1. Demand Elasticity, Optimal Mark-Up Rule, and Optimal Pricing

Jimmy is selling cups of coffee out of his hotel room in Orlando. He is charging $20 per cup.

a) If his marginal cost of production of a cup of coffee were negligible (MC 0), what must be the elasticity of demand for coffee (that Jimmy is facing at this price point) in order for $20 to be the optimal (profit-maximizing) price?

A fan of Jimmy's who works at the hotel and is majoring in economics at UCF has conducted a survey among players staying there. Her results indicate that Jimmy would sell 80 cups of coffee a day if he charged $18 per cup, 66 cups if charging $25/cup, and 50 cups at $33/cup.

b) Find the equation for this demand curve (Q as a function of p) and use it to compute the elasticity of demand for coffee faced by Jimmy at the price of (p =) $20. Can this price be optimal? If so, why? If not, should the price be raised or lowered, and why?

c) Jimmy is quoted as saying "You can't get coffee nowhere here. So I might bump it up to 30 bucks a cup. People here can afford it." Use the optimal mark-up rule to answer the following question: What must be his marginal cost of producing a cup of coffee in order for $30 to be the optimal price?

d) Suppose the city of Orlando finds out about Jimmy's business and demands that he pay a business license fee of $420 a month (which comes out to $14 a day). How would this change his optimal pricing decision? Justify your answer.