Bombay/6 Ave. Pizza and Joey Pepperoni's Pizza are located close to each other on Sixth Avenue in Manhattan. 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) Whatistheappropriateeconomicmodeltostudypricecompetitioninthislocalpizza market? (b) If you use Nash equilibrium to make a prediction, what price is each shop going to charge? Explain your reasoning. (c) Givetwopossiblepracticalmeansbywhichthetwoshopscouldearnmorethanpredicted in (b). (d) If Bombay/6 Ave. Pizza reduces its unit production cost to 70 cents, how will your prediction in (b) change? From now on, return to the case where both shops have the same cost of 80 cents. Suppose that the market size has doubled and there are 900 potential customers. Suppose each existing shop's production capacity of 600 pizzas remains unchanged. As a result, no shops can serve the whole market solely. (e) IseachofthefollowingpricingstrategiesaNE?Justifyyouranswer. (i) Each shop sets a price of 80 cents; (ii) Each shop sets a price of $2. Suppose 2 Bros. Pizza opens a shop 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. (f) FindaNashequilibriumofthepricecompetitionamongthethreeshops.Justifyyour answer.