Question

The demand and supply for a good are respectively QD = 16 – 2P + 2I and QS = 2P – 4 with QD denoting the quantity demanded, QS the quantity supplied, and P the price for the good. Suppose the consumers’ income is I = 2

i)Determine the price-elasticity of demand if P = 2.

ii)Determine the income-elasticity of demand if P = 2.

iii)Determine the price-elasticity of supply if P = 4.

iv)) Determine consumers’ expenditures at the equilibrium.

Answer 1

The demand and supply equations for consumers is given as:

QD = 16 – 2P + 2I

QS = 2P – 4

P= Price of the commodity.

I= incoome of the consumer.

i) The formula for price elasticity of demand is given as:

The demand equation is:

QD = 16 – 2P + 2I

It is given that P=2,thus, Qd= 16- 2*2 +2I = 12+ 2I

The price elasticity of demand at P= 2 becomes,

-2*(2/12+ 2I) = -2/ 6+I

ii) The income elasticity of demand is given by the formula,

The demand equation is:

QD = 16 – 2P + 2I

When P=2, Qd= 12+ 2I

The income elasticty of demand is given by:

2*(I/12+2I) = I/6+2I

iii) Price elasticity of supply is given as:

The equation for supply is given as:

QS = 2P – 4

When P=4, Qs= 2*4 - 4 = 4

The price elasticity of supply becomes:

2*(4/4) = 2