Table III. Comparison of subsidy policy... | Emerald Publishing

Table III.

Comparison of subsidy policy and cooperative pricing strategy

	Independent pricing	Incentives to passengers (Δd/person)	Incentives to travel agency or cruise company Δs/person	Cooperative pricing in a coalition
Equilibrium service price p_a	$\frac{8 α – ζ}{8 β}$	$\frac{8 α – ζ + 5 β \cdot Δ d}{8 β}$	$\frac{8 α – ζ}{8 β}$	$\frac{2 α – ζ}{2 β}$
Equilibrium market demand Q	$\frac{ζ}{8}$	$\frac{ζ + 3 β \cdot Δ d}{8}$	$\frac{ζ}{8}$	$\frac{ζ}{2}$
Profit for travel agency π_a	$\frac{ζ^{2}}{64 β}$	$\frac{{(ζ + 3 β \cdot Δ d)}^{2}}{64 β}$	$\frac{ζ^{2}}{64 β}$	$\frac{ζ^{2}}{24 β}$
Profit for cruise company π_b	$\frac{ζ^{2}}{32 β} - c_{f}$	$\frac{{(ζ + 3 β \cdot Δ d)}^{2}}{32 β} - c_{f}$	$\frac{ζ^{2}}{32 β} - c_{f}$	$\frac{43 ζ^{2}}{384 β} - c_{f}$
Profit for cruise port π_c	$\frac{ζ^{2}}{16 β}$	$\frac{ζ^{2} - {(3 β \cdot Δ d)}^{2}}{16 β}$	$\frac{ζ^{2}}{16 β}$	$\frac{37 ζ^{2}}{384 β}$

	Independent pricing	Incentives to passengers (Δd/person)	Incentives to travel agency or cruise company Δs/person	Cooperative pricing in a coalition
Equilibrium service price p_a	$\frac{8 α – ζ}{8 β}$	$\frac{8 α – ζ + 5 β \cdot Δ d}{8 β}$	$\frac{8 α – ζ}{8 β}$	$\frac{2 α – ζ}{2 β}$
Equilibrium market demand Q	$\frac{ζ}{8}$	$\frac{ζ + 3 β \cdot Δ d}{8}$	$\frac{ζ}{8}$	$\frac{ζ}{2}$
Profit for travel agency π_a	$\frac{ζ^{2}}{64 β}$	$\frac{{(ζ + 3 β \cdot Δ d)}^{2}}{64 β}$	$\frac{ζ^{2}}{64 β}$	$\frac{ζ^{2}}{24 β}$
Profit for cruise company π_b	$\frac{ζ^{2}}{32 β} - c_{f}$	$\frac{{(ζ + 3 β \cdot Δ d)}^{2}}{32 β} - c_{f}$	$\frac{ζ^{2}}{32 β} - c_{f}$	$\frac{43 ζ^{2}}{384 β} - c_{f}$
Profit for cruise port π_c	$\frac{ζ^{2}}{16 β}$	$\frac{ζ^{2} - {(3 β \cdot Δ d)}^{2}}{16 β}$	$\frac{ζ^{2}}{16 β}$	$\frac{37 ζ^{2}}{384 β}$