Tutorial 5. Public Goods.

ECON 290 - CANADIAN MICROECONOMIC POLICY IRYNA DUDNYK Tutorial 5. Public Goods. Problem 1. The purpose of this problem is to help you understand the difference in market demand for purely private and purely public good. For each of the following situations suppose that private marginal benefits are given by M P B = 10 − Q, where Q is the quantity of a good, keep in mind that M P B measures the maximum price a person will be willing to pay for an additional unit of the good. a) Suppose the good is purely private, for example, apples. On a diagram plot individual demand for apples and construct market demand for apples if there are two consumers in the market. Market demand for private good is obtained by adding quantities demanded at each price. You can construct market demand by points: at price P = 10 none of the consumers is willing to purchase any quantity, then total quantity demanded is Q = 0, this is the first point on your diagram (0,10); at P = 9 each person will demand 1 apple and the total quantity demanded in the market is 2 · 1 = 2, the second point is (2; 9) and so on. You can also use algebra: from the MPB you can find individual quantity demanded as a function of price Q1 = 10 − P is demand by the first person and Q2 = 10 − P is quantity purchased by the second person at each price; market demand is the sum of individual quantities QM = Q1 + Q2 , substitute the expressions for the individual demands (plug 10-P for Q1 and Q2 ), simplify and single out price as a function of QM . Both methods give you exactly the came market demand curve. b) Suppose the good is purely public, for example a street lights installed in the neighborhood. On a diagram plot private marginal benefits and construct market demand for the public good if there are two consumers. Pure public good is nonexcludable and nonrival in consumption. Nonexcludable means that if one of the consumers purchases one unit of the good, the other consumer will be able to consume that unit as well and there is no way to preclude the second consumer from enjoying the benefits. Nonrival means that the fact that the second person is consuming the good does not diminish the benefits to the first person. When you construct the market demand for public good use the notion of ‘maximum amount all consumers will be willing to pay in order to purchase an additional unit’. You can construct the market demand curve by points: for example, for the first unit Q = 1 of the good each of the consumers is willing to pay P=9 dollars, it means that the maximum that both will be willing to pay in order to ‘install’ the first unit of the public good is 18, so one of the points on the market demand for the public good is (1, 18); for the second unit one person will pay up to 8 dollars, max. that two will pay is 16, the second point is (2, 16) etc. You can also notice that when you construct market demand for public good you are summing up the individual marginal benefits for each unit DM = 2·M P B. c) Compare the two diagrams. What will happen to the shape of market demand curves if we add more consumers in each case? 1 [idudnyk@sfu.ca] ECON 290 - CANADIAN MICROECONOMIC POLICY IRYNA DUDNYK Problem 2. Marginal cost of planting a tree is constant and is equal to M C = 25 dollars. There are 15 people living in a small town who have different preferences over the trees planted on the streets (trees are obviously a public good). Five people have high marginal benefits given by M BH = 100 − .5Q and the remaining ten people have low marginal benefits M BL = 50 − .25Q, where Q is the number of trees planted on city streets. a) Plot individual M Bs and the M C on a diagram. What is the maximum number of trees that can be potentially privately provided in this town if people do not share costs? Do you think it is possible that no trees will be privately provided? b) Find and plot on a diagram social marginal benefit curve. Calculate socially optimal number of trees planted in town. c) How will your answer to parts (a) and (b) change if the number of people in town increases? d) Recall Cause theorem: under certain conditions private negotiations will achieve efficiency in presence of externalities. Using the logic of Cause theorem discuss whether it is possible that people in town can reach efficient outcome. Discussion Questions 1. Summarize the main differences between pure private and pure public goods. Explain why in case of pure public goods private markets are likely to fail to achieve efficiency. 2. Is pollution abatement a public good? Explain your answer. 2 [idudnyk@sfu.ca]