**Karthik Shashidhar, Resident Quant at the Takshashila Institution and B.CLIP faculty, discusses a few concepts in economic reasoning. **

How much would you value a pen? I’m talking about a stainless steel fountain pen here, made by the Parker Pen Company. It is a three year old pen in excellent working condition.

Let us say that Anjali values it at Rs. 100 and Babu values it at Rs. 50. Now, what if I tell them that I’m willing to sell the pen, and that the price at which I’m willing to sell is Rs. 75? Will either of them buy the pen?

It might be intuitive to see that Anjali will buy the pen at Rs. 75, while Babu will not. Notice that Anjali values the pen at Rs. 100, which means by paying Rs. 75, she is getting hold of a good that is worth Rs. 100 to her. It is a clear win for her! Why will Babu not buy the pen? Given that he values the pen at Rs. 50, he will only get Rs. 50 worth of goods by spending Rs. 75 – clearly a losing deal.

**Insight 1: Price and value are not the same thing. Value is what a particular good is intrinsically worth to you. Price is the rate at which the good is traded.**

What would happen if I were to set the price of the pen at Rs. 40? Now, you might see that both Anjali and Babu will want to buy the pen. If the price is Rs. 150? It is intuitive to see that neither will want to buy the pen at that price.

Now let us expand the problem. What if there are a thousand different potential customers, rather than just Anjali and Babu? Let us assume once again that each of them values the pen independently. Now, how will the number of people who want to buy the pen depend on the price?

**Insight 2: If you value a good that is for sale at an amount that is higher than the price at which you can buy it, you should buy. **

If we were to price the pen at Rs. 50, how many units will it sell? This is exactly equal to the number of people who value the pen at greater than or equal to Rs. 50! If we are to price the pen at Rs. 49? Then it will sell exactly as many units as the number of people who value the pen at greater than or equal to Rs. 49!

You might see a mathematical insight here – the number of people who are willing to buy the pen at Rs. 49 is either greater than or equal to the number of people who are willing to buy it at Rs. 50. How is this so? The people who buy it at Rs. 50 are those who value the pen at an amount greater than or equal to Rs. 50. Now, if an amount is greater than or equal t Rs. 50, it is also greater than Rs. 49. So everyone who values the pen at greater than or equal to Rs. 50 (i.e. people who are willing to buy at Rs. 50) will buy it at Rs. 49. And there are more – what about those people who value the pen at Rs. 49? They may not buy when the price is Rs. 50, but they will definitely buy when the price is Rs. 49! Adding these to the number of people who have valued the pen at an amount greater than or equal to Rs. 50, we find that the number of people who want to buy the pen at Rs. 49 is greater than or equal to the number of people who want to buy at Rs. 50.

Now, we can generalize this rule.

**Insight 3: For a particular good, the number of people who will want to buy at a lower price is greater than or equal to the number of people who will want to buy at a higher price. **

Now, let us look at selling. Let us assume that everyone in the class has an identical pen. Let us say that once again it is a stainless steel fountain pen made by the Parker Pen Company. Once again, each member of the class values the pen differently. Now, what if I offer to buy their pens at Rs. 50? Who is going to sell to me?

People who will sell me the pen at Rs. 50 are those that value their pens at an amount lower than Rs. 50! Let us say Chetan values it at Rs. 40. By selling the pen to me at Rs. 50, he is giving up a good which is worth only Rs. 40 to him, and getting Rs. 50 in return. Hence, he will sell it to me.

Let us say Diana values the pen at Rs. 60. She will not sell it to me at Rs. 50, because by doing so she is giving up a good worth Rs. 60 and getting only Rs. 50 in return! Hence, the people who will sell to me at Rs. 50 are those that value the pen at Rs. 50 or lower. The people who will sell to me at Rs. 100 are those that value the pen at Rs. 100 or lower.

Like in buying, we have a similar law in selling. **The number of people who are willing to sell a good at a particular price is less than or equal to the number of people who are willing to sell the good at a higher price. **

The proof of this is similar to that of the buying case, hence it is left as an exercise to the reader.

Now that we know when people buy and when people sell, can we generalize a trade? If A sells something to B at a particular price, what does that tell you about the valuations that A and B put on the good? That A has sold the good means that he values the good at an amount less than or equal to the price at which it was sold to B. That B has bought the good means he values it as an amount greater than or equal to the purchase price!

**So, you notice that whenever a trade takes place (unless it is under coercion or any other extraordinary circumstances), both the buyer and the seller are better off than they were before the trade! **In other words, voluntary trade is always good.

