Restaurants in a town with a thriving restaurant scene are in a zero economic profit equilibrium. One of these restaurants pays $50,625 in commercial rent every year, and the sum of its costs for wait staff and raw materials depend on how many tables were served per week according to the equation 0.9q^2 where q is the number of tables served by the restaurant per week.

a. If the restaurant is maximizing its profit, how many tables are served per week, and what was the average amount customers were spending on the meal per table?

The restaurants face an aggregate demand function of Q=22,635-P, where Q is number of tables served per week across the town, and P is the average amount that a party spends on the meal.

b. How many tables are served across the town per week, and how many restaurants are there?

The pandemic triggered an economic lockdown, such that the restaurant could only serve customers via home delivery. This resulted in contraction of demand for the restaurant to Q=10,000-P.

c. In the short run (with the same number of restaurants in the market), what is the new market equilibrium Q and P after this shift in demand?

d. Should these restaurants stay open during lockdown? How do you know?