Question

a) School of Business of UEW has an extensive collection of Managerial Economics books. The school is planning to raise funds to build new lecture halls and offices for students as well as lecturers. Three local institutions have expressed an interest in buying the school’s collections. The individual demand equation for each of these three individual institutions is :

Qd1=Qd2=Qd3=50-2.5P

where P is measured in Ghana Cedis per book

(i) What is the market demand equation for the school’s books?

(ii) How many more books can the school sell for each cedi reduction in price?

(iii) If the school has 90 books in all, what price should the school charge to sell the entire collections?

  

b) Given that Qd= 220-5P

and Qs= -20+3P

are the demand and supply functions for Fante Kenkey and fish with shito on UEW campus? The University Management has consulted you to:

(i) Calculate the equilibrium price and quantity for the good.

(ii) If per unit tax of ten cedis ( Ghc 10.00 ) is imposed on the good, calculate the new equilibrium price and quantity after tax.

(iii) Using a diagram, present your solutions in (i) and (ii) above.   

Answer 1

( a )

( I ) Market demand = Qd1 + Qd2 + Qd3 = 50 - 2.5P + 50 - 2.5P + 50 - 2.5P = 150 - 7.5P.

( II ) Market Demand = ( 150 - 7.5P ) = Taking common 7.5 from the equation = 7.5 ( 20 - P ).

Therefore, for each cedi reduction, the university can sell 20 more books.

( III ) Quantity supplied = 90. At equilibrium Qd = Qs = 150 - 7.5P = 90.

- 7.5P = 90 - 150

- 7.5P = - 60

P = 60 / 7.5 = 8.

8 * 90 = 720.

( b )

Qd= 220 - 5P.

Qs = -20 +3P

( I ) At equilibrium = Qd = Qs = 220 - 5P = - 20 + 3P = - 8P = - 240

P = 240 / 8 = 30

Putting value of P in Qd = 220 - 5*30 = 70.

New Price after tax = 30 + 10 = 40.

Quantity = 220 - 5*40 = 20.