Download Econ 440 Homework 1: Consumer Preferences, Competitive Equilibrium, Monopoly Pricing - Pro and more Assignments Economics in PDF only on Docsity! Econ 440 September 2007 Peter Norman Homework 1 Due in class Tuesday September 18. 1. Tweedeldum and Tweedeldee consume two goods only: weekday wireless minutes and weekend wireless minutes. Tweedeldum has signed on with a service that gives him 1000 weekday minutes, but no weekend minutes and Tweedeldee has a service that gives him 1000 weekend minutes, but no weekday minutes. If you want to make life easy, assume that weekday minutes cannot be used in the weekend and the other way around. (a) In a carefully labeled graph, put in the endowment described above together with some preferences for Tweedeldee and Tweedeldum. Draw the preferences in such a way that both Tweedeldee and Tweedeldum prefers 500 weekday minutes and 500 weekend minutes to their initial endowment. (b) Explain carefully what a competitive equilibrium is in this environment and illustrate how a com- petitive equilibrium would look like graphically in a NEW GRAPH. Dont change the preferences or the endowment! (c) Consider the following alternative trading institution. Tweedeldum
rst suggests an allocation. Then Tweedeldee either agrees, in which case they consume the allocation suggested by Tweedeldum. If Tweedeldee doesnt agree, they both consume their respective endowments. In a new graph, show how Tweedeldum will choose the allocation. Will this trading institution result in a Pareto Optimal equilibrium? 2. Suppose that Jim has preferences represented by UJ (x1; x2) = min fx1; x2g and Dwight has preferences given by UD (x1; x2) = x1 + 2x2 + 3 (a) Draw the indi¤erence curves for Jim and Dwight. (b) Suppose that Jim is endowed with eJ = (2; 8) and Dwight is endowed with eD = (6; 2) : Derive (exactly) the equilibrium price ratio and the equilibrium consumptions and illustrate in a carefully drawn graph. 3. Consider a monopolist producing a good facing a linear inverse demand p (y) = 1 y. Also assume that the cost function for the monopolist is given by C (y) = y2: (a) Formulate the pro
t maximization problem for the monopolist (assuming that the monopolist is restricted to linear pricing). (b) Solve the monopoly problem and illustrate in a carefully drawn graph. 4. Carrboro Mad Cows is a professional hockey team. The ticket price is $5 and they have an audience of 3000 for each game in a building with 5000 seats. (a) Assume that the costs of admitting an extra spectator is zero. Can this pricing be consistent with pro
t maximization? Explain, using a graph. 1
