Question

Suppose a perfectly competitive market has the following inverse supply and demand curves:

Supply: P= 5+2Q Demand: P = 50-Q.

1) Solve for the perfectly competitive Pe and Qe, and calculate consumer+producer surplus at Pe, Qe.

2) Suppose each unit of good produced created a negative externality to society valued at $1 per unit. Calculate the social optimum Pe and Qe for this case and compute consumer+producer surplus.

3) Show graphically the welfare loss if the externality is ignored.

Answer 1

1). Perfect competition EQUILIBRIUM is at where market supply is EQUALS to market demand.

5+2Q=50-Q

3Q=45

Qe=45/3=15

Pe=5+2Q=5+2*15=35

Highest price CONSUMER willing to pay or price at demand Q=0

P=50-0=50

Minimum price at which producer wants to sell or price of supply at Q=0

P=5+2*0=5

CONSUMER surplus=0.5*Qe*(highest price CONSUMER willing to pay - Pe)

=0.5*15*(50-35)=0.5*15*15=112.5

Producer surplus=0.5*Qe*(pe- minimum price at which seller want to sell)

=0.5*15*(35-5)=0.5*15*30=225

CS+PS=112.5+225=337.5

2).social marginal cost =private marginal cost + externalities cost

Supply curve is nothing but producer marginal cost function.

So ,

Social marginal cost=5+2Q+1=6+2Q

Again market demand =social marginal cost or social optimal supply

50-Q=6+2Q

3Q=44

Qe=44/3=14.66

Pe=50-44/3=(150-44)/3=106/3=35.33

CS=0.5*44/3*(50-106/3)=0.5*44/3*44/3=107.5

PS=0.5*44/3*(106/3-5)=0.5*44/3*91/3=222.4

CS+PS=107.5+222.4=329.9

3).