Question

The supply and demand for 9-volt batteries are given by QD = 230 – 10P and QS = 30P – 10, where P is the price per four-pack and Q measures the number of four-packs.

a. What are the levels of consumer and producer surplus at the equilibrium price?

b. Suppose that a hurricane causes widespread blackouts, shifting the demand curve for 9-volt batteries outward, with the new demand curve equal to QD = 690 – 10P. If the government sets a price ceiling equal to the pre-hurricane price (the old equilibrium price), what is the level of consumer surplus?

c. If the government did not impose the price ceiling, what would consumer surplus equal? Are consumers better off with the price ceiling?

Answer 1

a. Equilibrium Price and quantity will be decided where Qs=Qd

230 – 10P = 30P – 10

240= 40P

P*= 6

Q= 30*6-10= 180-10

Q*=170

Demand choke price= $23

Supply choke price=$0.33

Consumer surplus is the area below the demand curve and above the price level.

CS= 1/2*(23-6)*170= $1445

Producer surplus is the area above the supply curve and below the price level.

PS= 1/2*(6-0.33)*170= $481.95

B.

New Equilibrium Price and quantity will be decided where Qs=Qd

690 – 10P = 30P – 10

700= 40P

P**= 17.5

Q= 690-10*17.5

Q**=515

With price ceiling of $6, price cannot rise more than $6

New Qd at $6=690-10*6= 630

Supply at $6= 30*6-10= 170

Price when Qd at 170=690-10P

P= $52

Consumer surplus=

CS= 1/2*(69-52)*(170)+ (52-6)*(170)

=$9265

C if the government did not impose price ceiling

Demand choke price= $69

Consumer surplus is the area below the demand curve and above the price level.

CS= 1/2*(69-17.5)*515= $13261.25

Conauemr surplus is lower under price ceiling, consumers are not better off with price ceiling.

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