 In this module, we will look at the solutions of the revision paper, the second revision paper. I hope you've been able to solve these. These are actually the questions are all related to whatever we have done in the course and so we'll just go over it quickly. The first question is comment on whether the following good services, bads, rival, non-rival, excludable, non-excludable, public, private. Explain your answer. So we'll start with the first one, biogas plant. So when you look at a biogas plant, a biogas plant is manufactured by a company, it is supplied, it is sold at a price and if someone uses the plant, it will not be available to someone else. So basically this is very clearly this is going to be rival as well as excludable. It is sold only once a price has been paid and so this is very clearly this is a private good. Let us look at the next one, the Eastern Freeway. The Eastern Freeway is a road in the city of Mumbai connecting this suburbs to the main hub then going all the way up to CST and this is a freeway. There is no toll being charged. So in the sense if now in this case, in the case of a road, if there are many cars coming on it, there would be congestion. So if we say that there is no congestion, then this can be, this will be non-rival. Someone using the freeway does not affect the ability of someone else to use the freeway. If you think of congestion, then it could be rival and since it is being made free, we are not, it is non-excludable and this can be treated as a public good. We could change the rules and if we have toll, then it is excludable. If we are looking at congestion, then it could also be rival but in this case, we can consider it as a public good. C is urban air pollution. This is a big problem in most cities in India now and if we look at this, in a sense someone's breeding the polluted air does not affect someone else's ability to breed that polluted air. So essentially this is non-rival and generally this is also going to be non-excludable. Of course now people are putting air purifiers and looking at ways in which one can actually remove this so that could change. So this is what is a public bad and that is why since it is a public bad, the normal rules of market are not very good at controlling this and then we need to have regulation, we need to have different kinds of methods. Now let us look at the last one here. This is cable television. In cable television, this is actually going to be non-rival. In general, again depending on the bandwidth, there is no congestion. You are watching cable television does not affect someone else's ability to watch it and you have these set-top boxes so only if you pay the charge, you are going to be able to get the channel so it is excludable and this is a private good though it is non-rival. So with this we look at, so you can just summarise whatever we have done in the course related to private goods and public goods and these examples illustrate this. So let's move forward with the next part of the question. One, E. And this question says, IIT is charged 2 lakhs per year as annual fees to students for undergraduate education. While the full cost of IIT education is about 6 lakhs per year. It may be a little more than that but for the point of view of this question, we just put it as 6 lakhs per year. There is a proposal to recover the full cost of IIT education from the undergraduate students. Consider a society with 1% families containing IIT students. Would the proposal pass the Pareto condition? So currently the students are paying 2 lakhs and the increase in fees would be 6 lakhs. So if we look at a Pareto condition, the percentage of families, the families who are with students who are currently doing the education, they would not be, they would not, their condition, their utility would decrease because they would have to pay an additional amount. So it will clearly not pass the Pareto condition. Others would not be affected but if we increase this, the existing students would, their utility would decrease and hence that would not pass the Pareto. Then the second thing is, would it be based on the Pareto compensation principle? Now the compensation principle would not be, would not apply in this case because possibly with this additional money which is coming in, maybe the rest of the society will have to pay less but then there is no way in which they can compensate or provide the 1% of students with the difference in this amount. So it will not pass a compensation principle either, not pass the compensation test. Now suppose the next part of the question is if the society has to pay an equal tax to bear the cost or recover the full cost from the students. So these are the two options. So clearly 99% of the population who would not want to, even though the amount would be less, they would not want then increase in the taxes for education. The 1% would of course say that an equal tax can bear the cost. So from a voting point of view, the solution would, we will get an option where an equal tax to bear the cost will lose and the full cost would be born from the students because it is only 1%. Now the last part of the question is provide an economic argument justifying continuing the subsidized fee. So if we look at higher education typically as a public good and if we look at the products of that education resulting in an