Problem 1: (50 marks) Suppose that people in a town eat one type of food. The market demand for food is: P (P) = 4,500 30P Assume that there is a dominant firm (DF) in the food market called Acme Foods and a competitive fringe. The fringe has a fixed capacity of 1000 food units/period while the dominant firm can vary its output to serve all households. The marginal costs of each types of firm are constant as follows: MCDF = $20/unit & MCFringe = $ 40/unit. For simplicity, ignore fixed costs. Quantity units = units/period, price units ($/unit). Use dominant firm fringe model assumptions from class. Start out by assuming that the dominant form assumes the fringe will enter and slightly undercut it and that the DF will profit maximize given this and will accommodate entry. a) Find Acme Co's residual demand and inverse residual demand and plot on the above graph. b) Write down Acme Co's variable Profits equation. c) Write down the first order condition and solve it to find Acme Co's profit maximizing quantity and price. d) Find the second order necessary condition to show this is a maximum. Problem 1: (50 marks) Suppose that people in a town eat one type of food. The market demand for food is: P (P) = 4,500 30P Assume that there is a dominant firm (DF) in the food market called Acme Foods and a competitive fringe. The fringe has a fixed capacity of 1000 food units/period while the dominant firm can vary its output to serve all households. The marginal costs of each types of firm are constant as follows: MCDF = $20/unit & MCFringe = $ 40/unit. For simplicity, ignore fixed costs. Quantity units = units/period, price units ($/unit). Use dominant firm fringe model assumptions from class. Start out by assuming that the dominant form assumes the fringe will enter and slightly undercut it and that the DF will profit maximize given this and will accommodate entry. a) Find Acme Co's residual demand and inverse residual demand and plot on the above graph. b) Write down Acme Co's variable Profits equation. c) Write down the first order condition and solve it to find Acme Co's profit maximizing quantity and price. d) Find the second order necessary condition to show this is a maximum