Price Determination

Prologue:

ছাত্রজীবনে “price” কীভাবে ঠিকহয়, সেটা ঠিকমতো কখনও বুঝতামনা।আপনি বলতেন, demand ও supply দাম নির্ধারিতহয়। প্রভাতস্যারপড়াতেন, দামহলো cost ওপর একটি markup।আবার কৃষ্ণেন্দু স্যার বলতেন, auction মাধ্যমেও দাম নির্ধারিত হতেপারে।কর্পোরেট জীবনে এসে product price determination নিয়ে কয়েকটি প্রজেক্টে কাজকরার সুযোগ হয়েছে।প্রজেক্টগুলো খুব ইন্টারেস্টিংহয়।আমাদের একটা টিম আছে , যারা ডেরিভেটিভ প্রাইসিং নিয়ে কাজকরেন।সেই price determination জন্য আবার একবিশেষ ধরনের calculus ব্যবহার করাহয়-Ito calculus।বিষয়টা খুবই ইন্টারেস্টিং, যদিওএই pricing model আমার পুরোপুরি মাথায় ঢোকেনা।আপনার সঙ্গে দেখাহলে কীভাবেঠিকহয়, সেবিষয়ে আবার একদিন আপনার কাছ থেকে শুনেনেব।

I received the above message from a former student. Bengali readers will recognise the content immediately. Non-Bengali readers can find the translation below.

In student life, I never quite understood how “price” is determined. You used to say that demand and supply dictate the price. Prabhat Sir taught us that price is a markup on cost. Then again, Krishnendu Sir would say that price could also be determined through an auction.

After entering corporate life, I’ve had the chance to work on several projects related to product pricing. These projects are very interesting. We have a team that works on financial derivative pricing; they use a specific type of calculus for that price determination—Ito calculus. It’s a very interesting subject, though I don’t fully grasp this pricing model. When we meet, I’ll take some time to hear from you again about how it actually works.

Motivation:

When I Googled ‘price determination,’ I got something along the lines of the supply-and-demand phrase used in the letter above. The letter appears to be a bit like a complaint, that we taught him different kinds of things so that he became confused. On checking, he did say that this was not a complaint but that he wanted to understand matters. My very distinguished colleague, the late Professor Krishna Bhardwaj, wrote an account entitled the Rise to Dominance of the supply-demand theories. It was another dimension to the discussion that supply and demand was the neoclassical way of doing things, and that this was somehow thought not to be an effective way to understand how price was determined. Some people actually thought this was clearly the wrong way to go about trying to understand price determination. And the Google phrase also indicates a quite murky picture. Given this background and my student’s letter, I have been tempted to offer the following.

Explanation

To clarify, price determination refers to the process by which the price at which a transaction occurs is determined. The words demand and supply, when used in economics, mean some specific things; for instance, demand at a given price means what a consumer wants to buy at that price and the market demand or aggregate demand at a price means the total amount that consumers want to buy at that price; similarly, supply at a price means what firms would wish to sell at that price and the aggregate or market supply at a price means the total amount that firms would like to sell at that price. Sometimes the words market or aggregate are dropped so that we have to make out from the context whether we are talking about the aggregate or only about some individual response. Stated this way, it is clear that demand and supply make sense when buyers and sellers treat price as a given and passively react to it. Thus, the constructs demand and supply make sense when the markets are perfectly competitive. Yet those who use demand and supply do not seem to be aware of this, and purchases and demand are used interchangeably, as are sales and supply. This naturally confuses people.

It should be made clear that the main factors influencing price determination include the market structure (e.g., perfect competition vs imperfect competition), the production process (e.g., constant returns to scale vs other types), and whether uncertainty is involved in the transaction. There is no single method suitable for every case. Let us try to explain further.

As explained above, Demand and Supply are constructs for perfectly competitive markets; they cannot be used when those conditions do not exist. In monopolies, a supply curve is absent; in monopsonies, a demand curve is missing. Price determination differs in these cases[1] For details in this connection, see, my lecture reprinted here : ” On Wages and Employment”, Indian Journal of Labour Economics, Vol. 49, 2006, pp., 63-77. . Under constant returns to scale, the supply curve disappears; it is a straight line indicating that firms will sell any amount at the constant marginal cost, even with imposed perfect competition. The demand-supply analysis fails under these conditions since the price is determined by that constant marginal cost independently of anything else. For a single primary factor[2] For an example, see my paper, ” Stability in an Economy with Production” in Trade Stability and Macroeconomics, edited by G. Horwich and P.A. Samuelson, Academic Press, 1973, pp. 243-258., the production possibility locus becomes a straight line, and its slope sets the price ratio—the cost of production. Demand has no part in determining price here. Cost of production plus a markup shows entrepreneurial returns.

Auctions often set prices for art and land. But I have bid at the sabji mandi in Mehrauli, where farmers bring their vegetables and sellers gather. There, one unit equals five kgs or a “dari” stone. When I bid the highest for a basket of tomatoes, I won the basket, not very attractive to me, buying so much; but I had participated just to enjoy the moment. Or consider a standard discriminating monopolist of the worst type who extracts the total consumer surplus by charging consumers exactly the maximum they are willing to pay for each unit. This too is kind of an auction, isn’t it? All these methods use the same price determination paradigm. Professor Patnaik and Professor Ghosh Dastidar refined the process for cases where supply and demand analysis is inapplicable. You heard about the price determination adapted to each of our distinct contexts. I hope this explains the issue.

The activities of your team members are focused on a different context, viz., uncertainty. Uncertainty affects both the timing and the nature of commodity transactions. Derivatives introduce an unpredictable outcome. Your colleagues use stochastic calculus to estimate results in such contexts and guide bidding. I do not wish to go into details here. But I hope the general principle involved has become more transparent.