ECON 290 - CANADIAN MICROECONOMIC POLICY
IRYNA DUDNYK
Tutorial 6. Public Goods cont’d. Congestible Public Goods, Pricing of Public Services.
Problem 1. The purpose of this problem is to help you understand the free-rider problem. Recall Problem 2 from Tutorial 5 about small town and trees: 5 people with M BH = 100 − .5Q - consumers with high benefits 10 people with M BL = 50 − .25Q, consumers with low benefits from trees SM B = 1, 000 − 5Q, M C = 25, efficient output of the public good QE = 195. Suppose that the people in the small town want to implement Lindahl scheme for the provision of the trees. Check whether the efficient Q = 195 is achievable in Lindahl equilibrium. Suggestions: Equilibrium quantity of the public good under Lindahl scheme must satisfy the following conditions 1. Each person’s contribution should be such that each person demands the same amount of the public good. Since we only want to check whether Q = 195 can be achieved in equilibrium, simply find the per unit contributions (individual prices) at which all people demand 195 trees. Substitute Q = 195 into the demand to find the prices. 2. Sum of the contributions per unit is equal to the MC. Of course if prices are sufficiently low, people will demand any quantity, but that is of little help with the finance: what people are willing to pay together for each unit of the public good must be sufficient to pay the actual cost. Check whether sum of the contributions per tree covers the marginal cost of a tree.
3. Participation in the cost sharing agreement is voluntary - if somebody does not want to pay his share, he cannot be forced to participate. Which, in other words also means that is somebody prefers to play a free-rider strategy, he will not participate in sharing the cost. So let’s check whether anybody has an incentive to free-ride in this case. I suggest we pick a guy with low marginal benefits from trees. To check whether he will choose to free ride or share the cost we have to evaluate his net benefits in each case: Share cost if the person shares the cost, 195 trees will be provided. In this case the net benefits of sharing the cost are represented simply by the consumer surplus at Lindahl price and Q = 195. Free Ride if the person chooses to free ride while the remaining 14 people will provide trees according to their true marginal benefits, 194 trees will be planted1 . The net benefits under free riding are equal to the total value of 194 trees: the person enjoys the benefits of 194 trees, and does not pay a penny of the cost.
SMC=950-4.75Q, which equals to MC=25 at Q=194.7, for simplicity suppose that since the tree is indivisible, they have not enough money to make it to 195 trees, so they will purchase 194.
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[idudnyk@sfu.ca]
ECON 290 - CANADIAN MICROECONOMIC POLICY
IRYNA DUDNYK
Make a conclusion based on your calculations. Problem 2. This problem deals with a special case of goods. Let’s consider such things as: public transit system, bridges, ferries, highways. (a) Can we characterize goods above as public goods? Explain your answer. (b) City council asks you to give a recommendation on the optimal capacity for a new highway; council also wants to know whether there should be a toll and if yes, what should be the price. Use a demand-supply diagram to give a recommendation. The city council also points out to you that demand for the highway is cyclical during the day: it is high during rush hours and low during off-peak hours. City council wants to use public funds efficiently: highway should not be too large to be idle at any time, but of course should not be unreasonably narrow. City council also wants to provide efficient service: the highway should not be congested at any time. Suggestions: Demands draw two demand curves, one for rush hours and one for off-peak. Supply the supply of the ‘highway’ can be thought of as its capacity. After the highway is installed the capacity is fixed, what does a fixed supply look like? The question is where would you recommend to place this fixed supply. Hint: would you choose the horizontal intercept of the low or the high demand, or maybe something in the middle? Now, keep in mind that higher capacity highway will cost more to build, so taxpayers will not be happy about an unnecessarily wide highway. Pricing Recall that private demand reflects quantity demanded at each price. If price is zero, how much is demanded during rush hours and off-peak hours? Does zero price result in efficient ‘consumption of the highway’? Recall that if too many people, namely anything above capacity, decide to take the highway, cars will get in each other’s way and probability of the accident will be higher. What would be the best way to price the highway?
Discussion Question. Consider government provision of the the following services: transit and utilities - these are price excludable public goods that are financed through sales revenues. Things such as water, electricity and some means of transportation can be thought of as life necessities. Do you think government should allow low-income individuals use these services for free. Explain why yes or why not. Use a diagram to support your answer.
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[idudnyk@sfu.ca]