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Module 1: Arrow's Theorem and Demand Curves

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Surplus and Public and Private Good/Bads

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Okay, so now to get back to our usual analysis, when we talk in terms of creating, this figure is from Kolstad, we can do a similar kind of thing if we are looking at, let us say any goods and services if you are looking at coal or oil or natural gas, we are looking at the quantity and we have the price. So when we do this, we can create, first of all, a typical demand curve. So, that means at a certain price, if you are looking at let us say coal, at a certain price, there will be zero demand for coal and as the price decreases, the quantity increases, so this is the demand curve. On the other hand, if we look at the supply curve, we will find that there is a minimum amount of price which the supplier must get before they decide that they will supply the product. So, we will start with a minimum and as more and more quantity is demanded, more and more price, more and more price is there, more or more quantity will be supplied. Because at higher prices there will be others will come into the market and so, you will have a supplier curve something like this. So, here, if you see, we will get this point, which is the point of intersection, which will give the price at which we will operate in the market, we can draw a straight line through this and this then becomes the quantity demanded and this is the price. Now, what happens in this is if we look at this, you will find that, as we look at any particular amount of quantity, if we look at this point, at this point, people are willing to pay a higher price than the price here, since the market is clear that this price all the entire quantity is now available at that price. However, if the quantity required was lower, you are willing to pay an additional price but we are getting it at this price this difference is the surplus that is available to the consumer. And when we integrate this, this total amount, this is the consumer surplus. We will define this in a bit, in a similar fashion, if you look at a producer, producer is getting this price. The producer was willing to produce at this price as it goes on. So, at any point of time, you are getting this prize but you were willing to produce so this part shows the producer surplus and if you integrate this again over the entire range of quantities, we will get, this is the producer surplus and this total is consumer plus producer surplus. When you look at this, the consumer if I fixed some other price, if I had the market price at some other point, we would find it, suppose we added at letting us say, at a higher price, then the producer surplus would increase, the consumer surplus would decrease and the total would decrease. So, you can show that in this particular case the total surplus is maximized when we have this point as the intersection of the market-clearing price. So, that is an interesting kind of aside, we can show that this is the case. (Refer Slide Time: 05:14) Now, let us define these so, the consumer surplus as we have defined, as you can see in this case is that we have let us say consumption of q star units for a consumer, we talk about any consumer which is. (Refer Slide Time: 05:40) Let us redraw this and let us know to draw these curves and we can so, in general, this is the quantity and this is the price and this is the consumer surplus. So, you can see that this is the consumer surplus, this is p star and this is q star. So, if you look at this, it is the q star units for a consumer the area between the demand curve, this demand curve and the horizontal line p is an equal top star, this is the line p is an equal top star. This area between q is equal to 0 to q is equal to q star, this area under this curve is the consumer surplus. (Refer Slide Time: 07:16) And similarly, we can show the producer surplus. So, we can draw this and here now, again we have q star and p star and this is your price and quantity. So, in this case, when you define this, this is how we have turned this and now, we are looking at the producer surplus as the production of q star units for a producer, which we were talking about this is the point and the area between the horizontal line p is an equal top star, this is p is an equal top star and the supply curve between q is equal to 0 and q is equal to q star, this is the producer surplus. So, with this we have defined, formally define the consumer surplus and the producer surplus. And, to quickly sort of sum up first we have looked at the Arrows Impossibility Theorem, which says that there is no need theory of social choice which meets all the six axioms that we had. And then having said that, we then looked at the kinds of when we talk about a market. We talked about the movement so, that we are on the Pareto frontier, no Pareto improvements are possible, there are no inefficiencies in trade and no inefficiencies in production. (Refer Slide Time: 09:25) And then we said that there are these theorems of welfare economics, where we says that the competitive economy, market equilibrium is Pareto optimal. And then any Pareto optimum that we have can be achieved by the market