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Economics/Question On Consumer Surplus Calculation

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Dear Professor,    

I have this question in mind for quite some time. Here is a situation. John goes to the game store to buy a new video game, for which he is willing to pay up to $10. He picks out one he likes with a price tag of exactly $10. At the cash register, he is told that his video game is on sale for half of the posted price. What is his consumer surplus?

Clearly there are two possible answers, $0 or $5. I was thinking the answer was $0 as he was willing to pay $10 knowing that the market price was $10. Definition of consumer surplus is the price at which consumer is most willing to pay minus actual market price. However, due to a discount, he actually benefits from buying the game and has a surplus or gain of $5. I'm having a dilemma here mainly due to the definition which says ACTUAL market price. Does actual mean original market price before discounts or does it mean actual price which is after discount (apologies for the confusion). What is your take on this paradox (if it is actually one) ?  

Thank you for your time once again professor. Many thanks!

Regards,
Justin

Answer
constraints
constraints  
Hi Justin:

Thank you for placing a well-worded, straightforward question on consumer surplus in juxtaposition with two alternative answers that are grounded on equally persuasive –though not necessarily, on a theoretical plane, equally cogent –lines of reasoning. You are kind to ask for my opinion on the seeming “paradox” –an apparent logical incongruity that in fact stems from the concept of marginal utility. To resolve this incongruity and to clinch the argument for what should be considered the valid answer, I would first like to take “market price” as the first point of departure in my attempt to attend to your query.

MARKET PRICE: THE FOUR DETERMINANTS
Market price is the economic price for which a good or service is offered in the market. By market in this modern world is meant a sphere of activities between buyers and sellers who, confronted with the forces of supply and demand subject to production and budget constraints, come to agreements to make transactions of commodities at acceptable prices. Market doesn’t need to be in a physical entity such as brick-and-mortar stores of Target or Wall-mart; market may as well be online such as eBay.

The price at which buyers can fetch a commodity from the sellers of the commodity is the MARKET PRICE, which is determined by market mechanism –the forces of supply subject to the production constraint and demand subject to the budget constraint. Four things work together.

  (a) Demand and (b) demand price. The buyers in general have a demand function which shows willingness to buy different quantities at different prices, more of a commodity when price of the commodity is lower and less of the commodity when price of the commodity is higher, because buyers confront a budget constraint (affordability) defined by the amount of available wealth and the prevailing prices. [You have already had a good grounding in demand; look at the attachment for budget constraint.] Buyers’ demand depends on the marginal utility derived from the last unit of the commodity. The price buyers are willing to pay depends on the budget. So, on the buyer side, there are (a) demand and (b) price.

  (c) Supply and (d) supply price. The sellers in general have a supply function which shows willingness to offer different amounts of the commodities at different prices, more of a commodity when price of the commodity is higher and less of the commodity when price of the commodity is lower, because sellers confront a production constraint defined by the amount of available funding and the prevailing factor prices (wages, rent, etc.). Sellers’ supply depends on the marginal efficiency they have in production. The price at which they are willing to offer the commodities for sale depends on their production constraint which is defined by their available resources and the prices of the factors [look for the production constraint in the attachment]. So, on the seller side, there are (c) supply and (d) price.

NEITHER BUYER NOT SELLER HAS INDIVIDUAL INFLUENCE IN MARKET PRICE
From the above, we see INDIVIDUALLY price is not influenced by either the buyer or the seller. The price comes about through common actions of the buyers and sellers. When that happens, different buyers and different sellers are affected differently. I would like to put it this way: this is like the law of the averages. Now what happens?

In general, a buyer is willing to pay a price based on the marginal utility of the product. Mind it, however, that marginal utility doesn’t depend on demand only. Supply plays a vital role, too. Here comes the question of “paradox.” As Adam Smith says, “Nothing is more useful than water; but it will scarce purchase anything. A diamond, on the contrary, has scarce any value in use; but a very great quantity of other goods may frequently be had in exchange for it.”

So, marginal utility also depends on supply –water, being abundant even if immensely valuable, “sells for next to nothing because its last drop is worth next to nothing [Samuelson].” Market price being determined so, let me bring the topic of discount under our purview of analysis. Let me iron out your confusion as to whether market price also includes sales.

MARKET PRICE IS SIMPLY WHAT SETTLES TRANSACTION IN MARKET
Market price is what seller is bound by market mechanism to ask for and what buyer is called upon by market mechanism to pay for. To a great extent, just as a cog in a machine has but to perform the task a machine is designed for, an individual buyer or seller has simply to accept the market price. Just as all cogs in a machine must work in unison, so must all buyers and sellers of a particular commodity must work in conformity with the market mechanism. In a sense, therefore, it is an “invisible hand” of the market that determines the market price.

