Presentation in week 5 - Lecturer: François Gerard Answers to week 5 problem set as coursework PDF

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Lecturer: François Gerard
Answers to week 5 problem set as coursework...

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ECN 352: Problem set for Week 5 1 Questions about the material A1 MD represents the marginal damage avoided due to pollution reduction. In this case as cost reduction is essentially a benefit, we treat it like MD like its MB. MC is the marginal cost associated with pollution reduction. Thus, the optimal pollution level is where MD=MC.

This is because the MC is rising with Q whilst MD is falling with Q. Thus, as pollution reduction Q rises, we net societal benefit from pollution reduction (MC-MD) falls as can be seen from the convergence of the two curves. Beyond Q*=31.6, the cost of pollution reduction MC exceeds the benefit in MD so it is no longer worthwhile. For any Q before 31.6 there is still some higher level of pollution reduction that is worthwhile where the marginal damage averted exceeds the marginal cost of pollution reduction. A2 By setting a tax per unit of pollution, governments are incentivising polluters to reduce pollution. Polluters will reduce pollution provided that the marginal cost of reducing pollution is less than or equal to the tax per unit.

As cost minimisers (profit maximisers), polluters will reduce pollution provided that the marginal cost of doing so is less than the tax per unit associated with polluting.

A3

The optimal level of pollution reduction Q* would rise to Q2 if MD rose. This is because for every level of Q, the marginal damage averted MD rises. Thus, the range of Q for which the marginal damage averted exceeds the marginal cost associated with pollution reduction and pollution reduction is worthwhile. The tax to generate such change would also rise For the tax to reduce pollution, the MC of pollution reduction must be less than the tax per unit as it must be cheaper to not pollute (increase Q) than to pollute (decrease Q). As MC=10+Q*, the MC rising means that the tax per unit of pollution would also have to rise so that the optimal Q is achieved.

A4

The optimal amount of pollution reduction Q*, will fall to Q2 following a rise in the marginal cost of pollution reduction. This is because if the marginal cost of pollution reduction rises for every level Q, the range for which the marginal damage averted from pollution reduction exceeds the marginal cost of pollution reduction and for which pollution reduction is worthwhile decreases. As we can see on the diagram with the new MC2 curve, any Q beyond Q2, the cost of pollution reduction (MC) exceeds the damage averted MD. For a tax to bring the optimal amount of pollution reduction, the MC of reduction must be less than or equal to the tax per unit from polluting. As MC=10+Q*, and we have established that Q falls here, the tax per unit will also fall.

A5

If the marginal damage was constant and didn’t depend on Q, then a rise in the marginal cost would have no effect on the optimal level of pollution reduction Q*=31.6 Due to the Q* value being unchanged, there will be no change in the tax per unit required to bring about this optimal pollution reduction.

B1 When we are finding the socially optimal level, we have to have MB= MCA = MCB. We can solve for QA in terms of QB; 50+3QA = 20+6QB QA=2QB-10 Then we can set MB=MCB and then plug in for QA in terms of QB and then solve for QB; 20+6QB = 590-3Qtot 20+6QB = 590-3(QA+QB) 20+6QB = 590-3((2QB-10)+QB) 20 + 6QB = 620-9QB 15QB = 600 QB=40 Then we can plug in for QA and we get: QA=2QB-10=80-10=70 QA=70 So, the social optimum level of pollution reduction is QA=70 and QB=40.

B2 We had that both A and B were producing 80 units of pollution each, so in total we had 160 units of pollution. The socially optimal level makes it so that A reduces its level of pollution by

