John runs the only carwash in town; he is a monopolist. John estimates his daily demand for carwashes is given by the expression Q = 100?4P, where Q is the number of carwashes drivers will purchase at price P. It costs John $5 in electricity, soap, etc to run the carwash once. Additionally, John has fixed costs of $300/day.

a. What price should John set for a carwash? What will be his daily profit at this price?

b. If John were to lower his price by $1, he would sell more carwashes, and still be able to charge a price
above his marginal cost. Explain intuitively why it would not be profit-maximizing to do so.

c. What is John's elasticity of demand at his profit-maximizing price? Is it elastic or inelastic? If it is elastic, why does he not lower his price, as this would surely bring in many more customers? If inelastic, why does he not raise his price?