriction re normlly used to protect locl producers from foreign competition, so in this cse triff mkes no sense. t is tx rte on profits. The solution of the mximiztion prolem gives ( ) [ ] ( ) β γ β α τ Q ( ) [ ] ( ) β β γ β α τ α P The profit s function of is given y ( ) ( ) ( ) ( ) [ ] ( ) nd Where β γ β α γ β τ π k k K k K t With the expected present vlue of the current profits eing () ( ) ( ) ( ) ( ) [ ] ( ) ρ µ σ τ π ρ k t k k K t dt e t E 3 Numericl Results 3. Bseline cse Consider set of seline prmeter vlues to ttiin the numericl solution. Assume tht α5, β-.5, γ, τt t, σ., µ, ρ.5, nd ID. Figure shows the effect of chnges in the prmeters of the demnd nd cost functions on the trigger exchnge rtes (, ). The upper left pnel shows the cse of chnges in α, which cn e interpreted s chnges in the mrket size. This is the cse of n exogenous shift in demnd tht cuses equilirium prices nd quntities to rise.

7 rises nd flls s α increses, leding to decrese in the degree of hysteresis. The higher price nd quntity push operting profits up. Therefore, if the firm is exporting; going multintionl would e profitle t higher. However, if the firm is multintionl; to ndon the host country it will require lower ecuse the higher profits mke exporting more profitle. However, it should e noticed tht in smll mrkets the trigger exchnge rte is more sensitive, while in medium nd lrge mrkets the trigger exchnge rtes hrdly vry. The upper right pnel of Figure shows tht lower solute vlues of β mke hysteresis decrese. Notice tht lower solute vlue of β implies in solute vlue higher price elsticity of the demnd function, which is /β. A higher price elsticity increses operting profits, so we cn pply resoning similr to the cse of mrket size. The lower left nd right pnels of Figure show the cse for γ nd. In oth cses ( ) decreses (increses) with higher vlues of these prmeters, pushing the degree of hysteresis down. Notice tht n increse in these prmeters pushes operting profits down, so if the firm is exporting it will undertke the multintionl proect if the cost of investment is lower, which implies tht the exchnge rte would hve to e lower. imilrly, if the firm is multintionl it will require higher exchnge rte to stop producing in the host country nd ecome n exporter. [INERT FIGURE ] 3. Txtion 7

8 We re interested in results tht show the effect of tx policy on the decision of where to locte production. Tx reduction could e used s tool for ttrcting or voiding reloction of firms. Figure shows how the trigger exchnge rte rects to chnges in txtion in oth countries. The solid lines re the trigger exchnge rtes when the domestic tx rte vries from zero to five times the foreign tx rte. The dshed lines re the trigger exchnge rtes when the foreign tx rte vries from zero to five times the domestic tx rte. The results in oth cses support the intuition. Consider the cse of chnges in the tx policy of the domestic economy. If the firm is exporting, decrese in the domestic tx rte respect to the foreign tx rte will drive down, so it cn e interpreted s wy of deterring the firm from going multintionl. Along the sme lines, if the firm is multintionl reduction in the domestic tx rte will drive down, so the multintionl firm will soon ecome n exporter, which cn e interpreted s n incentive to ttrct the domestic firm to produce in its own country. A similr rgument pplies in the cse of chnges in foreign txtion reltive to domestic txtion (dshed line). If the firm is exporting, decrese in the foreign tx rte respect to the domestic tx rte will drive up, so it cn e interpreted s wy of ttrcting foreign direct investment, nd if the firm is multintionl the sme policy will lso drive up, which is wy of voiding reloction. [INERT FIGURE ] We lso compute the totl tx pid y the firm in stte. T k [ ] K ( ) t (( τ ) ) With the expected present vlue of txes eing 8

