Economics 325: Public Economics Section A01 University of Victoria Midterm Examination #1 VERSION 1

Transcription

1 Economics 325: Public Economics Section A01 University of Victoria Midterm Examination #1 VERSION 1 Section 1: Multiple Choice (3 points each) Select the most appropriate answer, and circle the corresponding letter on your exam paper. Questions 1-3 refer to the following diagram of a perfectly competitive market. No externality is present. 1

2 1) What is the change in social welfare (aggregate net benefits) going from the equilibrium quantity to Q=300? A) It falls by $2,500 B) It rises by $6,750 C) It falls by $1,250 D) It rises by $1,250 2) What is the variable cost of producing 100 units? A) $25 B) $100 C) $2,500 D) $10,000 3) What is the deadweight loss associated with producing 100 units of the good? A) $1,250 B) $2,500 C) $5,000 D) $7,500 Questions 4-8 refer to the diagram below. The MSC curve is given to denote the presence of an externality in this market. 2

3 4) Which of the following statements about this market is/are true? I. Equilibrium quantity is 100. II. Efficient quantity is 50. III. There is a negative externality in this market. A) I and II only B) I only C) III only D) I, II, and III E) None of the statements is true. 3

4 5) At equilibrium, total external benefit in this market is A) $0 B) $2,500 C) $3,375 D) $5,000 6) What is the maximum gain in social welfare that can be achieved (relative to equilibrium) with a policy intervention? A) $0 B) $1,250 C) $3,375 D) $4,375 7) Which of the following policies would bring about the efficient quantity? I. A tax of $50 per unit. II. A subsidy of $50 per unit. III. A quota at Q=100. A) I only B) II only C) I and III only D) II and III only 8) What price will consumers pay for this good under the efficiency-inducing policy? A) $25 B) $50 C) $75 D) $100 END SECTION 1. 4

5 Answer each question as clearly and concisely as possible on the exam paper. Use of carefully labeled diagrams, where appropriate, is strongly encouraged. Section 2: True, False, or Uncertain (5 points each). Respond to each of the following statements by labeling the statement true, false, or uncertain. Then justify your claim. Answers that do not provide justification will receive zero points. 1) (5 points) In light of the Coase Theorem, government intervention is probably not needed to solve major externalities and public goods problems. False. The Coase Theorem tells us that if we assign property rights to an externality (e.g. allow a polluter to dump in a river; or allow a fisherperson to have rights to a clean river) AND if there are zero transactions costs (i.e. costs of negotiating) and zero monitoring costs (i.e. everyone can tell who is contributing to the externality and how much) then government intervention (taxes, subsidies, command and control, etc.) is not required to solve the problem. Those assumptions are likely to fail in cases of major externalities and public goods problems. It would be great if everyone paid me for my contributions to a public good, according to their marginal willingness to pay. But even if I had the right to demand those payments from people, it would be incredibly costly to collect from everyone who owes me. And if polluters are going to pay me for the right to pollute the air I breathe, I have to be able to figure out how much each polluter has contributed, in order to bill them for the damage they ve caused me. Policy is going to be a better approach to solving problems like these examples. While Coase may be sensibly applied to neighbours sorting out issues over loud music, keeping trees trimmed, weeds controlled, etc. 2) (5 points) In equilibrium, with no government intervention, contributions to public goods will be zero. False. In general, we can expect some people to make some contributions to public goods (so long as MPB>MPC) simply because it s in their self interest. The problem is they re unlikely to contribute as much as would be socially optimal for them to contribute. Some argue that people contribute to public goods beyond their own self interest that they exhibit altruism. So people may give to charities that preserve the environment or help the poor because they get increased happiness from seeing other people become 5

6 better off. This is another reason (beyond self-interest) that people will contribute to a public good. END SECTION 2 Section 3: Short Answers 1) (14 points total) Consider the market for packs of cigarettes. Assume that the market is otherwise competitive, but that a negative consumption externality (second-hand smoke; and the fact that other taxpayers pay for medical care for smokers) is present. Demand and supply for packs of cigarettes are given in the diagram below. Diagram for Question 1 (Market for Cigarettes) 6

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8 Unless otherwise stated, provide a numeric answer to the questions below. a) 3 points What is social welfare (aggregate net benefits) in equilibrium? You must show your work to receive credit. Equilibrium occurs where MPC=MPB, at Q=200. SW=TSB-TSC TSB at Q=200 is the area of the trapezoid under the MSB curve between Q=0 and Q=200. This has an average height of 5 and a base of 200, or an overall area of TSC at Q=200 is the area of the trapezoid under the MSC curve between Q=0 and Q=200. This has an average height of 5 and a base of 200, or an overall area of So, SW=TSB-TSC= =0. You can also use the formula SW=CS+PS-TEC But isn t the first way of doing things much simpler? Always go with the easy approach, if it s appropriate. And here you ve got the MSB and MSC curves so TSB and TSC are easy to find. Note that if you said SW=CS+PS, you re missing the point of externalities! Go back and think carefully about why that statement is wrong in this context. b) 3 points Clearly illustrate and label in the diagram the area that best represents deadweight loss in equilibrium in this market. You don t need to provide a number. I asked you to do this in the diagram because there are two triangles with the same area, one of which captures DWL. I ve shaded that triangle above. If you want to remember this formulaically, it s the area bounded by Q eff, Q eq, MSC, and MSB. A better way to think of it is that if we were to move from Q=200 to Q=100, we d gain a cost reduction equal to the trapezoid under MSC between Q=100 and Q=200; and we d forgo the benefits given by the trapezoid under MSB between Q=100 and Q=200. Taking the difference of those two trapezoids yields the shaded area above the DWL. This is the social welfare we forego by being someplace (in this case, the equilibrium) other than the efficient quantity. 8

