Question

Uber has a monopoly on ride-sharing services. In one town, the demand curve on weekdays is given by the following equation: P = 50 - Q. However, during weekend nights, or peak hours, the demand for rides increases dramatically and the new demand curve is P = 100 - Q. Assume that marginal cost is zero.

a. Determine the profit-maximizing price during weekdays and during peak hours.

b. Determine the profit-maximizing price during weekdays and during peak hours if MC = 10 instead of zero.

c. Draw a graph showing the demand, marginal revenue, and marginal cost curves during peak hours from part (b), indicating the profit-maximizing price and quantity. Determine Uber’s profit and the deadweight loss during peak hours, and show them on the graph.

Answer 1

Total revenue during weekdays

$Price \times quantity$

$PQ = (50-Q)Q = 50Q- Q^2$

Marginal revenue is

$\frac{\Delta TR}{\Delta Q}=50-2Q$

$Q=25$

$P = 25$

During peak hours

$PQ= (100-Q)Q$

$= 100Q-Q^2$

$MR=100-2Q$

$MC =0$

$Q= 50$

$P= 50$

When Marginal cost changes to 10

Weekdays;

$50-2Q =10$

$Q=20$

$P=30$

Weekends and peak hours

$100-2Q =10$

$Q= 45$

$P= 55$