Question

Question 1. (i) The demand and supply functions for a good are given by D = 50 - 0.5P and S = 20 +0.25P (Where P is price) (a) Calculate quantity demanded when price is Rs 10 (b) Calculate quantity supplied when price is Rs 20 (c) Calculate the equilibrium prices and quantities (d) Calculate the shortage/ surplus if government imposes a regulatory price of Rs 60. (e)If the demand curve shifts to D' = 100 - 0.5P, compute the new equilibrium price and quantity. (5 Marks) (ii) (a) With the aid of examples, explain and illustrate price elasticity of demand and income elasticity of demand. (9 Marks) (b) Using these concepts explain and comment on measures which might be taken to increase the revenue of a typical small business in your country. (11 marks) Question 2 Compare perfect competition and monopoly in respect of price, output and profits. (25 MARKS)

Answer 1

D = 50 - 0.5P

S = 20 + 0.25P

a. Qd when P = $10,

Qd = 50 - 0.5 * 10 = 45 units.

b. Qs when P = $20

Qs = 20 + 0.25 * 20 = 25 units.

c. At equilibrium, Qd = Qs,

50 - 0.5P = 20 + 0.25P

50 - 20 = 0.25P + 0.5P

30 = 0.75P

P = 30/0.75

P = $40

Q = 50 - 0.5 * 40

Q = 30 units.

d. Equilibrium price is $40 but if the government imposes a regulatory price, which is set above the equilibrium price, called as price floor, then there would be a surplus of goods in the market.

Surplus = quantity supplied - quantity demanded

Qs at P = $60

Qs = 20 + 0.25 * 60 = 35 units.

Qd at P = $60

Qd = 50 - 0.5 * 60 = 20 units.

Surplus = 35 - 20 = 15 units.

e. At equilibrium, Qd' = Qs

100 - 0.5P = 20 + 0.25P

100 - 20 = 0.25P + 0.5P

80 = 0.75P

P = 80/0.75

P = $106.67

Q = 100 - 0.5 * 106.67

Q = 46.67 units.