5. Elasticity and Revenue Along a Linear Demand Curve: Consider the following demand curve:

Q = 100 - P

a. Compute the (own) price elasticity of demand at P = 99, P = 50, and P = 1. State at each of these prices whether demand is inelastic, elastic, or unit elastic.

c. Suppose a firm sells output at price P, and that demand is given by the above demand curve. Find an expression for the firm's revenue as a function of the price.

d. At what price does the firm maximize its revenue? Hint: revenue is maximized at the point where the derivative of revenue with respect to price is equal to zero. The derivative of a function of the form f(x) = A + Bx + Cx2 is f'(x) = B + 2Cx.

e. Briefly explain how the price you found in part d is related to the elasticity of demand. In particular, explain why prices that are higher or lower than the revenue-maximizing price cannot maximize revenue.