Answer to Question #163166 in Microeconomics for Precious

Question

Market surveys show that there are two types of consumers for frozen yogurt. The first type like frozen yogurt and have an inverse demand curve of P =5 − 21Q. The second type is crazy about frozen yogurt and has an inverse demand curve of P = 20 − Q. In the town of Smallville, there are only 2 consumers: one of them likes frozen yogurt and the other is crazy about frozen yogurt.

Using the individual demand curves above, derive the market demand for frozen yogurt in Smallville. Plot the market demand curves.

2. Suppose that the market supply for frozen yogurt in Smallville is given by QS = 2+P. Find the equilibrium price and quantity. How much does each consumer buy at the equilibrium price?

Answer 1

(a)Market demand curve=q1+q2

Q1 for p=5-21Q

$P=5-21Q$

$21Q=5-p$

$Q1=5/21-p/21$

Q2 for p=20-Q

$P=20-Q$

$Q2=20-p$

Market demand curve

$Q1+Q2$

$=5/21-p/21+20-p$

$=20.2-1.05p$

(b)

$=20.2-1.05p=2+p$

$P=8.08$

$Q=2+p$

$Q=2+8.8$

$AtQ=10.8$

At equilibrium price , the buyers will buy

$Q1=5/21-p/21$

$Q1=-3.88$

At $Q2=20-p$

$Q2=11.12$