Rent Dissipation in Chartered Recreational Fishing: Inside the Black Box

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D                                           D*

∫[M¾ (∙)H_qq_z(i) + MB_sS _z(i) ]^dD ^{- [w}VN(i)^{n + w}V(i) ] — + μHqqzɑɔ

0N

= λD^*φHqqz(i)

with a virtually identical interpretation to those for fixed factors. Factoring of this condition
yields the following expression:

This equation closely resembles the standard profit maximization condition that the value of the
marginal product of an input be equated to the marginal factor price, but with three key
differences. First, our model works at the scale of the regional industry so that prices of outputs
are not exogenous to the social planner maker. Second, the production processes under
consideration are for the production of catch and non-catch quality at a given (but endogenous)
level of trips so that benefits of quality change are measured with respect to shifts in the
consumer demand function. Finally, χ_q^* and χ_S^* represent the optimal “prices” of catch and non-
catch quality and reflect the full dynamic implications of these quality changes.

Calculating (17) for another variable factor j and forming the ratio of these conditions
yields the following expression:

χq qz g)⁺ χS Sz g) = ^wVN g) ^n+wv g)
χq_l qz(j )⁺ χS* Sz(j )    ^wVN(j ) ⁿ⁺wv(j ).

If inputs are exclusive contributors to either catch or non-catch quality, this equation reduces to
the standard cost-minimizing tangency condition between the expenditure frontier and the
marginal rate of technical substitution. More generally, (18) is identical in form to the condition

15

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