Answer to Question #202248 in Microeconomics for Nii-Amo Justice

Question

Suppose that the demand and supply functions for good X are

 

 P=6.25 -1/8 Qd

 P=1.75 + 1/10 Qs

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 is the effect of a price ceiling of 3?

e. What happens to equilibrium price and quantity if the demand function becomes P=7.375 -1/8 Qd

 

f. What happens to equilibrium price and quantity if the supply function becomes

 

 P=4 +1/10 Qs

(demand is P=6.25 -1/8 Qd)

Answer 1

Solution:

a.). At equilibrium: Qd = Qs

First derive the demand and supply function from the inverse demand and supply functions given:

$P = 6.25 - \frac{1}{8}Qd$

Qd = 50 – 8P

 

$P = 1.75 + \frac{1}{10}Qs$

Qs = 10P – 17.5

Therefore:

50 – 8P = 10P – 17.5

50 + 17.5 = 10P + 8P

67.5 = 18P

P = 3.75

Equilibrium price (P) = 3.75

Substitute in the demand and supply equation to derive the equilibrium quantity:

Qd = 50 – 8P

Qd = 50 – 8(3.75)

Qd = 50 – 30 = 20

Qd = 20

Equilibrium quantity = 20

b.). This will mean that the price is below the equilibrium price which will result in a shortage since the quantity demanded will exceed the quantity supplied. This is because the amount that producers want to sell is less than the amount that consumers want to buy, which results in excess demand.

 

c.). This means that the price will be above the equilibrium price, which will result in a surplus. This is because the quantity supplied will be much higher than the quantity demanded, thus creating a surplus. This is because the amount that producers want to sell is more than the amount that consumers want to buy, which results in excess surplus.

 

d.). A price ceiling of 3 will prevent the price from rising above the equilibrium price or a particular level. Since the price ceiling is set below the equilibrium price of 3.75, the quantity demanded will increase from 20 to a larger quantity that will exceed the quantity supplied resulting in shortages or excess demand. 

e.). First derive the demand function from the inverse demand function given:

$P = 7.375 - \frac{1}{8}Qd$

Qd = 59 – 8P

Qs = 10P – 17.5

At equilibrium: Qd = Qs

59 – 8P = 10P – 17.5

59 + 17.5 = 10P + 8P

76.5 = 18P

P = 4.25

New equilibrium price (P) = 4.25

Substitute in the demand and supply equation to derive the equilibrium quantity:

Qd = 59 – 8P

Qd = 59 – 8(4.25)

Qd = 59 – 34 = 25

Qd = 25

New equilibrium quantity = 25

Both the equilibrium price and quantity will increase.

e.). First derive the supply function from the given inverse supply function:

$P = 4 + \frac{1}{10}Qs$

Qs = 10P - 40

Qd = 50 – 8P

At equilibrium: Qd = Qs

50 – 8P = 10P – 40

50 + 40 = 10P + 8P

90 = 18P

P = 5

New equilibrium price (P) = 5

Substitute in the demand and supply equation to derive the equilibrium quantity:

Qd = 50 – 8P

Qd = 50 – 8(5)

Qd = 50 – 40 = 10

Qd = 10

New equilibrium quantity = 10

The equilibrium price will increase, while equilibrium quantity will decrease.