Suppose that the quantity supplied S and quantity demanded D of T-shirts at a concert are given by the following functions where p is the price.
S(p)=−200+40p
D (p )=1150-50 p.
a. Find the equilibrium price for the T-shirts at this concert. The equilibrium price is
b. Determine the prices for which quantity demanded is greater than quantity supplied.
c. What will eventually happen to the price of the T-shirts if the quantity demanded is greater than the quantity supplied?

Law of demand and supply states that; the higher the price, the lower the quantity demanded

We have:

(a) The equilibrium price

This is when the demand and supply are equal

i.e

So, we have:

Collect like terms

Divide both sides by 90

Hence, the equilibrium price is

(b) Price when demand is greater than supply

In (a), we have the equilibrium price to be:

Using the law of demand and supply;

When the price is less than 10.56, the quantity demanded will be greater than the quantity supplied

(c) When quantity demanded is greater than quantity supplied

When the quantity demanded exceeds the supply, there will be shortage of T-shirts.

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Step-by-step explanation:

The demand function is expressed as

D(p )=1150-50p

The supply function is expressed as S(p)=−200 + 40p

Where

p represents the price

A) The equilibrium price is the price at which the quantity supplied and the quantity demanded would be equal. Therefore

1150 - 50p = - 200 + 40p

40p + 50p = 1150 + 200

90p = 1350

p = 1350/90

p = 15

The equilibrium price is $15

b) For quantity demanded to be greater than quantity supplied, the price would be

1150 - 50p > - 200 + 40p

40p + 50p > 1150 + 200

90p > 1350

p > 1350/90

p > 15

The price would be greater than 15

c) if the quantity demanded is greater than the quantity supplied, the prices of the T shirt would increase.

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step-by-step explanation: