Suppose the demand for down pillows is given by Q^D = 100 - P, and that the supply of down pillows is given by Q^S = -20 + 2 P.

a. Solve for the equilibrium price.

b. Plug the equilibrium price back into the demand an solve for the equilibrium quantity.

c. Duble-check your work by plugging the equilibrium price back into the supply equation and solving for the equilibrium quantity. Does your answer agree with what you got in (b)?

d. Solve for the elasticities of demand and supply at the equilibrium point. Which is more elasticit: demand or supply?

e. Invert the demand and supply functions (in other words, solve each for P) and graph them. Do the equilibrium point and relative elasticities shown in the graph appear to coincide with your answers? Explain why or why not.