Answer to Question #168160 in Microeconomics for Ana

Question

Suppose that the demand and supply functions for good X are

Q_d = 50 - 8P

Q_s = -17.5 + 10P

a.      What are the equilibrium price and quantity?

b.      What is the market outcome if price is $2.75? What do you expect to happen? Why?

c.      What is the market outcome if price is $4.25? What do you expect to happen? Why?

d.      What happens to equilibrium price and quantity if the demand function becomes Q_d = 59 - 8P?

e.      What happens to equilibrium price and quantity if the supply function becomes Qs = -40 + 10P (demand is Q_d = 50 - 8P)?

Answer 1

a. Given the quantity demand, Q_d= 50 - 8P and the quantity supplied, Q_s= -17.5 + 10P are given, the equilibrium condition is given as:

$Qd=Qs$

50 - 8P = -17.5 + 10P

18P = 67.5

P^*= 3.75

Q^* = -17.5 + 10(3.75)

Q^* = 20

b. when the price is given as P=$2.75, the new quantity demanded becomes

Q^d= 50 - 8(2.75)

Q^d= 28

what happens is that there is an excess demand of (28 - 20 = 8) of that particular good. This is because consumers want more at the lower price than at the equilibrium price $3.75. Since the supply does not change, consumers are increasing their demand causing an excess demand of the good in the market given the constancy of the supply.

c. when P=$4.25, the quantity supplied, Q^s, becomes

Q^s= -17.5+10(4.25)

Q^s=25

at an increased price of $4.25 (which is above the equilibrium price, $3.75), the suppliers are willing to sell more to the market. This has the potential of increasing the quantity of good in the market and leading to an excess supply of 5 (25 - 20) as demand doesn't change.

d. when quantity demanded changes to Q^d = 59 - 8P, the new market equilibrium becomes

59 - 8P=-17.5 + 10P

18P=76.5

P^*₀=$4.25

and

Q^*₀=-17.5+10(4.25)

Q^*₀=25

e. The equilibrium price and quantity changes when the quantity supplied becomes

Q^s = -40 + 10P.

Therefore: 50 - 8P= -40 + 10P

90= 18P

P_e^* = 5

while: Q_e^*= 50 - 10(5)

Q_e^*= 10