Question

4. Suppose the supply curve for apples is given by QS -2P, where QS is the quantity offered for sale when the prices is P. Also, suppose the demand curve for apples is given by QD- 182-4PI, where QD is the quantity of apples demanded when the price is P and the level of income is erw a) Find the equilibrium P and Q when I -6 b) Find price-elasticity of demand at the equilibrium when 6, and give an interpretation in terms of percents and classify the elasticity (elastic or inelas tic

Answer 1

a) When I = 6, Qd = 182 - 24P

At equilibrium, Qd = Qs

182 - 24P = 2P

182 = 26P

P = 7

Q = 2×7 = 14

b) Price elasticity of demand = dQ/dP × P/Q

dQ/dP = -24

P/Q = 7/14 = 0.5

Price elasticity = -12

Since the absolute value of price elasticity of demand is greater than 1, it is highly elastic.

c) Income elasticity of demand = dQ/ dI × I/Q

dQ/dI = - 4× 7 = -28

I/Q = 6/ 14 = 3/7 = 0.43

Income elasticity of demand = -12

Again, the income elasticity of demand is highly elastic.

d) At equilibrium,

2P = 182 - 4PI

2P ( 1 + 2 I) = 182

P = 91/ (1 + 2I)

Q = 2P = 182 / (1 + 2I)

e) Price elasticity of demand :

dQ/ dP = - 4I

P/Q = P / (182- 4PI)

Price elasticity of demand = -4PI / (182 - 4PI)

For this to be unit elastic,

4PI / (182 - 4PI) = 1

8PI = 182 or PI = 22.75

f) Income elasticity of demand = - 4P × I / (182 - 4PI) = - 4PI/ (182 - 4PI)