Problem 1 - A New Restaurant in Town [18 points]

A new restaurant - Uovo - has just opened in West L.A. It is serving the upscale market, with truly outstanding pasta that is flown in overnight from Bologna, Italy. Uovo offers a fixed-price menu with appetizer, three dishes of pasta, and a delicious tiramisu for dessert. The restaurant faces the following demand function:

Q=5004P

where Q is the number of guests per day. The marginal cost is constant at $45 per customer (including expenses for ingredients and personnel). The restaurant is paying a rent of $1,000 per day.

1. [6 points] What is the profit-maximizing number of guests that Uovo should serve each day, and what price should Uovo charge to maximize profit?
2. [3 points] What is the elasticity of demand at the optimal price and quantity? Is demand elastic or inelastic at this point? From what we learned in class, does it make sense for the restaurant to operate in this area of the demand curve (elastic/inelastic part)?
3. [4 points] What is the profit of the restaurant at the optimal price and quantity, and what is its markup as a percentage of its price (Lerner Index)?
4. [2 points] After seeing how well the restaurant is running, the landlord decides to raise the rent. How would that affect the optimal price that the restaurant is charging and its optimal number of customers?
5. [3 points] What kind of market is the restaurant operating in? What do you expect to happen in the long run as a result of the restaurant's high profits? How would this affect the restaurant's demand curve?