enhanced income for society and every graduate from the IITs based on the income that they are going to earn over their lifetime and their career and the taxes that they pay to the government. So from an economic viewpoint the enhanced ability to earn will compensate for the subsidized fee. The second thing is that in general we can develop we also thinking in terms of creating new knowledge and providing an opportunity for all. So that means every individual has this opportunity and depending on their abilities they can get through this and then they can upgrade their upgrade their abilities and then they can contribute to society and in many cases the graduates would actually also create employment and create. This of course is a debatable issue but in many cases you will see that a lot of literature talks about higher education actually being a public good and this is something which benefits society in the long run. So the other option of course is to provide loans but depending on the average income taking a large amount of loan for education becomes a barrier for several families and this has an equity impact. Let's move ahead to the second question. The second question is a standard supply demand curve which we have we had also solved it in the when we had done that module if you look at this this is a supply curve for coal in a country is given as P is equal to 2500 plus 5Q demand curve is given as 8500 minus 10Q where P is the price in rupees per ton Q is the quantity in appropriate units say million tons annually plot the supply and demand curve determine the equilibrium price and quantity what is the consumer surplus and producer surplus show these on the plot what is an externality in the case of coal production list some of the externalities if the government decides to impose a carbon tax on all the coal sold that means 500 rupees per ton of coal show the new equilibrium point is the tax efficient does it result in a change in the total surplus what could be the justification for the carbon tax. So let's start with the first thing is let's let's draw quantity on the x axis dan price on the y axis and if we look at this and the sub-demand curve will be given as let's take this is Dd this is 8500 minus 10Q and so this is 8500 and the supply curve is so let's say somewhere here 2500 2500 plus 5Q this is the point of intersection this is the equilibrium quantity equilibrium price and these points this is the consumer surplus because this is the price paid is P0 but at zero quantity the demand we are willing to pay so much so this is the consumer surplus and this one is the producer surplus this is consumer surplus producer surplus this is the total surplus so this is what we have done we can calculate this let us just calculate from the equation let's put down 2500 plus 5Q is equal to 8500 minus 10Q so we get 15Q is equal to Q is equal to 6000 by 15 400 units let's say million tons what is the price? price is going to be 2500 plus 5 into 4400 sorry and this comes to 4500 rupees per ton so we can go back to this and write down this is 4500 and this one is 400 and this is 850 okay so now we have done this show these on the plot what is an externality and externality is basically something which influences and the utility of a consumer or the production function of a producer without its own permission so in the case of cold production what are the externalities that we have? well we have in the mining there would be a lot of dust and there would be a lot of land modification and in the case of there would be also pollution in terms of both air quality as well as water and so these are the kind of things and then the use of coal when we look at it we will have carbon dioxide and we have emissions so these are some of the externalities and if the government decides to impose a carbon tax on all the coal sold incidentally there is already a carbon sess today and it is probably around 400 rupees per ton so we have said here suppose there is a carbon tax of 500 rupees per ton how would the equilibrium change and is the tax efficient so what this would mean is that if you look at the supply curve for every ton we are adding another 500 so this will now start from 3000 and we would have it as something which would be should be parallel to this so now this will be the new point new point is Q dash P dash we can calculate this let us calculate it by looking at how much will this pay we can 3000 now plus 5 Q is 8500 minus 10 Q so 15 Q is 5500 Q is 5500 by 15 367 million tons what has happened is we have now the equilibrium point has shifted and we are now using less amount of coal and the price now is 3000 plus 5 2100 by 3 which comes out to be 4833 rupees per ton so now we have shifted from the earlier case where we had the price of the initial equilibrium point was 4000 sorry 400 million tons and 4500 and this has shifted to 367 million tons and 4833 so if we go back to the figure that we had this is 367 this is 4833 now if you look at the total surplus you will see that the total surplus has decreased so the tax of cost is not efficient from that point because the total surplus has decreased from an economic viewpoint however the justification is that if we look at the cost of carbon and the social cost of carbon and incorporate that then you will find that overall there is a benefit because we are reducing the