Answer to Question #206995 in Microeconomics for Acute

Question

Sharp Inc., a wholly Ghanaian owned company specializes in the production of hand 

sanitizers branded as Quin. The company has branches in all the regions in Ghana with its 

head office located at Cape Coast. It employs 1,200 people and pays an average of GHȼ

550.00 as income tax to the government of Ghana on a monthly basis. Suppose that seven 

thousand, eight hundred and twenty (7,820) units of Quin are produced and supplied by Sharp 

Inc. but the quantity demanded for Quin is eight thousand (8,000) units. Ceteris Paribus, a 

GHȼ 20.00 change in the price of Quin results in a change in quantity demanded for and 

supplied of 4 and 5 units, respectively. [Hint: change in X due to change in Y is given as ]. 

Given the above information:

a) Determine the equilibrium price and equilibrium quantities of Quin.

Answer 1

Solution:

a.). Equilibrium price and equilibrium quantities of Quin:

At equilibrium: Qd = Qs

Determine Qd and Qs:

Let Supply function be X and Price be Y:

Quantity supplied changes by 5 units as a result of 20 change in price:

Q = a +bp

b = $\frac{-4}{20} = -0.2$

P = 20

8000 = a + 0.2(20)

8000 = a + 4

8000 – 4 = a

a = 7996

Qd = 7996 – 0.2P

Let Demand function be X and Price be Y:

Quantity demanded changes by 4 units as a result of 20 change in price:

Q = a +bp

b = $\frac{5}{20} = 0.25$

P = 20

7820 = a - 0.25(20)

7820 = a - 5

7820 + 5 = a

a = 7825

Qd = 7825 + 0.25P

Set Qd = Qs

7996 – 0.2P = 7825 + 0.25P

7996 – 7825 = 0.25P + 0.2P

171 = 0.45P

P = 380

Equilibrium price = GHȼ 380

Substitute in either the demand or supply function to get equilibrium quantity:

Qd = 7996 – 0.2P

Qd = 7996 – 0.2(380)

Qd = 7996 – 76

Qd = 7,920

Equilibrium quantity = 7920