Tossa College of Economic Development Assignment for welfare Economics 1. Assume that a very large number of firms in an industry all have access to the same production technology. The total cost function associated with this technology is TC(q) = 40q – 24q2 + 4q3. If the demand function for the industry’s product is Q = 19 – P, find numbers of firms when the market is at its LR competitive equilibrium? 2. Assume that the taxi industry in the Dessie City is perfectly competitive. Also assume that the constant marginal cost of a taxi ride is birr 5 per trip and that each taxi is capable of making 20 trips a day. We will let the demand function for taxi rides each day be D(p) = 1100 – 20p. a) What is the perfectly competitive price of a taxi ride? b) How many ride will the residents of Dessie city make every day? c) How many taxis will operate in Dessie City? d) Calculate the price that will equate demand with supply e) Calculate the profit that each taxi will earn per day 3. Consider an economy with the supply of balls Qs = 4p and the demand for balls given by Qs = 270 – 5p. a) Calculate the equilibrium price and quantity. b) Graph the supply and demand functions. c) Calculate both the consumer and producer surplus. d) calculate the new equilibrium price and quantity. e) Draw a graph marking the after tax consumer surplus and producer surplus as well as the tax revenue f) Calculate the consumer surplus, the producer surplus, and the dead-weight loss. g) Calculate the dead-weight loss imposed by the tax. 4. A monopoly sells its good in Dessie city , where the elasticity of demand is –2, and in Addis Ababa, where the elasticity of demand is –5. Its marginal cost is $10 A. At what price does the monopoly sell its good in each country if resales are impossible? B. What happens to the prices that the monopoly charges in the two cities if retailers can buy the good in Addis Ababa and ship it to Dessie at a cost of (a) $10 or (b) $0 per unit? 5. A monopoly sells in two countries, and resales between the countries are impossible. The demand curves in the two countries are p1=100 – Q1, p2=120 – 2Q2. The monopoly’s marginal cost is m = 30. Solve for the equilibrium price in each country. 6. Two players, Row and Column, are driving toward each other on a one-lane road. Each player chooses simultaneously between going straight (S), swerving left (L), and swerving right (R). If one player goes straight while the other swerves, either right or left, the one who goes straight gets payoff 3 while the other gets –1. If each player swerves to his left, or each swerves to his right, then each gets 0 (remember, they are going in opposite directions). If both go straight, or if one swerves to his left while the other swerves to his right, then the cars crash and each gets payoff –4. A. Write the payoff matrix for this game. B. Find all of the game's Nash equilibrium in pure strategies C. Find a Nash equilibrium in which Row uses a pure strategy and Column mixes between two of his strategies. Clearly identify which strategy or strategies have positive probabilities for each player, and what Column's mixing probabilities are. (Hint: Which of Row's pure strategies could make Column willing to put positive probability on two of Column's pure strategies?) D. Find a Nash equilibrium in which both Row and Column mix between two of their strategies. Clearly identify which strategies have positive probabilities for each player, and their mixing probabilities are. (Hint: Pick two pure strategies for each player— because the game is symmetric, it's natural to try the same two strategies for each—and figure out what the mixing probabilities would have to be on just those two strategies. Then compare each player's expected payoff with what he could get by switching to his third strategy.)
