Wednesday, September 12, 2012

Never Reason from a Price Change

In introductory microeconomics, professors introduce the concepts of substitute and complement goods. In my Econ 101 class at the University of Michigan, the professor stated the concept as:
If two goods are substitute goods, an increase in the price of one increases the demand of the other.
If two goods are complementary goods, an increase in the price of one decreases the demand of the other.
This might make sense in most situations, but my Sumnerian senses are tingling -- why are we reasoning from a price change? What is causing the price of one good to increase, and how does this change whether the demand of the other good to increase or decrease?

Let us first consider the case of substitute goods. If two goods are substitutes for each other, it seems logical to consider that if supply in the second good contracted, pushing prices up, then people would substitute out of that second good and increase demand for the first good. If cars become harder to produce and become more expensive, it's logical that the demand for bicycles will increase. However, does this hold up if the price change was because of a demand shock? If cars became more expensive because demand increased, it seems peculiar to think that the demand for bicycles also increases. Just because it's a price change doesn't mean it's the price change you were looking for.

A similar scenario plays out in the case of complement goods. If two goods are complements, it seems logical to consider that if the supply for one good increases, then the price decrease would increase the demand for the second good. If tortilla chips become easier to make, we can expect the demand for salsa to increase. But does the same hold true if it was a demand shock that caused the price change? If people start demanding more potato chips, pushing up the price, what do we expect will happen to the demand for chip dip?  We would expect it to increase -- directly contrary to what the definition suggests.

Reasoning from a price change fails because it neglects whether the price change in one good is from a change in production technologies or from a change in preferences. If it's a change in technology, the standard analysis applies. However, if it's a change in preferences, we need a more nuanced view that encompasses both modes of analysis.
If two goods are substitute goods, an increase in the equilibrium quantity of one decreases the demand of the other.
If two goods are complementary goods, an increase in the equilibrium quantity of one increases the demand of the other.
So in the market for cars and bicycles, if the equilibrium quantity of cars increases, whether from a supply expansion or a demand contraction, then the demand for bicycles will decrease. This is true regardless of what happens to the price of cars. Similarly, if the equilibrium quantity of potato chips increases, then the demand for chip dip increases -- regardless of where the price for potato chips go. This makes sense because it encompasses the lay person view of substitutes and complements. If I ride my bike more, I drive less. If I eat more chips, I buy more salsa.

The fact that this isn't taught on the first pass around is understandable -- you don't want to confuse the auditorium of 300+ students with a model of both supply and demand when you're introducing the demand curve. But it does pose a problem when there are exam questions such as "Does an increase in price of a complement good raise the demand of the original good?" To which I have to say, "it might". A possible solution is to ask "Holding the demand of a complement good constant, does raising its price raise the demand of the original good?" This would be more comprehensive, and those who understand can better answer the question, while those who don't understand can forget about the first clause and just answer the second question.

13 comments:

  1. typo increase >> decrease:
    if the equilibrium quantity of cars increases, whether from a supply expansion or a demand contraction, then the demand for bicycles will increase.
    substitutes. Not salsa.
    Tho I prefer corn & tortilla chips.

    And of course in an inflation, the prices might all increase.

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  2. Yichuan,

    The problem with these constructions is that what's really going on is not a sequential pairing of changes in demand, but rather a change in preferences causing two markets to shift simultaneously into a new equilibrium. The directionality runs both ways. Nick Rowe has a really good post about "artsy nonlinearity" in economics which captures this point.

    So I suppose I would write them:

    If goods A and B are substitutes, then a shift in preferences which causes demand for good A to increase will simultaneously cause demand for good B to decrease. If goods A and B are complements, then a shift in preferences which causes demand for good A to increase will simultaneously cause demand for good B to increase.

    The whole point of complements and substitutes is the underlying preferences, which really gets into indifference curves and isoquants and isocost functions -- but that's not Econ 101 at all.

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    1. Doesn't have to be preferences that shift, supply shocks will do.

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  3. Yichuan

    I think you're taking Sumnerian scepticism too far.

    In micro, we reason from price changes because price is an independent variable. In macro, we shouldn't because we seek to explain the price level/ inflation.

