Q: The weekly demand function for butter in the province of Quebec is Qd = 20000 ? 500Px + 25M + 250Py where Qd is quantity in kilograms purchased per week, P is price per kg in dollars, M is the average annual income of a Quebec consumer in thousands of dollar, and Py is the price of a kg of margarine. Assume that M = 20, Py = $2, and the weekly supply function is such that the equilibrium price of one kilogram of butter is $14.
a. Calculate the cross-price elasticity of the demand for butter (i.e. in response to changes in the price of margarine) at the equilibrium. What does this number mean? Is the sign important?
b. Calculate the income elasticity of demand for butter at the equilibrium.
c. Calculate the price elasticity of demand for butter at the equilibrium. What can we say about the demand for butter at this price-point? What significance does this fact hold for suppliers of butter?
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Whenever I work on a question such as this, I like to tabulate all the relevant information at my disposal. From the question we know that:
M = 20 (in thousands)
Py = 2
Px = 14
Q = 20000 - 500*Px + 25*M + 250*Py
We can substitute and calculate for Q:
Q = 20000 - 500*Px + 25*M + 250*Py
Q = 20000 - 500*14 + 25*20 + 250*2
Q = 20000 - 7000 + 500 + 500
Q = 14000
We can add this information to our table:
M = 20 (in thousands)
Py = 2
Px = 14
Q = 14000
Q = 20000 - 500*Px + 25*M + 250*Py
On the next page we'll answer part A.
