Question

The custom T-shirt printing business has many competitors, so that the perfect competition model may be con- sidered 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.

(a) Determine the market equilibrium

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)

(b) Determine the new demand curve.

(c) Determine the change in equilibrium quantity.

(d) If your answer to the previous question is different from 10%, explain the difference in values.

Now go back to the initial demand curve and suppose there is an in- crease 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%.

(e) Determine the new supply curve.

(f) Determine the change in equilibrium price.

(g) If your answer to the previous question is different from 10%, explain the difference in values.

Answer 1

Sol :

Equilibrium is the point where demand and supply are equal to each other.

a.) Demand = 120 - 1.5P

Supply = -20 + 2P

Equilibrium = 120 - 1.5P = -20 + 2P

= 140 = 3.5P

= 140/3.5 = P

= $40 = price (Equilibrium)

Equilibrium quantity = 120 - [1.5 × (40)]

= 120 - 60

= 60

b.) Suppose that there is increase in demand by 10% fro every price , then

New demand curve will be = 120 + 110% × (1.5P)

= 120 + 1.65P

c) equilibrium price = 120 + 1.65P = -20 +2P

= 140/3.65 = P

= 38.35 = Price

Equilibrium quantity = 120 + 1.65 (38.35)

= 183.27

Change in quantity = 183.27 - 60 = 123.27

d) quantity is increases to 183.27 from 60 before the change in demand .

Thsi is becuase of the following :

(i) When demand increases , it will shfit the demand curve to the right.

(ii) this will create the excess demand in the market , which will increase the price of the goods.

(iii) a new Equilibrium will be established at higher prices and higher quantity .

(Note : As per the policy, we have to solve only 4 sublarts of the question. )