Bleecker Street Pizza and Keste Pizza & Vino are located close to each other on Bleecker Street in the West Village. There are 450 potential customers every day, and suppose that each of them is willing to pay up to $2 for a slice of pizza. Since the two shops are selling almost identical pizza, customers always prefer to buy from the cheaper one. (If they charge the same price, then they will split the market equally.)

It is also known that each pizza shop can supply at most 600 slices of pizza every day, and the production cost for each slice of pizza is 80 cents. Suppose that the owner of each shop takes a short-run perspective and only wants to maximize each day's profits, and no shops are going to shut down in the short run.

a) What is the appropriate economic model to study price competition in this local pizza market?

b) If you use Nash equilibrium to make a prediction, what price is each shop going to charge? Explain your reasoning.

c) Give two possible practical means by which the two shops could earn more than predicted in (b).

d) If Bleecker Street Pizza reduces its unit production cost to 70 cents, how will your prediction in (b) change? Explain.

From now on, return to the case where both shops have the same cost of 80 cents. In addition, suppose that the market size has doubled and there are now 900 potential customers but each existing shop's production capacity of 600 pizzas remains unchanged. As a result, no shop can serve the whole market alone.

e) Is it a Nash equilibrium for each shop to set a price of 80 cents per slice? Justify your answer.

f) Is it a Nash equilibrium for each shop to set a price of $2 per slice? Justify your answer.

Suppose a new shop, John's of Bleecker, opens close to the existing two shops and sells the same pizza. It can supply 400 slices of pizza each day, and its production cost is also 80 cents. Customers still prefer to buy from the cheaper shop, and if more than one shop charges the same lowest price, they split the market equally.

g) Find a Nash equilibrium of the price competition among the three shops. Justify your answer.