Question

The custom T-shirt printing business has many competitors, so that the perfect competition model may be considered a good approximation. Currently the market demand curve is given by Q = 120 − 1.5 p, whereas the market supply is given by Q = −20 + 2 p.

1. Determine the market equilibrium, consumer surplus, and producer surplus.

   Suppose there is a T-shirt craze that increases demand by 10% (that is, for each price, demand is now 10% greater than it was before the price increase).

2. Determine the new demand curve.

   Now go back to the initial demand curve and suppose there is an increase in the cost of blank T-shirts, an essential input into the business of selling custom T-shirts. Specifically, for each unit by each supplier, the production cost goes up by 10%.

3. Determine the new supply curve.

Answer 1

a)

Demand curve is given by

Qd=120-1.5p

Supply curve is given by

Qs=-20+2p

Put Qd=Qs for equilibrium

120-1.5p=-20+2p

3.5p=140

p=$40 (equilibrium price)

Quantity demanded at a price of $40=Qd=120-1.5*p=120-1.5*40=60 units

Quantity supplied at a price of $40=Qs=-20+2*p=-20+2*40=60 units

Equilibrium quantity =Qd=Qs=60 units

Consumer surplus is the area under demand curve and above market price. To find the CS, we need to find the price at which quantity demanded is zero i.e. the point where demand curve intersects price-axis

So, put Qd=0

120-1.5p=0

p=$80

Consumer Surplus=CS=1/2*(80-40)*(60-0)=$1200

Producer surplus is the area above supply curve and below market price. To find the PS, we need to find the price at which quantity supplied is zero i.e. the point where supply curve intersects price-axis

So, put Qs=0

-20+2p=0

p=$10

Producer Surplus=PS=1/2*(40-10)*(60-0)=$900

b)

New demand curve is given by

Qd'=(1+10%)*Qd

Qd'=1.1*(120-1.5p)

Qd'=132-1.65*p

c)

In this case, marginal cost is increased by 10%

In case of perfect competition, marginal cost is equal to market price. So, price will increase by 10% at each production level. New supply curve is given by

Qs'=-20+2*(1+10%)p=-20+2.2p