Answer to Question #163002 in Microeconomics for Ada

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

Question 1

P = Price

(Q, Qd) = Quantity demanded

Qdm = Market Demand

# = Naira

P= 5-½Q → Qd = 10-2P

P = 20 - Q →Qd = 20-P

(I)Qd = 10-2P (those who like frozen yoghurt)

a) When P = 0

Qd = 10 -2(0)

Qd = 10

b) When P = 5

Qd = 10 - 2(5)

Q = 10 - 10

Q = 0 →(10,0)

(II)Qd = 20 - P (those who are crazy about frozen yoghurt)

When P = 0

Qd = 20 - 0

Qd = 20

When P = 20

Q = 20 - 20

Q = 0 → (20,0)

Market Demand (Qdm) = Qd1 + Qd2

→Qdm = 10 - 2p + 20 - p

→Qdm = 30 - 3p

When P = 10 When P = 0

Qdm = 30 - 3(10) Qdm = 30 -3(0)

Qdm = 30 -30 Qdm = 30 - 0

Qdm = 0 Qdm = 30

QUESTION 2

Qs = 2 + P

E = Qdm = Q3

→30 - 3P = 2 + P

30 - 2 = P + 3P

28 = 4P

P = 7

Q3 = 2 + p

Q3 = 2 + 7

Q3 = 9

→ The consumer buys at an equilibrium price of #7 and equilibrium quantity of 9 units= P + 3P

28 = 4P

P = 7

Q3 = 2 + p

Q3 = 2 + 7

Q3 = 9

→ The consumer buys at an equilibrium price of #7 and equilibrium quantity of 9 units