forces, providing resources of the economy are appropriately distributed before the market is allowed to operate. We also noted that the market says nothing about fairness or distribution of resources between individuals and equality or inequality. We then talked about the different assumptions which are there for creating a market and talked about the definition of the equilibrium, market equilibrium, the consumer surplus and the producer surplus. And we said that the equilibrium which is obtained maximizes the sum of the consumer and the producer surplus and this is the basis for saying that okay, the market is a good thing to happen. We will see the assumptions which are there in terms of creating this analysis for the market, many of these assumptions often will not be relevant in the real world. And then there are distortions in the market, where there is a need for government intervention, there is a need for policies and we will take a look at some of this. (Refer Slide Time: 10:49) You can look at more details in the book by Kolstad or the book by Webb and you can look up the Lawrence Summer Memo. We are going to now look at in the next module, we will look at the different kinds of goods and services, we will look at what is known as public goods and private goods and how do we differentiate this and then we will take that forward and look at how do we look at goods and services and the environment and try to see how we can include the environment in the calculations that we are doing for the market equilibrium. We have seen the concepts of market equilibrium and we said that the market equilibrium gives us a Pareto optimal. It is a solution on the Pareto optimal frontier, we also said that the market equilibrium maximizes the total surplus, that is the consumer surplus and the producer surplus. (Refer Slide Time: 11:47) So, let us take a simple example to illustrate the concepts that we have just learned. So let us look at an example, we have a supply curve for petrol in a country where the price is given as 10 plus 2Q. So, it is a linear supply curve and, if the price is more, more of the producers will be willing to supply. So, that is a P plus is 10 plus 2Q, the demand curve, on the other hand, is given us P is equal 100 minus 4Q, where Q is the quantity and let us say that the P is the price in rupees per litre, this is an aggregate demand curve. So, the Q would be for the country as a whole may be in terms of some millions of litres or millions of tons, but we will just look at it as a unit, physical unit and P is the price in rupees per litre. (Refer Slide Time: 13:02) So, the question which is asked is plot the supply and the demand curves and determine the equilibrium price and the quantity, what is the consumer surplus and the producers surplus and show these on the plot. (Refer Slide Time: 13:19) So, let us just do this, let us draw first, right down the axis this is Q, this is P and when we look at the supply curve that is 10 plus 2Q. So, when Q is equal to 0, the price will be 10 and it will increase as a straight line. And here when this is the supply curve P is equal to 10 plus 2Q. In the demand curve when Q is equal to, when the price is 100, there is no consumption and then when the price is 0, this will come to 4Q is equal to 100, so Q will be equal to 25. And we will get something like this, this is 100, this is the demand curve. This point becomes the equilibrium point and this is the producer is getting this price. Let us calculate that price, let us equate the two, that is 10 plus 2Q is equal to 100 minus 4Q, let us just use another piece of paper and so you get 10 plus 2Q is 100 minus 4Q. So, we get 6Q is equal to 90 and Q is equal to 15, whatever units million tons, million litres, put this back in the price. So, the price is 10 plus 2 into 15 that is going to be 30 plus 10 that is going to be 40. So, the price is 40 rupees per litre. And the quantity is 15 whatever million, tons. So, now, when you look at this, if you go back to the figure, this is going to be 40 and this is 15. The shaded area that we have is the surplus of the producer because the producer is getting 40 rupees per litre and for at any quantity less than 15 when we look at it you are getting 40 but we were willing to pay the supply curve says it is a smaller value. So, at any point, this is the surplus, which is the producer surplus when you sum it up over the total amount of Q this is the amount. So, if we look at what is the producers surplus, this is the producer surplus, we can find out this area, this area is going to behalf, it is a triangle, half base into the height and this base are if you look at this, this is 10 half into 30 and 15. So, producer surplus is going to be 15 into 15, 225 units. The consumer surplus is like this at a price of 100, the consumer will not buy, there will be no demand, but at any other price, the actual willingness to pay is this value and the actual payment is only 40 rupees. So, this much is the consumer surplus, if you aggregate it over all the consumers, this triangle which is shown here, which I am now shading, this is the consumer surplus. So, the consumer surplus here if you look at it, if this triangle the area is going to be half into this is 40, 100 minus 40 is 60 into 15 so, this is going to be 30 into 15, 450 