CO2 and then the benefit to the benefit to society offsets the loss which is there for the consumers and the producers and so the justification for the carbon tax is that we would like to see that we use we use we reduce the total CO2 emissions and then we are trying to give an disincentive for using coal which has a high carbon content so this was the calculation for the second problem now let us move on to the next problem so here we are looking at consider a decision being taken in your hostel so that we can invest in a flower garden between two wings now the way this works is that the hostel has a large number of 300 residents out of which 100 residents are willing to pay a little more they have a marginal willingness to pay P is equal to 100 minus 2 Q because they can have a direct view of the garden while the other residents if they are passing by will see it but they do not have it from their room so the 200 residents have a marginal willingness to pay S 60 minus 3 Q where Q is the number of flowering plants and P is the willingness to pay in rupees marginal cost of supply of a flowering plant is constant at 150 rupees so at 150 rupees you can buy one plant and then put it in the garden so the question is how many plants should be put in the garden so we want to sketch the aggregate demand and supply curves and determine the optimal number of flowering plants and then the question further asks is this a lindal equilibrium is this feasible to implement what are the difficulties in implementing the lindal equilibrium so now this is a public good and the supply though is something where there is a price for the supply but the good of having a garden is something which is non-excludable and it is a private good and it is how much of that public good should we be providing and when we look at this if we try to sketch this if we look at the marginal willingness to pay and P and the quantity Q you will see that individual the individual who are have a direct view of the garden have a marginal willingness to pay P is 100 minus 2 Q so this will go on to when it becomes 0 beyond so this will be 50 so we can just join this this is the individual demand curve and there are 100 such individuals for the other set those who are not having a direct view of the it will start from 60 P is equal to 60 minus 3 Q so it will go on till 20 and here N2 is equal to 60 the demand the the supply the curve will be shown clearly as straight line at 150 now here what happens is that we aggregate based on the number of part the plans which are there at any value of Q we can find out how much people are willing to pay from these 2 curve so when it's between 0 and 20 you will have sorry the N2 is equal to 200 so these 200 people will be willing to pay from here so we can take any point here and just take the values which will be here and multiply so we will get if it is at if 0 let's just write this as if 0 less than Q less than equal to 20 what will happen is the total willingness to pay aggregate demand curve P will be 100 x 100 minus 2 Q plus 200 x 60 minus 3 Q so this is 10,000 minus 200 Q plus 12,000 minus 600 Q equal to 22,000 10,000 plus 22,000 minus 800 Q so if we look at this total amount that we are willing to pay this is going on so it will start from 22,000 and then come down when Q is equal to 20 this will be P will be 22,000 minus 860,000 so this is going to be 20,000 so what will happen here is that when we do this curve the aggregate curve P we start from 22,000 and then we go to when we take 20 let's take 50 in the case of this 22 10 6000 this is the aggregate demand curve from here onwards from 20 to the next point it is only going to be equal to P is equal to 100 into 100 minus 2 Q because all those the remaining this set of individuals are not willing to pay anything beyond 20 it is going to be this so when we look at this this is going to be equal to 10,000 minus 200 Q now if the the supply price here is 150 so if we put this as 150 then this is going to be equal to 9,850 is equal to 200 Q 9850 by 200 so we rounded off to the smallest whole number which comes to about 49 so this we have a line here which is the demand curve which is 150 at around this we actually it will intersect it will intersect almost at this point so this is if you draw it proportionately you will find that this is the value which is there so this is now the question it is a lindal equilibrium because we are asking individuals what is their willingness to pay and then we are aggregating that is this feasible to implement it is difficult to implement one is because it is difficult to get the demand curves of the individuals stated demand curves accurately and there is an incentive to understand the willingness to pay because you enjoy the quality but you will pay based on your based on the marginal willingness to pay so others may get a better share so basically the issue is the difficulties in implementing the lindal equilibrium is the ability to individual demand curves and the point that there is an incentive for individuals to understate their willingness to pay so that they actually end up not paying this but theoretically the lindal equilibrium is an interesting concept and there is this whole issue in terms of when we try to price a public good or a public bad these are the kind of problem so this is what we have solved in this question