International recycling firm joint ventures and optimal recycling standards

Abstract

In this paper, we consider a Southern economy consisting of an upstream duopoly market for recycled materials and a downstream perfectly competitive market for final goods. In our model, the Northern and Southern recyclers can form a joint venture (JV) if bargaining is successful. Then, if we assume that the marginal cost of the Southern recycler is higher than that of the Northern recycler, we obtain the following main results in the case where the JV is established. First, a stricter recycling standard decreases the Southern recycler’s share of profits from the JV, even though it increases its overall profit. Second, the recycling standard lowers the price of recycled materials and thus decreases the price of final goods. Third, if the Southern government sets the recycling standard optimally, the optimal standard in the JV may be lower than that in the monopoly of the Northern recycler. The optimal standard in the JV then falls lower with an increase in the marginal cost of the Southern recycler. Finally, if the Southern government sets the excise duty optimally, a stricter recycling standard might increase or decrease the optimal duty level. However, in the case of the JV, it will decrease the amount of waste even when the ex-ante recycling standard is low, as long as the market for final goods is large.

Appendix 1: Comparative statics of the recycling standard and the excise duty

In the case of the JV, from (15)–(17) and (20)–(22), the impacts of the recycling standard, e, and the excise duty, t, on the output of recycled materials, y^J, their price, r^J, the profit of the JV, π^J, the share of recycler N in the JV, β, and recycler N’s (S’s) profit from the JV, π ^J _N (π ^J _S ) are as follows:

$$ \partial y^{J} /\partial e = \left( {\omega + ew^{*} } \right)/2 > 0, $$

(51)

$$ \partial r^{J} /\partial e = - \left( {a - t - w^{*} } \right)/2e^{2} < 0, $$

(52)

$$ \partial \pi^{J} /\partial e = \omega w^{*} /2 > 0, $$

(53)

$$ \partial \beta /\partial e = 4c^{R} \left( {a - t - w^{*} } \right)\left( {\omega - ec^{R} } \right)/3\omega^{3} > 0, $$

(54)

$$ \partial \pi_{N}^{J} /\partial e = \left\{ {w^{*} \left( {3\omega + 4ec^{R} } \right) + 4c^{R} \left( {\omega - ec^{R} } \right)} \right\}/12 > 0, $$

(55)

$$ \partial \pi_{S}^{J} /\partial e = \left\{ {w^{*} \left( {3\omega - 4ec^{R} } \right) - 4c^{R} \left( {\omega - ec^{R} } \right)} \right\}/12, $$

(56)

$$ \partial y^{J} /\partial t = - e/2 < 0, $$

(57)

$$ \partial r^{J} /\partial t = - 1/2e < 0, $$

(58)

$$ \partial \pi^{J} /\partial t = - \omega /2 < 0, $$

(59)

$$ \partial \beta /\partial t = 4ec^{R} \left( {\omega - ec^{R} } \right)/3\omega^{3} > 0, $$

(60)

$$ \partial \pi_{N}^{J} /\partial t = - \left( {3\omega + 4ec^{R} } \right)/12 < 0, $$

(61)

$$ \partial \pi_{S}^{J} /\partial t = - \left( {3\omega - 4ec^{R} } \right)/12 < 0. $$

(62)

In these equations, only the sign of (56) is undetermined. Here, if we evaluate ∂ π ^J _S /∂ e in (56) at c^R = (a − t)/2, we have the following equation:

$$ \partial \pi_{S}^{J} /\partial e|_{{c^{R} = \left( {a - t} \right)/2}} = \left( {a - t - w^{*} } \right)\left\{ {\left( {1 - 2e} \right)w^{*} - \left( {2 - e} \right)\left( {a - t - w^{*} } \right)} \right\}/12. $$

(63)

Therefore, we find that $\partial \pi_{S}^{J} /\partial e|_{{c^{R} = \left( {a - t} \right)/2}} < 0$ if e ≥ 1/2. This result may arise when the demand parameter a takes a large value relative to the sum of the excise duty and the price of virgin materials, and the recycling standard is then more than one-half. Even in the case of e < 1/2, it is possible for (63) to be negative as long as a is relatively large.