units. Total surplus then becomes, it is also known as the market surplus, total surplus or market surplus. The market surplus is 450 plus 225 is 675 units. So we have solved this, we have got the equilibrium point and we have got the total surplus, we have got consumer and the producer surplus. (Refer Slide Time: 19:21) Now, the question is that if the government decides to fix a price of let us say rupees 50 per litre, explain what happens to a consumer and producer surplus, is this price-fixing efficient from an economic viewpoint? So, in a sense, for instance, if you see actually in India today, the X refinery price of petrol, of petroleum products on that on top of that is taxes and duties. So, the actual price that we pay for petrol is almost double of what is the price X refinery. And this is because the government uses that as a revenue mechanism, also wants to discourage the consumption of oil. After all, we have so much oil imports, but if we now just said that let us say instead of 40 we would like to make this at 50 at this point, then what happens to the consumer surplus and the producer surplus? Now, what would happen is in this case, if you see this area is reduced from the consumer surplus so, consumer surplus will reduce by this quantity. The actual equilibrium value of supply would reduce and we can calculate this by putting in, this point can be just calculated by looking at 100 minus 4Q is equal to 50, so Q will be 12.5, this will be 12.5. Now, when you look at this, you will find that now, the consumer surplus has decreased by this amount and the producer surplus, on the other hand, has now become this amount because the amount, of course, presuming that all of this money is going to the producer and not to the government as a tax. If we fix this, then this is this amount of rea is increased while this is decreased and this is the total. But as compared to the earlier case, this small triangle that we have is the dead loss and this is the inefficiency because of the price-fixing and as we saw earlier, the total surplus that is producer surplus and consumer surplus is maximized at the point where we have the market equilibrium, where the points intersect and if we fix any other price, the total surplus would reduce. So, you can cross-check and you can calculate for 50 rupees and you can calculate this area and you will see and so, this is the reason why we say that the market is efficient and market equilibrium is the point at which we can get the Pareto optimality and the efficiency. Of course, this is subject to all the assumptions that we have made for the operation of the market. We have seen the concept of Pareto optimality of market equilibrium and then we saw the concept of consumer surplus, producer surplus and identified the point at which we would get an efficient price. Now, when we look at different kinds of goods and bads and services so for instance, we are looking at buying electricity, we are looking at buying batteries, we are looking at garbage, disposal of garbage, we look at the environment in terms of the air quality, you can look at using and getting a benefit from a park. So, you can see that all goods and services are not of the same type and especially when we trying to understand the impact of energy systems on the environment and we would need to be able to differentiate some of the qualities of these goods and bads that we are talking of and typically in the economic literature, we talk about public and private goods and bads. So, in this module, we will look at what are the characteristics of goods and bads and based on these characteristics, how do we classify goods as public goods and private goods and when we know that there are public goods or private goods, what does it mean when we want to aggregate and look at the kind of demand curves that we can get. So, this is the sequence in which we will develop this thought. (Refer Slide Time: 02:20) So, there are two concepts that we are going to look at, one is excludability and the second is a rivalry. So, we will look at what we understand when we say that a good is excludable and what do we understand when we say that a good is a rival good or a non-rival good. So, in both these cases excludable non-excludable. (Refer Slide Time: 02:41) So, a good is excludable if it is feasible and practical to selectively allow consumers to consume the good. So, for instance, if you look at this pen, if I buy this pen and then this pen belongs to me, then someone else cannot buy the same pen, so that is a sense of saying what we mean by excludable. If you are looking at consumption, we are looking at a certain amount of, you look at an apple, if you consume an apple, then that apple is not therefor someone else to consume. So, when we want to differentiate between private and public goods and bad, we want to look at two characteristics, one is excludability and the second is a rivalry. So in the case of excludability, we want to make sure that if I am supplying electricity, those who are paying for the electricity can be provided that electricity and if you don’t pay for it, you will not have access to it. If I am looking at in any market when you buy something, it is possible in the market for you to get access to it only if you make that payment if you are going, so it is