Question

Chocolate Market research has revealed the following information about the market for chocolate bars. The demand schedule for chocolate is represented by the equation D = 1,600 − 300P where D is the demand for chocolate and P is the price of chocolate. The supply schedule for chocolate is represented by the equation S = 1, 400 + 700P where S is the supply of chocolate. a. Calculate the equilibrium price and quantity of chocolate. b. Chocolate makes people happy, which angers the Puritan Party (they do not like puppies much either). Suppose that the Puritans seize power and impose a quota of S = 1,000. How much has consumer welfare fallen as a result of quota? c. Has the total level of spending in the market for chocolate risen or fallen as a result of the quota? d. Given your answer in (c ) above, is the demand for chocolate price elastic or price inelastic?

Answer 1

a)

In equilibrium, quantity demanded is equal to quantity supplied. So,

D=S

1600-300P=1400+700P

1000P=200

P=$0.20

D=1600-300*0.2=1540

S=1400+700*0.2=1540

Equilibrium price=$0.20

Equilibrium quantity=D=S=1540

b)

In presence of quota, supply curve changes to

S'=1000

Set D=S' for equilibrium

1600-300P=1000

300P=600

P=$2.00

Let us calculate the price at which quantity demanded is zero

1600-300P=0

P=1600/300=16/3

Consumer Surplus is the area under the demand curve at market price.

Consumer Surplus in initial state=CS1=1/2*(16/3-0.2)*(1540-0)=$3952.67

Consumer Surplus when quota is places=CS2=1/2*(16/3-2.0)*(1000-0)=$1666.67

Decrease in consumer welfare=Decrease in consumer surplus=3952.67-1666.67=$2286

c)

Total spending in initial state=P*Q=0.2*1540=$308

Total spending in case of quota=P*Q=2*1000=$2000

We observe that total spending has increased post quota.

d)

We observe that there is a increase in total spending despite a price hike. It means that demand is price inelastic.