70 and B by 40, so the total unit of pollution reduction is 110 units. So, there is 160-110= 50 units of total pollution in the social optimum. B3 If we were to give firm A and B an equal number of pollution reduction permits, they would divide the level of reduction (110 units) equally between the firms so both firms would have to reduce 55 units each, so they are allowed to produce 25 units of pollution each. This would be inefficient. This is because now the requirement of a social optimum, MB =MCA =MCB, does not hold when we have QB=QA=55. So, we could improve the efficiency by having firm B produce one more unit of pollution and firm A producing one unit less. The unit of total pollution would not change, and the unit of pollution reduction would not change either, but the cost of abatement would go down by 250-218 = 132. So it is more cost-effective to have A reduce more pollution than B, so again it is inefficient. B4 We can now start from where we have both firms produce 25 units of pollution each, like in A3. B will have an incentive to buy the right to pollute by buying pollution permits, if the firms are allowed to trade the permits. This is because it costs more for B to reduce pollution than it does for A. B can make both firms better off by paying A minimum firm A´s MC and maximum firm B´s MC for a permit of pollution. The firms will keep making sales of profit like this until the social optimum is reached (so when MB = MCA =MCB), and until the cost of one more unit of pollution reduction is the same for the two firms. B5 When finding the amount of tax that is needed to reach the socially optimal amount of pollution reduction, we must find T so that: MCB (social optimum) = T = MCA (social optimum). The MCA is equal to 260 when QA=70, and same for MCB when QB=40, which is the socially optimal level of QA and QB. So, the tax would be T=260 to reach the social optimum. So, B would reduce 40 units of pollution, and A reduce 70 units of pollution. We then see that a tax on pollution would achieve the social optimum. C1 The socially optimal level of each firm’s pollution reduction is when MC^A = MC^B =MB. Solving this gives for Q^A in terms of Q^B gives us 20+4Q^a=10+8Q^B =400-4(Q^A+Q^B) giving us Q^A=2Q^B-2.5. And solving for Q^B thus gives us 10+8Q^B=400-4((2Q^B*2.5) +Q^B) giving us Q^B=20. Putting this back into the equation gives us the value of Q^A=37.5. Therefore, the socially optimal level of each firm’s pollution reduction is 57.5 units of pollution.

C2 Before, each firm polluted 80 units respectively (total 160). Therefore, to find out How much total pollution is there in the social optimum we must subtract 57.5 (optimal level of each firm’s pollution reduction) by 160 (total before) giving us 160-57.5= 102.5 units C3 The reason why it is inefficient to give each firm an equal number of pollution permits (if they are not allowed to trade them) is as splitting the permits in half (57.5/2=28.75) this means each firm will pollute 51.25 units respectively. However, this is inefficient as if both Q^A and Q^B equal 28.75 this breaks the social optimality condition (MC^A=MC^B=MB) as the firm with higher MC is rewarded with more permits while the firm with a lower MC is punished with less permits. Therefore, it would be optimum to allow firm A to pollute an extra unit and for firm B to pollute one less. C4 It is efficient in this case to allow firms to trade pollution permits as we know from past C3 that individually a firm can produce 51.25 units as well as the fact that firm A would reduce its pollution by an additional unit if it was paid more than 139 while firm B (due to a higher marginal cost) would be willing to pay more than 240 for the ability to pollute an extra unit. Thus, if TPP (tradable pollution permits) are allowed, both would increase profits as for firm B it is more profitable to buy permits then to reduce its pollution by a unit. Indeed, permits would be traded till the socially optimal level of pollution. C5 The social optimum can be achieved using a uniform tax on pollution. The reason for this is if a tax was set at 170 (we get this from MB = (57.5) = 400 − 4(57.5) = 170), both firms A and B would have to reduce pollution to the point where MC^A = MC^B = 170. This means that each firm must reduce pollution until the marginal cost is greater than marginal benefit, which if solved gives us 20 + 4Q^A=170 therefore Q^A = 37.5 while for Q^B we get 10+8Q^B=170 gives us 20.

2 Questions about the assigned reading A To summarise, the paper aims to identify the impacts of deworming programs on specifically education and health outcomes directly and as a result of externalities. The infection rates of worms is a huge issue and the paper estimates it affects a quarter of the world population. Research question is analysing the effect that treating intestinal helminths and thereby reducing transmission of such illnesses had on school absence, school participation, health participation and academic test scores as a means to justify treatment. Researchers build on the current literature which argues that there is a great underestimation of the benefit of treatment which is largely attributed to failing to acknowledge the external benefits of treatment. So the authors want to analyze the effect of deworming on a randomised

