Answer to Question #163016 in Microeconomics for Akinyinka dami

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 Lagos, there are only 2 consumers: one of them likes frozen yogurt and the other is crazy about frozen yogurt.

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

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

Answer 1

1.

First type:

$Q=\frac{5-P}{21}$

Second type:

$Q=20-P$

2.

$2+P=\frac{5-P}{21}+20-P$

$\frac{43}{21}P=\frac{383}{21}$

$P=8.9$

$Qgeneral=10.9=11$

First type:

$Q=-0.19=0$

Second type:

$Q=11.1=11$