feasible and practical to selectively allow consumers to consume the good. Similarly, in the case of a bad, bad is excludable if it is feasible and practical to selectively allow consumers to avoid consumption of the bad. For instance, if I am looking at garbage, that is being created in the household and if I have a mechanism by which I can take that garbage and I can pay the municipality a certain amount to be able to dispose of the garbage, then that garbage is excludable. So, when we talk about excludability, it means that we can, we have a mechanism by which we can ensure that good is only available to an individual. So it is feasible and important is not only that it is feasible but it is practical to selectively allow consumers to consume the good. Once we can do that, then that provides us with the basis for creating a price and a mechanism for excluding those who are not paying that price. So, this is a particular characteristic that we are looking at excludability. (Refer Slide Time: 05:37) The second concept that we want to understand is the concept of rivalry. And in the case of rivalry we are talking of a good or bad is rival if one person's consumption of a unit of the good or bad diminishes the amount of the good or bad available for others to consume. Which means that if I have a fixed amount of some good if you have a set of, I have bought a set of pens and if a person it takes 5 of those pens, those are not available for the other person. So in a sense of, if you are looking at food, if you are looking at bananas or apples, if we, if I consume that banana that is not available for consumption by someone else. On the other hand, there could be a sun, a sunset, and you are enjoying the beauty of the sunset. My enjoying the beauty of the sunset does not affect someone else's ability to enjoy that. So, then it is non-rival. So you understand the difference between rivalry and non-rivalry. A rival good is where someone's consumption of that good diminishes the amount of the goods available for the others to consume. So, these are two important characteristics. (Refer Slide Time: 07:11) And what we try to do is we create a matrix which says let us have 4 quadrants, let us say that we have excludable and non-excludable and then we have rival and non-rival. So, what we will find is that if we are looking at the good, that is rival and excludable, this good is called a private good, that means that we are saying that this is going to be, we are looking at this quadrant, where goods are rival and excludable these are also called pure private good and this is ideal for a situation where it can be tackled by the market. At the other extreme, you would have goods which are neither rival, non-excludable. So, this is in this quadrant, this is pure public good, this is where it is non-rival and non-excludable and a pure public good and we will see that for pure public goods there are problems with the market trying to provide pure public goods, and we will prove and see what that means. Okay, so we talked about how the difference between rival, we have talked about characteristics like rivalry and excludability. And then we have used that to characterize goods as pure public goods, pure private goods in a similar fashion, it can be pure public bad and pure private bad. So, once we have done this, and if you have understood these concepts, now, we should be able to classify different kinds of goods and services. So, I have a list of different goods and services and let us spend a little bit of time thinking about each of these and characterize them as public and private goods. (Refer Slide Time: 10:47) So, let us start with the first one, fairly simple think about it a pizza, is it excludable, is it rival? So pizza is excludable, you order it, you pay for it then only you get it. So it is possible to when it is made it is only given based on the payment. So it is excludable. Is it rival? Yes, once you consume it, it is not available for someone else to consume so, pizza is a rival, excludable and hence it is a pure private good. Let us look at higher education, we will talk about this, think about it and we will come back to this and we will discuss this in more detail. This will depend on the assumptions that you have and the kind of belief systems it is not a direct calculation, we will talk about both rivalry and excludability. If you look at ice cream, again the same concept just like the pizza, and so it is both rival and excludable and it is a private good. Now, look at a lighthouse, the lighthouse is in the earlier days, this would be provided on the shore and it would provide light for ships in a particular location. So, in this case, is it rival, is it excludable, in general, if you have any ship in the vicinity, they would be able to see that light and unless you do some kind of a technological change, basically it is accessible to everyone. So, it is not excludable, if you had some modification in technology where you could provide that access only based on some fee, then it would have been excludable but as of now it is not excludable, is it rival? It is not rival, in the sense that if one ship sees the light, it does not affect this light being seen by the other ship, it is at a height and so this is non-rival, non-excludable, it is pure public good.