9 If you like it stated a slightly different way, the increased cost to society of going from Q=100 to Q=200 is the trapezoid under MSC. The increased benefit to society is the (smaller) trapezoid under MSB. Therefore SW falls by the difference in these trapezoids when we move from the efficient quantity to the equilibrium. This difference is the DWL associated with being at the equilibrium. Try to get the intuition for this. c) 2 points What would be the price producers would receive, if the optimal tax (the tax that maximizes social welfare) were imposed? The purpose of a tax to address a negative externality is to internalize the externality that is to make the agent who causes the externality feel the pain of the externality through the tax. This way, even though they still don t care about the externality, they do care about the tax. So if we perfectly match the pain of the tax (to the agent causing the externality) to the pain of the externality, the agent causing the externality will act as if they care about the externality. The tax doesn t have to match the externality at every Q. Just at Q eff, because that s where we want to end up. So the optimal tax (i.e. the tax that maximizes social welfare by moving the market to Q eff ) is the tax that is equal to the marginal external cost (the pain caused by the externality) at Q eff. This is $5 in this case, as you can see in the diagram above. If we impose a per unit tax of $5, this will push the market to a new equilibrium at Q=100. I m assuming the tax is placed on producers, so I illustrate this above by putting in a taxed MPC curve for producers. This is just MPC+t* or MPC+5. It s just a vertical shift upwards by the amount of the tax. Here the price paid by consumers is $10. Producers get this payment per unit from consumers but then hand $5 over to the government in the tax they pay. Therefore they are left with only $5 per unit in their pocket. So $5 is the price received by producers. This is labeled P s above. d) 3 points What would be consumer surplus with the optimal tax in place? You must show your work to receive credit (for partial credit you can shade and clearly label the relevant area in the diagram above). Consumer surplus is the total private benefit consumers get from Q=100 minus their total expenditure (which includes tax payments). This is the small triangle labeled above. This has an area of $2.50*100/2=$125. 9

10 e) 3 points What would be government revenue with the optimal tax in place? You must show your work to receive credit (for partial credit you can shade and clearly label the relevant area in the diagram above). Government revenue is the yellow area shaded above. This is just Q*t. Or 100*$5=$500. Make sure you re clear on the intuition for why GR=Q*t. 2. (12 points total) Question 2 (public goods) refers to the diagram below: 10

11 There are only three consumers in this market for a public good. They have individual demand curves D1, D2, and D3, respectively. a) 4 points Carefully draw the marginal social benefit curve for the public good on the diagram above. (see diagram above) Remember, you get the MSB curve by vertically aggregating the individual MPB curves (demand curves). One way to do this is to, at each vertical gridline, add up the MPB for each person, and plot the sum as a point on the MSB curve. Try this if you got it wrong. You have to get your hands dirty practicing this stuff to get used to it. b) 3 points If the marginal cost of providing the public good is $45 per unit, what is the efficient quantity of the good? You must clearly show your work to receive credit. I ve illustrated the marginal cost curve on the diagram above. Note that if the marginal cost is a constant, this line is horizontal. Some people wanted to draw a MC curve with a slope of 45. That s incorrect. To find the efficient quantity, we set MSC=MSB. MSC=45, so that part s easy. We need an equation for MSB representing the segment of the MSB curve that the MSC curve intersects. Obviously, a picture is very useful here. Note that MSC crosses MSB in the middle segment of MSB. In order to find an equation for that curve, I project the line back to the y-axis (see the dotted line). By inspection we see that the equation for this line is MSB=125-(1/2)Q. How did I get this? Remember your slope-intercept formula from high school algebra? y=b+mx, where b=y-intercept and m=slope? Well y in this case is MSB; x in this case is Q; b is 125; and m is -1/2. So, setting MSC=MSB, we get 45=125-(1/2)Q. Rearranging gives us (1/2)Q=80, or Q=160. That s the efficient quantity. c) 5 points Suppose that there were no contributions to the public good. Calculate the deadweight loss in that situation. You must clearly show your work to receive credit (for partial credit you can shade in the area representing DWL in the diagram above). If there are no contributions, then the quantity of public goods is zero. I ve redrawn the diagram shading in DWL below. It s the area between MSB and MSC between Q=0 and 11

12 the efficient quantity (Q=160). These are all positive net benefits that could be had, if public goods were provided at the efficient level. To calculate the area, you should find the area of the trapezoid between Q=0 and Q=100, and the area of the triangle between Q=100 and Q=160. Trapezoid: 6750 Triangle: 900 Total DWL: $7650 END SECTION 3. END OF EXAM. 12