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Productivity and Taxes as Drivers of FDI

Productivity and Taxes as Drivers of FDI

nonnegative. We denote

nonnegative. We denote by ε the upper bound of the productivity factor, that isG( ε ) = 1.Note, however, that an ε -firm may choose not to invest at all (that is, to stick toits existing stock of capital,0KH) and avoid the lumpy setup costwith a low ε may not find it worthwhile to incur the setup costpresent value isCH. Naturally, a firmCH. In this case, its0 0− 0 ⎧ AHF( KH, L)(1 + ε) − wHL+ (1 −δ)K ⎫HV ( AH, KH, ε, wH) = max⎨ ⎬ .L⎩1+r⎭( 5 )The labor demand of such a firm, denoted byL A K w−0(H, H, ε, H), is defines byA F K L + = w .0H L( H, )(1 ε )H( 6 )A firm will choose to make a new investment if its present value with the investmentexceeds its present value without the investment. Naturally, a higher productivity firm(namely, a firm with a higher ε ) benefits more from investment; that is, the gap betweenV + and V − increases with ε (a formal proof is available in Razin and Sadka (2007) ).Therefore, there exists a cutoff level of ε , denoted by ε0, such that an ε -firm will makea new investment if, and only if, ε > ε0. This cutoff level of ε depends onA , C , K ,0H H HandwH. We write the cutoff ε asε00( AH, CH, KH, wH). It is defined implicitly byV ( A , K , ε , w ) − C = V ( A , K , ε , w ) .+ 0 −0H H 0 H H H H 0 H( 7 )7

That is, the cutoff productivity level is the level at which the firm is just indifferentbetween making a new investment, incurring the setup cost, and sticking to its existingcapital stock, avoiding the setup cost.The wage ratewHis determined in equilibrium by a clearance in the labormarket. We assume that labor is confined within national borders. Denoting the country’sendowment of labor by0L H , we have the following labor market-clearing equation:0ε0( AH , CH , KH , wH)− 0H ∫ (H, H, ,H) ( )−1N L A K ε w g ε dε0{ 1 ⎡ε0( , , , ) ⎤}+ N −G ⎣ A C K w ⎦ LCH H H H H Hε∫+ N L ( A , ε, w ) g( ε) dε= L .+H H H0ε0( AH , CH , KH , wH)0HDividing the latter equation through byNHyieldsε00 ( AH , CH , KH , wH)−10{ 1 ⎡ε0( , , , ) ⎤}00 ( AH , CH , KH , wH)L A K ε w g ε dε−0(H, H, ,H) ( )+ −G ⎣ A C K w ⎦ LεCH H H H H++ L ( A , ε, w ) g( ε)dε= Lε∫∫HH0H( 9 )where0H0≡ H His the amount of labor per firm. (Note that there are NH[ 1 − G( ε0)]L L Nfirms that make new investments, employing an extra fixed input ofCLH.)Note that no similar marker-clearing equation is specified for capital, because weassume that capital is freely mobile internationally and its rate of return (n ) is equalizedinternationally. The same description with the subscript S replacing H holds for thesource-country.8

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