Question

(i) A monopolist has the following total cost function:
C=50+10Q+0.5Q^{2}

^{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.

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