To get a commodity, a consumer a price demanded of him in market. Does the amount he pays reflect the value he derives from the commodity?  The paradox of value emphasises that the recorded money value of a commodity may be very misleading as an indicator of the total economic value of the commodity. The gap between the total utility of a commodity and its total market value arises because we receive more than we pay for as a result of the law of diminishing marginal utility. That’s what we call consumer surplus.


CAN WE VIEW PRICE AFTER DISCOUNT AS MARKET PRICE?
Now the question comes: Does the price offered by a seller for the commodity on sale, WHEN HE REALLY CAN SELL THE COMMODITY, constitute “market price.” Yes, because when “he can sell,” the “buyers buy,” and the transaction takes place.  The price at which the commodity is sold is the market price –it may be less than or greater than what the seller might have desired in the first place. We know very well that the supply curve tells us sellers reduce price when excess demand exists, buyers can afford more when price falls, demand extends, and simultaneously supply contracts because lower price is less lucrative. Price settles at a lower point –that is market price now wrought out my market mechanism.

Quite the same, discount is a form of reducing price, and we may construe that as being a glide down the supply curve from the northeast to southwest. Whether in Sears you hear “Buy One, Get One Free” or “Sale: 20% Off,” or “You Don’t Pay the Tax,” these are simply different gimmicks – variant ways of reducing price to clear the shelves in unsold inventory, bringing about a new market price, which alters the ratio of consumer surplus to producer surplus.
 
INVESTOPEDIA:  “Assume a consumer goes out shopping for a CD player and he or she is willing to spend $250. When this individual finds that the player is on sale for $150 [Mind it, Justin, this is exactly what you may call discount], the economists would say the person has a consumer surplus of $100.”

THE FINAL ANSWER: WHICH ALTERNATIVE STANDS?
When John goes to the game store to buy a new video game, for which he is willing to pay $10, and pays out $5, he gains a consumer surplus of $10–  $5 = $5, no matter for whatever reason price is reduced. It is immaterial to him. As Shakespeare would say, “What’s in a name: call a rose...” Similarly, we may say: What’s in a fall in price: Call it sale or by any other name, it will still produce the same sweet outcome of economic surplus of $5 to John. So your answer should be: $5.

By the way, when you say that John could have been willing to pay $10, knowing that the market price was $10, could consumer surplus be $0? Yes, it could –but on one condition! If the market price “did remain at $10,” which means the product had not been on sale in the first place. But the product was on sale which John couldn't foresee. Sure enough, too, the price John fortuitously and luckily discovered was not what he had been expecting, NOT $10. The premise breaks down. This condition doesn’t obtain. The syllogism doesn’t wash. This alternative is thus to be quashed.

Best of Wishes.  

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Eklimur Raza

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It appears some students in this website are confused about elasticity of demand and the slope of the demand curve when they are trying to figure out why rectangular hyperbola comes up in case of unitary demand curve. First, they don't know that RH can be depicted in a positive quadrant of price,quantity plane. Secondly, they make the mistake that the slope of RH is constant at -1. Two points could help them: first, e=1 at each and every point of the RH, because the tangent at any point shows lower segment=upper segment (another geometric definition of e); yet slopes at different points,dQ/dP, are different; second, e is not slope but [(Slope)(P/Q)]in absolute terms. Caveat: only if we measure (log P) along the horizontal axis and (log Q) up the vertical axis, can we then say slope equals elasticity --in which case RH on P,Q plane is transformed into a straight-line demand curve [with slope= -tan 45 deg] on (log Q),(logP) plane, and e= -d(log Q)/d(log P). [By the way, logs are not used in college textbooks --although that is helpful in econometric estimation of elasticity viewed as an exponent of P, when demand equation is transformed into log-linear form.] I have not found the geometrical explanation I have given in any textbook followed in undergraduate and college classes in Canada (including the book followed in a university where I taught for a short time and in the book followed in George Brown College, Toronto, where I teach.

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About 11 years' teaching economics and business studies, and also English, history and elementary French.Practical experience in a development bank, working with international donor agencies like the World Bank and the ADB. Experience in free-lance journalism, including Canada's "National Post."

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I teach micro- and macroeconomics at George Brown College (continuing education), Toronto, ON, Canada.

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Many articles and editorials, on different subjects, in English newspapers. Recently an applied Major Research Paper, based on a synthesis of the Solow growth model and the Lewis two-sector model, has be accepted by Ryerson University, Toronto. Professors Thomas Barbiero and Eric Cam, Ryerson University, accepted the paper.

Education/Credentials
Master degree in Interantional Economics and Finance and diploma with honours in Business Administration from Canada.

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Received First Prize in an inter-university Literary Contest.

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