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. 

Answer 1

a)

P = 50 - Q

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

MR= 50- 2Q

Week day

MR=MC

50- 2Q= 0

Q= 25

P= 50-25= 25

Peak

P = 100 - Q

TR=Q(100-Q)= 100Q-Q$^2$

MR = 100- 2Q

MR= MC

100-2Q= 0

Q= 50

P= 100-50= 50

b)

Week day

MR= MC

50- 2Q=10

Q= 20

P= 50- 20= 30

Peak

100 - 2Q=10

Q= 45

P=100-45= 55

c)

Dead weight= $\frac{1}{2} \times (55-10)\times 90-45)=1012.5$