Question

Given the demand equation Qx = 1200 – 0.6 Px + 0.8Y + 0.5Py + 1.9 A,

where Qx = Quantity demanded of Good X; Px = Price of Good X in Rs; Y = income of the consumer in Rs; Py = Price of Good Y; and A = Advertising expense in Rs thousands

a) Are goods X and Y substitutes?

b) Is the good X an inferior good?

c) How much is the own price elasticity of demand if Px= 10,000 and Qx = 5000

d) How much is income elasticity at Qx = 5000 and Y = 50,000

e) Explain the meaning of coefficient of advertising in the equation

Answer 1

a)

Coefficient of PY is positive meaning a rise in price of good 'X' will rise the quantity demanded of 'Y' which means these goods are substitutes.

b) Good 'X' is a normal good because it has a positive relationship with income.

c)

own price elasticity of demand

$\frac{\Delta Qx}{\Delta p}\times \frac{p}{Q}\\-0.6\times\frac{10000}{5000}\\=-2$

d)

income elasticity

$\frac{\Delta Qx}{\Delta Y}\times \frac{Y}{Q}\\0.8\times\frac{50000}{5000}\\=8$

e) The coefficient of advertising in the equation is positive meaning an increase in advertising expenses will rise the Quantity of X demanded.