9 E T ( () t ) e ρt dt t σ k [(( τ ) ) ] ( k ) µ k ρ K Figure 3 shows the expected present vlue of tx pyments in domestic currency y the firm in stte. The figure is drwn for t t.. It should e noticed tht with n equl tx rte in the rnge (, ) if the firm is multintionl it pys more txes. It is lso very striking tht if the firm is exporting, the differences in tx pyments re higher s long s tends to. Thus, if reches the firm will go multintionl even if the difference in tx pyments is higher. Therefore, with n equl tx rte, tx pyments re not determinnt in the decision whether to relocte of production. [INERT FIGURE 3] 3.3 Lor costs It is often rgued tht, in generl, reloction of production is ttrcted y low lor cost. In this section we wnt to know whether in the cse of exchnge rte uncertinty firm loctes production to tke dvntge of low lor costs. Let w e the wge rte in stte. As w is not explicitly defined in our model, let us work on the cost function in order to otin it. Eqution (7) could e generted y Co-Dougls production function s Q ( H L ) H L, > f where L re units of lor used in the production process nd H re units of ny other input. olving the prolem of minimizing cost, the cost function cn e written s 9

10 ( ) Q w r Q r w C,, where r is the price of input H. The input demnd functions re ( ) Q w r Q r w H,, ( ) Q w r Q r w L,, From our cost function (7), notice tht w r γ Finlly the lor cost cn e written s function of the exchnge rte ( ) L w LC The expected present vlue is () ( ) dt e t LC E t ρ Figure 4 shows the expected present vlue of lor costs in oth sttes. Notice tht in the rnge (, ) if the firm is multintionl it incurs lower lor costs. However, if the firm is exporting it ers higher costs. Notice lso tht cost differences re much higher s moves wy from. It is lso striking tht when the firm switches from exporting to setting up plnt in the host country lor costs re similr, which mens tht in this cse lor cost plys no role in ttrcting foreign direct investment. However, when

11 multintionl firm decides to ecome n exporter the chnges in costs re lrger. The explntion of this pprent contrdiction is tht the deprecition of the exchnge rte cn offset the higher lor costs, mking exporting more profitle thn eing multintionl. In ny cse we cn see tht lor costs re not determinnt in the decision where to locte production under exchnge rte uncertinty. [INERT FIGURE 4] 4 Conclusions We present model of n interntionl monopolist under exchnge rte uncertinty. We consider tht the firm hs the option to locte production domesticlly nd export to foreign mrket or to locte production in the host country nd serve it s multintionl. This decision is ffected y chnges in the prmeters of the demnd nd cost functions. Tx reduction cn e used s tool to ttrct nd void reloction. Much more interestingly, with equl tx rtes in the rnge of the exchnge rte in which the firm could e multintionl or n exporter, it would py more txes s multintionl. Our results on lor costs show tht the firm would incur lower lor costs s multintionl. However, we hve shown tht lor costs re not determinnt in the decision where to locte production under exchnge rte uncertinty.

12 References Ary, H. nd Grdezl, J. (6). Going Multintionl under Exchnge Rte Uncertinty, Blonigen, B.A. (997). Firm-pecific Assets nd the Link etween Exchnge Rtes nd Foreign Direct Investment, The Americn Economic Review 87, (3), Cmp, J.M. (993). Entry y Foreign Firms in the United ttes under Exchnge Rte Uncertinty, Review of Economics nd ttistics Novemer, 75(4), 64-. Dixit, A.(989). Entry nd Exit Decisions under Uncertinty. Journl of Politicl Economy 97, (3), Dixit A. nd Pyndyck, R. (994). Investment under Uncertinty, Princeton University Press. Golderg, Lind. nd Kolstd, C.D. (995). Foreign Direct Investment, Exchnge Rte Vriility nd Demnd Uncertinty. Interntionl Economic Review, 53, (4), ung, H. nd Lpn, H.A. (). trtegic Foreign Direct Investment nd Exchnge Rte Uncertinty. Interntionl Economic Review 4, (), 4-43.

13 Figure : Effect of chnges in the prmeters of the demnd nd cost functions on hysteresis 3

14 Figure : Reltive txes: domestic (solid line) nd foreign (dshed line). 4

15 Figure 3: Expected present vlue of tx pyments. olid lines () nd dshed lines ().] 5

16 Figure 4: Expected Present Vlue of Lor Costs in Domestic Currency. olid line () nd dshed line () 6