    In micro, don't reason from quantity changes.

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  4. Except is price an independent variable? It's the result of an interaction between demand and supply. So changes in price go hand in hand with changes in demand. Supply and Demand shocks can cause the same price changes, but those price changes go along with quantity changes. I don't think it's always true, but it seems to be a good idea to have a solid grounding in quantities in addition to price.

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  5. What is demand and supply? Demand is a curve that maps the locus of the heuristic 'At this price, this is how much I want to buy'. Supply is a curve that maps the locus of the heuristic 'at this price, this is how much I want to sell'.

    To not reason from a price change means to not deduce anything about the structure of a market or the underlying forces from a price change. But that's not what we are doing in micro (Marshallian partial equilibrium micro, that is) at all. Your professor is not making that mistake.

    What your professor's example denotes is the ex-post change in the ex-ante heuristic of the economic agents. Once a price has changed, this is how I will change my behaviour. It is analysis about shifts along my indifference curve.

    Whether that price change shifts my budget constraint itself (which is what you're worried about) is not even being discussed. It is 'ceteris paribus' in the analysis. If that treatment leaves you unsatisfied, you have the option of insisting that your demand curves must always be income-compensated demand curves. You can go the whole Marshallian hog - that's good economics.

    But Scott's pithy wisdom about the GE dynamics of inflation and price levels is not relevant here. And your reformulation of your professor's statements does not add much.

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    1. "Once a price has changed, this is how I will change my behaviour. It is analysis about shifts along my indifference curve."

      Here is where I differ. I argue that if you don't look at why the prices change, you can't make a point that you know how your behavior changes. If you prefer a substitute good more, and if the market does so, the price can rise for that substitute good while demand shifts out of the original good. My reformulations try to fill that gap, and I think they make intuitive sense. Holding the number of consumers constant, if the equilibrium quantity purchased of chips rises, people buy more salsa. If the equilibrium quantity of cars rises, people buy fewer bikes.

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    2. Ok,fair point. But in an indifference analysis, holding total real income constant, saying that you prefer more cars in period 1 compared to period 0 is the same thing as saying that you prefer less bikes in period 1 compared to period 0.

      So you can't really say that the demand for bikes goes down because the equilibrium quantity of cars goes up. You might as well say that the equilibrium quantity of cars has gone up because the demand for bikes has gone down.

      Demand for cars has gone up is isomorphic to saying that the demand for bikes has gone down.

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    3. So the best interpretation of the standard micro statement made by your professor is :

      If my preferences don't change, and I observe the price of cars going up, I will increase my relative demand for bikes.

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    4. Agreed. And I think that's what I was trying to get at. It's true, but the statement was not general enough, likely for pedagogical reasons.

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  6. Guys, you shouldn't have to invoke intermediate micro just to state how demand curves work. I was inclined to say, you're forgetting ceteris paribus. We are talking about the response of buyers' quantity demanded to a change in price, holding everything else constant. But then I read a Scott Sumner posts, where he says, "Of course, holding everything else constant, the price never changes." So I saw the need for a better statement.

    This is what I came up with: (to be used in the Micro 101 class lecture notes of a good professor)


    The Law of Demand:

    If the price (or cost of obtaining) of a good (sufficiently) falls relative to the prices of other goods, then people will offer to buy (or hold) more of that good, assuming that nothing else changes that would affect people's willingness to buy or ability to pay. And vice versa.



    If the price falls...
    then people will demand more of the good than they did at the higher price...
    and we move down along the demand curve.

    If something other than price changes...
    which increases people's willingness to buy the good...
    or* their ability to pay for it...
    then people demand more of the good at every price...
    and the demand curve shifts to the right.



    * In the case where income rises but the demand for a specific good does not shift, I model this as a relaxation of the budget constraint increasing demand for all goods, coupled with a change in the indifference curves decreasing demand for the specific good (reducing the buyer's willingness to pay), so that the particular demand curve holds constant. I.e. a rise in income leads to a rise in demand for all goods by default, which has to be cancelled by a decrease in willingness to spend income on the specific good.

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    1. Exercise: use my definition to state cross-price elasticity more precisely (in words, though).

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  7. PS. "Making cents of markets" love it.

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