We know that:
M = 20 (in thousands)
Py = 2
Px = 14
Q = 14000
Q = 20000 - 500*Px + 25*M + 250*Py
From Using Calculus To Calculate Income Elasticity of Demand we see that (using M for income rather than I as in the original article):
We can calculate any elasticity by the formula:
Elasticity of Z with respect to Y = (dZ / dY)*(Y/Z)
In the case of income elasticity of demand, we are interested in the elasticity of quantity demand with respect to income. Thus we can use the following equation:
Price elasticity of income: = (dQ / dM)*(M/Q)
In order to use this equation, we must have quantity alone on the left-hand side, and the right-hand side be some function of income. That is the case in our demand equation of Q = 20000 - 500*Px + 25*M + 250*Py. Thus we differentiate with respect to I and get:
dQ/dM = 25
So we substitute dQ/dM = 25 and Q = 20000 - 500*Px + 25*M + 250*Py into our price elasticity of income equation:
Income elasticity of demand: = (dQ / dM)*(M/Q)
Income elasticity of demand: = (25)*(20/14000)
Income elasticity of demand: = 0.0357
Thus our incomeelasticity of demand is 0.0357. Since it is greater than 0, we say that goods are substitutes.
We'll answer question (c) on the next page.
