A coal mining company who sells coal only for power generation faces the following direct demand function for coal, which includes the effects of changes in prices of natural gas and wind, since those are potentially competing generation technologies: Q_coal^d=1,200-10P_coal+5P_ng+.5P_w Png is the price of natural gas, which is assume to be $3/MMBtu and Pw is the price of wind power, which is assumed to be $70/MWh (units are not relevant for your task; this is just to be precise).

A. What is the own price elasticity of demand when Pc = $80/ton? Is demand elastic or inelastic at this price? What would happen to the firm's revenue if it decided to charge a price below $80?

B. What is the cross-price elasticity of demand between coal and natural gas at the prices given in part a? Are coal and natural gas complements or substitutes? Answer the same questions for wind, as well.

C. What is the cross-price elasticity between coal and wind? Are they complements or substitutes?