group basis rather than individual which allows for more variation within the group densities and can help compare cross group externalities, and just generally more accurately estimates the effects. The providers of the group split 75 schools into 3 within one of the poorer regions of Kenya and with highest infection rates over the course of three different time periods for financial reasons mostly. Essentially using difference in difference estimator in a cluster randomised trial The main results show that the direct effects on treatment group schools is that infection rates dropped (health benefit) and participation rose as a result (education benefit), with externalities within the school resulting in the same thing as programs did in administer the medication to everyone all at once so those who are now treated are less likely to spread it therefore others benefit. The externality results are similar with the control group (especially neighbouring schools), as the treatment of some schools’ benefit all as infection rates drop and students are participating more. The results of the paper show that that the full effect of these externalities fully warrant subsidization of the treatment and is cheaper than alternative ways to boost attendance. B The 75 schools chosen to be in the study were all in western Kenya, because the region had the highest infection rates within Kenya due to contaminated lakes and lack of access to hygiene facilities lead to quick spreading, so any proven positive externality effects whether within the treatment group or across the control group would of course affect western Kenya the most. As to the reason why we see health externalities, when students who had the infection get treated this reduces the rates of the infection to other students from within their own school of course (many students even within the treatment group did not get treated due to many reasons such as consent complication, absences, and dropouts) but also to other schools that are within a close proximity. So clearly there are benefits to third parties when the deworming program is implemented in a group. However, the extent to the benefit of these externalities differs depending on the type of infection, where the reduction of infection on other treatment groups and control groups is different and sometimes dependent on the type of group. C We can separately find results by first using variation in local density of treatment schools by randomisation which will help us get empirical results for the cross-school externality (and overall program effect) and secondly having to use non-experimental methods to attain the direct effects as well as in-school externalities. This is allowed due to randomisation at a group level, helping reduce the underestimation caused by randomization at an individual level, allowing us to compare the overall effect on schools better (direct and in-school externality) easier and easier to compare to nontreatments schools helping us gauge cross school effects as well. D In column (2) of Table VII: - Direct effect of deworming drug is given by coefficient for “(Group 1 Indicator) ∗ Received treatment, when offered” which is a value of -0.14 meaning a 14% point reduction (relative to

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group 2) in any moderate-heavy helminth infection in 1999 directly due to the treatment statistically different to 0 at 90% confidence The health externality effect within schools is given by the coefficient for “Indicator for Group 1 (1998 Treatment) School” which is a value of -0.12 meaning a 12% point reduction in any moderate-heavy helminth infection in 1999 due to the positive externality effect caused by the program statistically different to 0 at 90% confidence The health externality effect across schools is given by both coefficients “Group 1 pupils within 3–6 km (per 1000 pupils)”, which is a value of -0.26 meaning 26% point reduction in any moderate-heavy helminth infection in 1999 due to the presence of each additional 1000 Group 1 students within 3km of a school due to the positive externality caused by the program statistically different to 0 at 95% confidence, and “Group 1 pupils within 3–6 km (per 1000 pupils)” which gives us -0.13 a 13% reduction the same as the other coefficient but within 3 to 6km instead.

E That would be the same coefficient as the direct effect, as it represents the effect of those who actually received the drug within the group whereas the externalities would simply be the third-party effect of being in the same school as students who received treatment; a value of -0.14 meaning a 14% point reduction (relative to group 2) in any moderate-heavy helminth infection in 1999 directly due to the treatment statistically different to 0 at 90% confidence F The key lesson from this paper is that there are large health and school participation external benefits (to untreated students) from treating these intestinal helminths related health issues despite them not affecting academic test scores. These estimates of external benefits are so large that they warrant the full subsidisation of deworming so that these external benefits can be realised across all of society. The paper also teaches that in many studies that the true effect of externalities is underestimated due to various biases, and show that randomization at group level is more efficient in finding accurate values for all effects In regard to the limitations of this study, the rate of heavy infections was abnormally high in the region of Kenya studied even for LEDC standards. This can be seen in table 1. This draws into question whether the findings can be applied to regions where the heavy infection rate is less severe. Thus, the research may lack external validity. The other main limitation is having to use non-experimental methods to find the direct effect and within-school externalities, due to the randomization at group level. This made calculating all variables wanted possible, but more complicated. A possible solution would have been randomization at multiple levels rather than just individual or group wise, possibly randomizing both and also across the 3 groups as well. This might have allowed for the discovery of the true effect of externalities more accurately.

We can see that there are overall differences in school attendance between year one and year two. If these changes are due to other unobserved variables this could diminish the reliability of the studies. Finally, there is a lack of a predefined sampling strategy for school visits to assess attendance. G Given that the research indicates that the external benefits are such, we do believe that there should be government intervention in order to increase the take up of deworming drugs. In regard to what type of intervention is warranted in this context, given that the issue at hand is a positive consumption externality as we want people to consume more of this medication so as to realise the spillover effects. We believe that this is not a positive production externality as the focus is not on drug producers but on the children as drug consumers.

The market equilibrium Q1 is socially inefficient as SMB>SMC. We use a subsidy so as to shift the SMC curve down so that the new equilibrium is at Q*. This is socially optimum as beyond it the SMC>SMB and in the range before its SMB>SMC so the full benefits haven’t been realised. Thus, a subsidy is the optimal government policy for this situation. Also, because it is of its costeffective nature compared to alternatives in terms of both Education (attendance does not test scores)....