Monopolies at Sea: The Role of Onboard Sales for the Cruise Industry’s Growth and Profitability

Abstract

For 15 years or more, cruise ship tourism has been referred to as the fastest growing segment of the tourism sector (e.g. Charlier and McCalla 2006; Dickinson and Vladimir 2007; Dowling 2006; Hobson 1993; Petrick 2004b; Wie 2005; Yarnal and Kerstetter 2005), echoing a claim that is renewed annually by the Cruise Lines International Association (CLIA) in their “market overview”. According to CLIA, which represents over 80% of the ocean cruise capacities globally, the number of passengers travelling with their member lines has grown by 7.4% per year between 1980 and 2008 to 13.2 million (CLIA 2009).

Appendices

Appendix A: Proof of Sufficiency of First-Order Conditions

The first-order conditions (13.7)–(13.9) are sufficient for a local maximum of the Lagrangean L = [p _x – c _x  + (p _y – c _y )ap _y ^–ε – λ] (p _x  + b)^–δ – k (c _k – λ) if the (bordered) Hessian determinant

$$ \left| H \right| = \left| {\begin{array}{lllll} {\frac{{{\partial^2}L}}{{\partial {\lambda^2}}}} & {\frac{{{\partial^2}L}}{{\partial \lambda \partial {p_x}}}} & {\frac{{{\partial^2}L}}{{\partial \lambda \partial {p_y}}}} \\{\frac{{{\partial^2}L}}{{\partial \lambda \partial {p_x}}}} & {\frac{{{\partial^2}L}}{{\partial {p_x}^2}}} & {\frac{{{\partial^2}L}}{{\partial {p_x}\partial {p_y}}}} \\{\frac{{{\partial^2}L}}{{\partial \lambda \partial {p_y}}}} & {\frac{{{\partial^2}L}}{{\partial {p_x}\partial {p_y}}}} & {\frac{{{\partial^2}L}}{{\partial {p_y}^2}}} \\\end{array} } \right|, $$

evaluated in the optimum is positive (Chiang and Wainwright 2005). Since ${\partial^2}L/\partial {\lambda^2} = {\partial^2}L/(\partial \lambda \partial {p_y}) = 0$, the condition reduces to

$$ \left| H \right| = - {\left( {\frac{{{\partial^2}L}}{{\partial \lambda \partial {p_x}}}} \right)^{\!\!2}}\frac{{{\partial^2}L}}{{\partial {p_y}^2}} > 0. $$

It is clear that ${[{\partial^2}L/(\partial \lambda \partial {p_x})]^2} > 0$. Upon substitution from (13.7), ${\partial^2}L/\partial {p_y}^2 = (1 - \varepsilon )/\varepsilon$. Since by assumption, ε > 1, it follows that ${\partial^2}L/\partial {p_y}^2 < 0$ and that that (13.7)–(13.9) are indeed sufficient for a local maximum.

Appendix B: Derivatives of Net Onboard Revenue

Solving (13.17) for r _y yields

$$ {r_y} = {c_x} + {c_k} + b - \frac{{\delta - 1}}{\delta }{k^*}^{ - 1/\delta }, $$

so that total net onboard revenue can be written as

$$ {k^*}{r_y} = ({c_x} + {c_k} + b){k^*} - \frac{{\delta - 1}}{\delta }{k^*}^{1 - 1/\delta }, $$

which has the first and second-order derivatives

$$ \frac{{d({r_y}{k^*})}}{{d{k^*}}} = {c_x} + {c_k} + b - {\left( {\frac{{\delta - 1}}{\delta }} \right)^{\!\!2}}{k^*}^{ - 1/\delta } = {r_y} + \frac{{\delta - 1}}{{{\delta^2}}}{k^*}^{ - 1/\delta } > 0 $$

$$ \frac{{{d^2}({r_y}{k^*})}}{{d{k^{*2}}}} = \frac{{{{(\delta - 1)}^2}}}{{{\delta^3}}}{k^*}^{ - 1 - 1/\delta } > 0 $$