managerial economics questions busi 681

l. (40 points) Jerry is a self-employed message therapist working 'om home. All of his costs are fixed, which means that to maximize his prot, all he needs to do is maximize revenue. Suppose that Jerry faces the following yearly demand function for an hour session: Q = 800 3P. a. b. Graph Jerry's demand mction. What is the prot-maximizing price Jerry should charge for his services? How many sessions will he do at this price? Show this point on the graph and shade the region that corresponds to Jerry's revenue. What is the elasticity of demand at Jerry's optimal price and quantity? Now suppose that Jerry has marginal cost equal to $10 per session. What are his optimal price and quantity now? How do they compare to the price and quantity you found in part b? Suppose that Jerry's true demand mction is 400 + 41"J 8P, where P0 is the price of a day of pampering at the local spa. For the past three years, the spa has charged $100 for a day of pampering, which is why we have used the mction Q = 800 8P until now. The spa has raised their price to $150. What is Jerry's new quantity demanded at his optimal price from part d? (bonus) At Jerry's optimal quantity from part d and the spa price of $100, what was the cross-price elasticity of demand for Jerry's service with respect to the price of a spa day? What is Jerry's new demand function after the increase in spa price? What are Jerry's optimal price and quantity now (with marginal cost equal to $10)? What did the increase in spa prices do to Jerry's optimal price and quantity