Reference no: EM132473318

Jerry is a self-employed message therapist working from home. All of his costs are fixed, which means that to maximize his profit, all he needs to do is maximize revenue. Suppose that Jerry faces the following yearly demand function for an hour session: Q = 2,500 - 10P.

a. For a generic revenue function, R(Q) = P(Q)*Q, the first derivative with respect to quantity (aka marginal revenue) is:

Using this fact, demonstrate whether the fact you found for part c holds true for revenue maximization in general (Hint 1: Remember how to maximize revenue).

b. If demand elasticity equals -1, what does this imply about how an increase in price would affect revenue? What about if demand is inelastic - elasticity greater than -1 (meaning between 0 and -1)? What about if demand is elastic - elasticity less than -1 (for example, e = -2)?

c. Now suppose that Jerry has marginal cost equal to $20 per session. What are his optimal price and quantity now? How do they compare to the price and quantity you found in part b?

d. For the generic revenue function in part d and a generic constant marginal cost of MC, find the relationship between the profit-maximizing price and elasticity. What does this show about elasticity at the profit-maximizing price and quantity?