dollars, D, represents debt outstanding in period 

 t, r is the real rate of interest on debt capital, p is 

 the real after-tax opportunity rate of return on 

 equity capital desired by fishermen, Qj is the real 

 price paid for the^'^ category of fishing vessels at 

 the retail level, a is the proportion of investment 

 financed with equity capital, i^. is the investment 

 tax credit rate, and Rjt represents the real level of 

 replacement investment in the j^^ category of 

 fishing vessels required in period t to offset losses 

 in productive capacity due to wearout. 



The entire term on the left-hand side of the 

 inequality sign in Equation (1) represents the 

 present value of the additional net cash flows gen- 

 erated by a permanent addition to the^'^ category 

 of fishing vessels. It is assumed that both the in- 

 terest and the principal payments, ((tP/SK^) and 

 r(dD/BK, ), vary over time as further expenditures 

 are required to maintain the productive capacity 

 of this addition to the capital stock at its original 

 level. The right-hand side of Equation (1) repre- 

 sents the initial downpayment minus the invest- 

 ment tax credit plus the present value of all fu- 

 ture cash outlays required to maintain the stock 

 of the j^^ category of fishing vessels at its new 

 level. 



To maximize the present value of their equity. 

 Gulf shrimp fishermen would continue to add to 

 the stock of the j^^ category of fishing vessels 

 until Equation (1) holds as an equality. Equiva- 

 lently, maximization of the present value of 

 owner equity requires thaf* 



pidX/dKj) = j^^ 



a 



ic + Z - A 



(1 - iy) 



(2) 



where F, represents the present value of the 

 stream of capacity depreciation of they '^^ category 

 of vessels and iy is the average income tax rate. 

 The term Z represents the present value of the 

 stream of after-tax interest payments and princi- 

 pal payments on debt while A represents the 

 present value of the stream of tax depreciation 

 allowances that can be claimed for each dollar of 

 investment as the stock of vessels is maintained 

 at its new level. ^ The right-hand side of this ex- 



4Equation (1) as well as the derivation of the implicit rental 

 price of vessels (c) assume that fishermen expect real prices (p) 

 and the marginal physical product of vessels dX/dK to remain at 

 current levels. These and other assumptions which allow us to 

 treat many components of Equation (1) as consoles are consis- 

 tent with those employed in Penson et al. (1981) and Coen 

 (1975). 



pression thus represents the implicit rental price 

 of the J^^ category of fishing vessels. 



The concept of the implicit rental price of capi- 

 tal has been widely employed in previous studies 

 of investment behavior as a determinant of the 

 capital stock which firms desire to hold (e.g., Coen 

 1968, 1975; Penson et al. 1981). Equation (2) sug- 

 gests that the implicit rental price of they*^^ cate- 

 gory of fishing vessels will increase if their pur- 

 chase price, the cost of debt, and equity capital, or 

 income tax rates increase. These effects, however, 

 will be offset to some extent by an increase in 

 the investment tax credit rate, the deductibil- 

 ity of tax depreciation allowances, and interest 

 expenses. 



Let us assume that output in this industry is a 

 function, in part, of the stock of fishing vessels 

 and that this production relationship is of the 

 Cobb-Douglas form. Letting p^ represent the par- 

 tial production elasticity associated with the 

 stock of the 7'^ category of fishing vessels (Kj), 

 the marginal physical product for these vessels 

 can be expressed as follows: 



idX/dKj) = i^jiX/Kj). 



(3) 



Substituting Equation (3) into Equation (2), the 

 desired stock of they'*^^ category of fishing vessels 

 at the end of year t can be expressed as follows: 



K*jt^^j{pX/Cjh 



(4) 



where Cj represents the expected implicit rental 

 price of they '^'^ category of fishing vessels given by 

 the right-hand of Equation (2). Equation (4) im- 

 plies that the desired stock ofj^^ category of fish- 

 ing vessels is directly related to the expected real 

 gross income from Gulf shrimp fishing and is in- 



^The nominal value of Z (the present value of the stream of 

 after-tax loan payments) in Equation (2) is equal to 



n 



il -iyW 2j d,(l + ^)''{1 + p)-' 



i = 1 

 n 



+ ^ ^ (e - d,)(l -I- (J))-'(l -h p)-' 

 ( = 1 

 while the real value of A (the present value of the stream of 

 depreciation allowances is equal to 



i^(hl(p + A> + pi> + ^)) 



where d^ is equal to the nominal interest payment on a loan of 

 one constant dollar, (J) is the inflation rate, e is the nominal 

 amortized loan payment on a loan of one current dollar, and 8 is 

 the tax depreciation rate given by 2ln where n is the service life 

 of the vessel. 



152 



