# Question

The Heritage Club at Harbor Town offers elegant accommodations for discriminating vacationers on Hilton Head Island, South Carolina. Like many vacation resorts, Heritage Club has discovered the advantages of offering its services on an annual membership or “time-sharing” basis. To illustrate, assume that an individual vacationer’s weekly demand and marginal revenue curves can be written:

P = $6,500 - $1,250Q,

MR = ∂TR/∂Q = $6,500 - $2,500Q,

Where P is the price of a single week of vacation time, and Q is the number of weeks of vacation time purchased during a given year. For simplicity, assume that the resort’s marginal cost for a week of vacation time is $1,500, and that fixed costs are nil. This gives the following total and marginal cost relations:

TC = $1,500Q,

MC = ∂TC/∂Q = $1,500.

A. Calculate the profit-maximizing price, output, profit, and consumer surplus assuming a uniform per unit price is charged each customer.

B. Calculate the profit-maximizing price, output and profit assuming a two-part pricing strategy is adopted for each customer.

C. Now assume that fixed costs of $4 million per year are incurred, and that 500 time-share customers (“owners”) are attracted when an optimal two-part pricing strategy is adopted. Calculate total annual profits.

P = $6,500 - $1,250Q,

MR = ∂TR/∂Q = $6,500 - $2,500Q,

Where P is the price of a single week of vacation time, and Q is the number of weeks of vacation time purchased during a given year. For simplicity, assume that the resort’s marginal cost for a week of vacation time is $1,500, and that fixed costs are nil. This gives the following total and marginal cost relations:

TC = $1,500Q,

MC = ∂TC/∂Q = $1,500.

A. Calculate the profit-maximizing price, output, profit, and consumer surplus assuming a uniform per unit price is charged each customer.

B. Calculate the profit-maximizing price, output and profit assuming a two-part pricing strategy is adopted for each customer.

C. Now assume that fixed costs of $4 million per year are incurred, and that 500 time-share customers (“owners”) are attracted when an optimal two-part pricing strategy is adopted. Calculate total annual profits.

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