Question

1. Given the demand function Q = 500 - 3P - 2P, +0.01Y where and P denote quantity and price of the good, Y is income, and price of an alternative good. is the a) If P=20, PA = 30, and Y= 5000, find (i) the price elasticity of demand (ii) the cross-price elasticity of demand (iii) the income elasticity of demand b) If income rises by 5%, calculate the corresponding percentage change in demand, Is the good inferior or superior?

Answer 1

Q = 500 - 3P - 2A + 0.01Y

Substitute the given values,

Q = 500-3(20) - 2(30) + 0.01(5000)

Q = 430

A)

Price elasticity of demand = (dQ/dP)(P/Q) = -3(20/430) = -0.14

Cross price elasticity of demand = -2(30/430) = -0.14

Income elasticity of demand = 0.01(5000/430) = 0.12

B)

Elasticity = % change in demand / % change in income

0.12 = % change in demand / 5

% change in demand = 0.6% increase

The good us superior, as demand increases as income increases.