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. [4]

b. Determine the profit-maximizing price during weekdays and during peak hours if MC = 10 instead of zero. [4]   

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. [8]

Answer 1

Solution

 Profit-maximization problem during weekdays is:

ma(50−q)q−cq

First order condition:

50−2q−c=0

$q=\frac{50−c}{2}$

​

Profit-maximizing price is:

$p=50−\frac{50-c}{2} ​$

$=\frac{100-50+c}{2}$

$=\frac{50+c}{2}$

Profit-maximization problem during surge hours is:

max(100−q)q−cq

First order condition:

100−2q−c=0

$q=\frac{100−c}{2}$

Profit-maximizing price is:

$p=100−\frac{100-c}{2}$

$=\frac{200-100+c}{2}$

$=\frac{100+c}{2}$