Question

(i) A monopolist has the following total cost function: C=50+10Q+0.5Q²

^{They face the market demand of: P= 210-2Q}

^{a. What is the profit maximizing price and quantity set by this monopoly? What is the monopolist's profit?}

^{b. Calculate the producer surplus, consumer surplus, and deadweight loss.}

^{c. If the price elasticity of demand faced by this monopolist at the equilibrium is -1.625, what is the Lerner Index?}

^{d. If the price elasticity of demand faced by this monopolist at the equilibrium is -4, what is the Lerner Index?}

^{e. Is the price markup charged by the monopolist higher in part c scenario or in part d scenario? Why?}

^{(ii) The supply of ride sharing drivers for the ride sharing companies Uber and Lyft is perfectly price elastic.}

^{f. Explain in detail what would be the equilibrium wage paid by Uber and Lyft.}

^{g. Suppose instead that Uber is a monopoly in the ride-sharing market. Uber introduces a tipping option on its app. With the tipping option, each rider tips t per mile, where t must be less than the wage drivers earn per mile. What is the new equilibrium wage, w**, paid by Uber?}

Answer 1

A)MC=10+q

P=210-2q

MR=210-4q

Profit Maximizing quantity at MR=MC

210-4q=10+q

Q=200/5=40

P=210-2*40=130

Profit=TR-TC=130*40 -(50+10*40+0.5*40*40)=5200-1250=3950

B) CONSUMERs surplus=1/2*40*(210-130)=20*80=1600

MC at Q=40 is=10+40=50

Producer surplus=1/2*40*(50-10) + 40*(130-50)=20*40+40*80=800+3200=4000

Perfect competition equilibrium quantity,

P=MC

210-2q=10+q

Q=200/3=66.67

Deadweight loss=1/2*(130-50)*(66.67-40)=40*26.67=1066.8

C) Lerner index=1/-(Elasticity of demand)=1/-(-1.625)=0.615

D) Lerner index=1/-(Elasticity of demand)=1/-(-4)=0.25

E)The higher the Lerner index the higher will be price mark.

So price markup is higher in part C.

It is because low Elasticity gives Monopolist opportunity to charge higher prices without losinuch Quantity demanded.