5. Richard Hammond is an amateur race car driver who likes to compete in local rally races. In order to train for these events he considers purchasing a membership to Fifth Gear, a rally car training center. Fifth Gear charges $800 for an annual membership fee plus $60 per training session.

d) Richard's demand for rally car training sessions is P = 90 - 3Q1/2, where P is the price per training sessions and Q is the number of training sessions per year. Will he join Fifth Gear?If so, how many training sessions will he purchase per year?

e) Suppose that the following year Fifth Gear decides to lower its membership fee to $500, but raise its cost per training session to $65. Will Richard join Fifth Gear given the new pricing structure? If so, how many training sessions will he purchase per year? How much better or worse off will Richard be under the new pricing relative to the previous year?

f) Now suppose that Fifth Gear decides to eliminate its membership fee. If all of its potential customers have the demand curve of P = 90 - 3Q1/2, what will be the price elasticity of demand if it charges $65 per training session?