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. $$\begin{array} { | c | c | }
\hline \text { Customer } & \begin{array} { c }
\text { Reservation Price } \
( \$ / \text { Rental } )
\end{array} \
\hline \mathrm { A } & 22 \
\hline \mathrm { B } & 16 \
\hline \mathrm { C } & 12 \
\hline \mathrm { D } & 8 \
\hline \mathrm { E } & 6 \
\hline \mathrm { F } & 4 \
\hline
\end{array}$$ What is the socially optimal number of bikes for Island Bikes to rent out each day?

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. $$\begin{array} { | c | c | } 
\hline \text { Customer } & \begin{array} { c } 
\text { Reservation Price } \
( \$ / \text { Rental } )
\end{array} \
\hline \mathrm { A } & 22 \
\hline \mathrm { B } & 16 \
\hline \mathrm { C } & 12 \
\hline \mathrm { D } & 8 \
\hline \mathrm { E } & 6 \
\hline \mathrm { F } & 4 \
\hline
\end{array}$$ What is the socially optimal number of bikes for Island Bikes to rent out each day?

Quizplus · Accepted Answer

The socially optimal number of bikes is 6 because it maximizes the total surplus in the market. At this quantity, the marginal benefit to society (the sum of the reservation prices of the six customers) is equal to the marginal cost to Island Bikes.

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