The Greening Role of Tour Operators

Abstract

This paper shows that the tour operators (TOs) can play a coordinating role in the adoption of environmental management upstream the tourism supply chain. This is done using a dynamic model to analyze the environmental management adoption by hotels in a tourism destination induced by a TO. The TO can create incentives to greening hotels’ management through the sharing of an environmental price premium. We show that the extent of green management adoption depends on interest rate, the willingness to pay for environmental quality, and hotels’ organizational inertia. We also show how the financial yields from green management are shared between TOs and hotels. Finally, we consider a destination manager that subsidizes hotels’ green management. If the destination manager does not take the greening role of TOs into account, she could mistake the true trade-off that she faces between the destination’s economic and environmental outcomes for the win–win setting that characterizes the general problem.

Appendices

Appendix I: Equilibrium Conditions

To solve expression (4) applying optimal control, we first build its Hamiltonian:

$$H = N\omega \left( {S_{\text{g}} } \right)^{\gamma } - NhS_{\text{g}} - \alpha \left[ {N\mu (h + g)} \right]^{2} + q\left[ {\mu \left( {h + g} \right)} \right]$$

where q represents the shadow value for the TO that is generated by one additional hotel deciding to be “green.” This shadow value corresponds to the discounted future stream of environmental price premiums generated by this new green hotel less the discounted future stream of payments, h, made to this hotel by the TO.

Then, the maximum principle conditions (Chiang 1992) are

$$\frac{\partial H}{\partial h} = - NS_{\text{g}} - 2 \alpha (N\mu )^{2} \left( {h + g} \right) + q\mu = 0,$$

(14)

$$\frac{\partial H}{{\partial S_{g} }} = N\omega \gamma \left( {S_{g} } \right)^{\gamma - 1} - Nh = rq - \dot{q},$$

(15)

$$\frac{\partial H}{\partial q} = \mu \left( {h + g} \right) = \mathop {\dot{S}g}\limits^{{}},$$

(16)

and the transversality condition (Chiang 1992):

$$\mathop {\lim }\limits_{t \to \infty } e^{ - rt} S_{\text{g}} = 0.$$

(17)

To obtain expression (5), we first obtain the value of “q” from (14)

$$q = \left[ {\frac{1}{\mu }} \right]\left[ {NS_{\text{g}} + 2\alpha (N\mu )^{2} \left( {h + g} \right)} \right].$$

(18)

Taking the derivative with respect to time, the expression (18) gives place to

$$\dot{q} = \left[ {\frac{1}{\mu }} \right]\left[ {N\mathop {\dot{S}_{\text{g}} }\limits^{{}} + 2\alpha (N\mu )^{2} \left( {\dot{h}} \right)} \right].$$

(19)

Then, from (15) and (18):

$$\mathop {\dot{q} }\limits^{{}} = - N\omega \gamma \left( {S_{\text{g}} } \right)^{\gamma - 1} + Nh + \frac{rNSg}{\mu } + 2\alpha \mu rN^{2} \left( {h + g} \right).$$

(20)

From (20) and (16) in (19),

$$\dot{h} = \frac{r}{{2N\alpha \mu^{2} }} Sg - \frac{\omega \gamma }{2N\alpha \mu }S_{\text{g}}^{\gamma - 1} + rh + \frac{2Nr\alpha \mu - 1}{2N\alpha \mu } g.$$

(21)

Combining (3) with (21) and (16) we obtain (5) and (6), respectively.

Appendix II: Stability Conditions

A steady state of the system (5), (6) is locally asymptotically stable when the determinant of the Jacobian evaluated at that equilibrium has a positive value while the trace is negative. It is locally asymptotically unstable when both the determinant and the trace are positive, whereas it is a saddle-point when the determinant is negative. Through linearization we obtain a system whose Jacobian is the following equations:

$$J_{11} = \frac{{\partial \dot{h}}}{\partial h} = r,$$

$$J_{12} = \frac{{\partial \dot{h}}}{{\partial P_{\phi }^{*} }} = \frac{r}{{2N\gamma \alpha \mu^{2} }}\left( {\frac{{P_{\phi }^{*} }}{\omega }} \right)^{{\frac{1}{\gamma }}} \frac{1}{{P_{\phi }^{*} }} + \frac{{\omega \left( {1 - \gamma } \right)}}{2N\alpha \mu }\left( {\frac{\omega }{{P_{\phi }^{*} }}} \right)^{{\frac{1 - \gamma }{\gamma }}} \frac{1}{{P_{\phi }^{*} }},$$

$$J_{21} = \frac{{\partial \mathop {\dot{P}_{\phi } }\limits^{{}} }}{\partial h} = \gamma \mu \omega^{{\frac{1}{\gamma }}} \frac{1}{{P_{\phi }^{{*\frac{1 - \gamma }{\gamma }}} }},$$

$$J_{22} = \frac{{\partial \mathop {\dot{P}_{\phi } }\limits^{{}} }}{{\partial P_{\phi } }} = 0,$$

where a star indicates a steady state value. From mere inspection, and given that $P_{\phi } \ge 0$, it is clear that the determinant of the Jacobian is negative and, therefore, the steady state is saddle path.