The weekly demand function for butter 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 consumer in thousands of dollars, and Py is the price of a kg of margarine. Assume that M = 20, Py = 2, and the weekly supplyfunction is such that the equilibrium price of one kilogram of butter is $14. (Hint: Use simple calculus).

1. 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?
2. Calculate the income elasticity of demand for butter at the equilibrium
3. 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?