Suppose Island Bikes, a profit-maximizing firm, is the only bike rental company in a small resort town. The marginal cost to Island Bikes of renting out a bike is $3, and Island Bikes has no fixed costs. Each day Island Bikes has six potential customers, whose reservations prices are listed below. $$\begin{array} { | c | c | }
\hline \text { Customer } & \begin{array} { c }
\text { Reservation Price } \
\text { (\$/Rental) }
\end{array} \
\hline \mathrm { A } & 22 \
\hline \mathrm { B } & 16 \
\hline \mathrm { C } & 12 \
\hline \mathrm { D } & 8 \
\hline \mathrm { E } & 6 \
\hline \mathrm { F } & 4 \
\hline
\end{array}$$ Suppose Island Bikes knows that customers whose reservation prices are at least $10 always rent bikes before noon, while those whose reservation prices are below $10 never do so. If Island bikes charges different price in the morning and in the afternoon, then what will be its daily economic profit?

Question

Suppose Island Bikes, a profit-maximizing firm, is the only bike rental company in a small resort town. The marginal cost to Island Bikes of renting out a bike is $3, and Island Bikes has no fixed costs. Each day Island Bikes has six potential customers, whose reservations prices are listed below. $$\begin{array} { | c | c | } 
\hline \text { Customer } & \begin{array} { c } 
\text { Reservation Price } \
\text { (\$/Rental) }
\end{array} \
\hline \mathrm { A } & 22 \
\hline \mathrm { B } & 16 \
\hline \mathrm { C } & 12 \
\hline \mathrm { D } & 8 \
\hline \mathrm { E } & 6 \
\hline \mathrm { F } & 4 \
\hline
\end{array}$$ Suppose Island Bikes knows that customers whose reservation prices are at least $10 always rent bikes before noon, while those whose reservation prices are below $10 never do so. If Island bikes charges different price in the morning and in the afternoon, then what will be its daily economic profit?

Quizplus · Accepted Answer

Island Bikes can use price discrimination and charge a higher price to customers with a higher reservation price. Since customers with a reservation price of at least $10 always rent bikes before noon, Island Bikes can charge a higher price in the morning and a lower price in the afternoon.

To maximize profit, Island Bikes should charge the highest price that each customer is willing to pay. The optimal pricing strategy for Island Bikes is as follows:

- Charge customer A $22 in the morning
- Charge customer B $16 in the morning
- Charge customer C $10 in the morning and $6 in the afternoon
- Charge customers D, E, and F $3 in the afternoon (since they have reservation prices below $10 and will not rent before noon)

With this pricing strategy, Island Bikes will rent out bikes to all six customers and make a daily economic profit of:

[(Price charged - Marginal cost) x Quantity sold] = [(22-3) x 1] + [(16-3) x 1] + [(10-3) x 1] + [(6-3) x 3] = $33

Therefore, the answer is C.

Suppose Island Bikes, a Profit-Maximizing Firm, Is the Only Bike