Question

Suppose the quantity of good X demanded by consumer 1 is given by: Q DX1 =62 – 3P X + 0.35I + 0.3P Y And the quantity of good X demanded by consumer 2 is given by: Q DX2 = 10 – 2.5P X + 0.2I + 0.6P Y Answer the following questions and ensure that you show ALL calculations.

(a) What is the market demand for good X? 3 marks

(b) Using the first demand function: (Q DX1 = 62 – 3P X + 0.35I + 0.3P Y ), and given: P X =$11, P Y =$22 and I=$120, determine the following and interpret your results:

i. price elasticity of demand (E D ) 3 marks

ii. cross price elasticity of demand (E XY ) 3 marks

iii. the income elasticity of demand (E I ). 3 marks

Answer 1

market demand for good X = Q DX1+Q DX2

=62 – 3P X + 0.35I + 0.3P Y + 10 – 2.5P X + 0.2I + 0.6P Y

MQDX =72-5.5Px+0.55I+0.9Py

given the first demand function Q DX1 = 62 – 3P X + 0.35I + 0.3PY

Q DX1 = 62-3*11+ 0.35*120+ 0.3*22 = 77.6 (at given values)

Price elasticity of demand = dQ/dPx*Px/Q = -3*11/77.6 = -0.43 (the demand is inelastic)

Cross Ed = dQx/dPy*Py/Qx = 0.3*22/77.6 = 0.085 ( the goods are substitutes but not close ones as the cross elasticity is positive but close to zero)

Income Ed = dQx/dI*I/Q = 0.35*120/77.6 = 0.54

A positive income elasticity shows that the good X is a normal good whose demand goes up with an increase in income.