**Marginal cost pricing**

Let us say I grow mangoes on my farm, and in season the trees collectively bear 100 fruits a day. Let us say that I am willing to sell each of these fruits at Rs. 10. I take them to the market, where other people from the village buy it from me. As long as the number of people who want to buy it from me is below 100, everybody is happy, for everyone gets the fruit they want, and I get adequate compensation for the fruits I’ve sold.

Over time, the population of the village increases and the demand for mangoes grows. Soon it goes beyond 100, and every day some people are denied their mangoes. Now, my intention is to maximize welfare, so it hurts me to see that people who want mangoes are not getting it. What do I do?

Let us say there is a neighbour who is willing to sell me mangoes, and I can sell his mangoes at Rs. 20 per piece. He has a large farm, so he can supply to me as much as I want every day, but I need to be the one going to the market and selling. What price do I sell them at?

Note that I need to have a constant price through the day. If, let’s say, I price mangoes at Rs. 10 per mango for the first 100 pieces and Rs. 20 thereafter (thus accurately reflecting my cost), there will be a rush among the people of the village to buy the first 100 mangoes. Given that they are no different (in terms of quality or any other “intrinsic value”) than the next few mangoes, this creates unnecessary commotion. As a welfare maximizer, I don’t like people fighting, and want them to come peacefully at any time they want and buy the mango at the known price. In other words, I need to price the mangoes uniformly. The question is what price I should charge for the mangoes. Let us assume that each day I expect to sell anywhere between 150 and 180 mangoes.

Instinctively, you might think that the welfare maximizing price is the average price. For example, if I know that the demand will not exceed 180, the average cost of the mangoes I will sell will not exceed (100 * 10 + 80 * 20)/180 = Rs. 14.44. Does that mean I can sell the mangoes at Rs. 14.44 as a welfare maximizing measure?

Let us see what happens then. If the price is 14.44, I am happy selling the first 100 mangoes, for they have cost me only Rs. 10 each. The question is if I will want to sell the 101^{st} mango. Note that the 101^{st} mango comes from the neighbour’s farm, and I can procure it at only Rs. 20. Now, if I have to sell it at Rs. 14.44, I make a loss on selling the mango. Not just the 101^{st} – every additional mango I have to sell thereafter I have to sell at a loss. In other words, I’m better off selling lesser mangoes than more mangoes! And if I don’t want to sell mangoes I’m making a loss on, in that case I’m not maximizing welfare!

Notice that at any price I set below Rs. 20, I have no incentive to sell any mangoes beyond the 100 I have grown in my own farm! As long as I have set a price less than Rs. 20 (even if it is Rs. 19.95) I have an incentive to pack up my shop early and not sell mangoes to everyone who wants it! Hence, a price less than Rs. 20 does not maximize welfare!

So what should I price mangoes at if I want to ensure maximum welfare? This has to be a price at which I’m as happy or happier selling more mangoes, as I am selling lesser mangoes. This can only happen when the price is greater than or equal to Rs. 20!

Essentially, irrespective of how many mangoes I managed to get (in limited quantities) at a lower price, in order to maximize welfare, I need to price the mangoes at the cost of the last mango I purchase! This means that in order to maximize welfare, I should price the good at the *marginal cost* of producing that good! In the case of mangoes here, my *marginal cost* (i.e. the cost of the last mango I buy) is Rs. 20, hence in order to maximize welfare I need to price the mangoes at Rs. 20. This is called *marginal cost pricing*.

Now, let us draw an analogy of an apartment complex. The complex gets a limited amount of BWSSB water a day, beyond which it needs to get water from tankers. Let us say that BWSSB charges Rs. 10 per kilo Liter, and supplies up to 1000 kL a day. Beyond that, the apartment association has to purchase water from tankers at Rs. 20 per kL. The question is how much the apartment association needs to bill its users for water.

The answer is the same as above. As long as the total demand exceeds 1000 kL a day (the price at which the association can purchase water at Rs. 10), water needs to be uniformly priced at Rs. 20 per kL, which is the marginal cost of purchase!

Now let us look at Bangalore city. Let us assume that BWSSB can sustainably draw up to 10000 kL of water a day from the lakes around Bangalore, and this costs them Rs. 5 per kL. Beyond that, they will need to draw water from the Cauvery, over a 100km away, at Rs. 10 per kL. What should BWSSB price the water at?

Again, it doesn’t matter that BWSSB is a public sector agency, providing a “public service”. We have seen that in order to maximize welfare, we need to price the good at the marginal cost. And the marginal cost of procuring water for the BWSSB is Rs. 10 per kL, hence, every unit must be priced at Rs. 10 per kL.

It doesn’t matter whether we are selling mangoes or water or electricity or brinjals. If our objective is welfare maximization, we will need to price the good at the marginal cost. This is a fundamental principle of economics.

*Photo credit: S Vishwanath, Rainwater Harvesting Club.*