Problem 5 Monopoly Suppose that in order to protect industry

Problem 5 Monopoly Suppose that in order to protect industry profits from recent cost increases, a in the giant cookie market merged to found 1 giant giant cookie manufacturer, with new cost function c(y)-96-2y-+6y2. Consumer demand remains Qd = 492-4 ll firms 3. F 5. Suppose the government institutes a price cap at p 70 in an attempt to move closer to the competitive equilibrium. Find the quantity produced, market price, consumer surplus, producer surplus, and deadweight loss. Who gains and who loses from regulation? Is the regulation welfare improving? 6. Calculate the elasticity of demand at the monopoly\'s optimal y 7. Explain why the giant cookie monopoly has little market power.

Solution

Ans a)

Demand is given as

Q=492-4p

P=(492-Q)/4=123-0.25Q

Ans b)

For Monopolist Profit maximising condition is MR=MC

C(y)=96-2y+6y^2

MC=-2+12y and R=Price*y=(123-0.25y)*y=123y-0.23y^2

MR=123-0.46y

MR=MC

123-0.46y=-2+12y

125=12.46y

125/12.46=y=10(approx.)

Price=123-0.25(10)=120

Profit=R-C=P*y-96+2y-6y^2=120*10-96+2(10)-6(10)^2=524

Ans c)

Consumer Surplus=1/2(123-120)*(10)=15

We have no Supply Curve for monopolist then no Producer surplus\\

If Prefect competition P=MC

492-y=-2+12y

494=13y

y=38

P=123-0.25(38)=113.5=113

Consumer Surplus=1/2(123-113)(38)=190

DeadWeight Loss=CS in Monopolist-CS in Perfect Competition=15-190=-175

Ans 6)

Elasticity of Demand=dy/y*p/dp=(dy/dp)*(p/y)

dy/dp=-4 and p/y=(123-0.25y)/y=123/y-0.25

Elasticity of Demand=1-(492/y)