Suppose we have the following hypothetical demand function:
Qx = 600 - 3px + 0.04I - 2pz
Where Px = $ 70, Pz = 68, I = $ 24,000 (disposable income per capita).
A. How can we Classify product X and Z relationship? Substitute goods, Complementary goods o Independent? Show calculations.
B. What is the reduced demand function?
C. If we increase the price 3%, what impact would have in increase in total revenues of product X?
D. Interpret in words the meaning of the coefficient of the variable I.
Given hypothetical demand function:
Qx = 600- 3px + 0.04I -2pz
Here the cross elasticity of demand can be calculated as:
dQx/dPz = -2
since the cross elasticity of demand is negative, the demand for X increases as the price of Z decreases, which means X and Z are complementary goods.
The demand function is linear in nature and can be reduced to a form:
Px = ax+ b
Price elasticity of demand can be calculated as
dQ/dPx = -3
which means the quantity goes down by 3 when the price of X goes up by 1.
So, if the price of X goes up by 3% or by a factor of 0.03, the quantity (and hence the revenue of X) will come down by 9% or by a factor of 0.09.
I denote the disposable income and its coefficient is the Marginal propensity to consume, i.e. the how much demand will increase per unit increase in disposable income.
hope this helps.