Lecture 2(a) Basics of Demand

1. Lecture 2(a) Basics of Demand

2. Why Study Demand • Obvious Reason: To help with forecasting revenues • What will happen to sales tax revenues collected from the sale of cigarettes if the price goes up as a consequence of the Federal Government’s lawsuit? • Less Obvious Reason: To help understand pricing strategies • Why do some firms make it difficult to buy “unbundled”--e.g., MS wants to sell Office or Explorer as a package?

3. What Is Involved in Building a Complete Theoryof Demand? • A complete theory is based on and begins with a theory of individual demand • And then considers how individual behavior aggregate to market behavior.

4. The Theory of Individual Demand is Organized by Conducting the Following Thought Experiment: What Determines How Much of _____ Do You Want to Buy? • Taste • Price of the Good • Income • Price of Other Stuff

5. Taste • While may be the most important factor, but it is also the factor that is most difficult to model and forecast. • Therefore, the conventional approach in microeconomics is to simply accept the consumers tastes as given (often pretentiously invoking the Latin expression non degustibus disputandem—which I think means, “there is no arguing about tastes” and which I have no idea how to spell.) • Interestingly, though, a small but brave group of economists have tried to formulate an economic theory of taste formation. In this class, though, we’ll mostly accept the consumer as he or she is.

6. The Relationship Between Price and Quantity • When price goes up, it seems very unlikely that a consumer will choose to buy more (although can you think of exceptions?) and there are good reasons to think that higher prices will cause consumption to fall . • (Note: this prediction assumes that only price changes.)

7. This Seems Obvious, but It is Worth Thinking About Exactly Why People Buy Less When Prices Go Up • Most consumers are likely to be faced with income constraints and so as the price of something goes up, they have less to spend on some goods. This is easy to understand, but we’ll give a simple example in class. • Most consumers have preferences over most goods that are consistent with diminishing marginal utility.

8. The relationship between prices of other goods and demand(How Would My Demand for X Change if the Price of Y Went Up?) • Suppose X is a ticket to the opera in Verona, Italy and Y is an airplane ticket to italy. • Suppose X is a ticket to the opera in Verona and Y is a ticket to the first round of the Italian Idol audition. • Obviously the relationship depends on the type of goods • X is a Substitute for Y, if an increase in the price of Y leads to an increase in the demand for X • X is a Complement for Y, if an increase in the price of Y leads to an decrease in the demand for X

9. The relationship between income and demand • If I were Bill Gates, how would my life be different? • I’d buy more rides on private jets than I do now. • But I’d buy fewer coach tickets than now. • The relationship between income and demand is ambiguous. Thus, we have the following definitions • Normal good: Any good such that as income goes up, demand goes up (e.g., Mercedes). • Inferior good: Income goes up, demand goes down (e.g., 1993 Mercury)

10. Another way to make the same points • What matters to most consumers is relative values, such as the price of one good relative to the price of another good and relative to the income of the consumer

11. A Useful Way to Describe Demand: Demand Function • It can be helpful in some circumstances to express demand relationships mathematically. The most common way this is done is to write out a demand function relating the quantity demanded to the other relevant variables. • Recall the Equibase problem where we might have assumed that the quantity of track programs demand (q) will depend on track attendance (A) the price of the program (P) and the price of a Daily Racing Form (Pd). Expressed in general notation, we would have written Q =f(A,P,Pd) • Of course these general expressions might not be that helpful, in which case you might decide to write down a more specific form of the function, such as in the Equibase problem where we assumed Q = A(Pd-P) and A=500, Pd=5 • We don’t have the time to talk about how one might find a specific functional form for a specific problem, except to point out that there are ways. In particular a number of specific statistical and econometric techniques have been derived to estimate demand functions. • Sometimes it is useful to write the demand relationship with Price on the left hand side of the equation. Of course this is just a different way of different way of saying the same thing, but to help distinguish them we will refer to the first expression (Q on the left hand side by itself) as the demand function and the second expression as the inverse demand functions. • When we draw a graph of such relationships it is conventional to put the price on the vertical axis and quantity on the horizontal axis. • Some economists (and most textbooks) make a fetish out of the distinction between a shift in the entire curve (usually caused by a change in one of the many factors that influence demand and referred to as a “change in demand”) and movement along the demand curve (caused by a change in price and referred to as “a change in quantity demanded”.)

12. Issues • Market demand vs individual demand. • At on level, this is just arithmetic. For example, if each of 60 students demand 3 beers at a price of $3, market demand will be 180. • But can you think of some goods where, an individual’s demand may be influenced by the number of others demanding the good? • Market demand vs firm demand. • This is something we’ll think a lot more about when we get to the part of the course on competitive markets, but for now think about why this distinction should matter. Also, think about why the market demand is probably less sensitive to price than an individual firm’s demand. • What exactly do we mean by a good? That is, a good can be distinguished by (among other things). • Geography (beer at the ball park versus beer at home) • Quality (diet beer versus heavy beer) • Since demand measures a flow (that is, the amount demanded over some period of time), what is the relevant time.

13. From Demand to Revenue • It is obviously possible to derive total revenue from demand simply by multiplying Q by P. TR=P*Q. • Since this is economics, we of course want marginal revenue • Words: MR is the change in TR when Q changes • For discreet changes: MR=Change in TR/Change in Q (approximate) • Calculus: MR = d TR/ dQ (precise)

15. This example is consistent with demand being given by Q= 1300- P or P=1300-Q • Thus Total Revenue = PQ= (1300-Q)Q = 1300 Q – Q2 • and Marginal Revenue = dTR/dQ = 1300 – 2Q • (Remember the numbers for MR derived in the table are only an approximation).

16. Puzzle: Why Does TR Increase and Then Decrease? • Good News: When price falls from to $500 from $600, you get 100 new passengers. Each of these contributes an extra $500 in revenues. • Bad News: In order to get the new customers, you had to cut the price of tickets by $100 (from $600 to $500) for 700 passengers who would have been willing to fly without the price reduction. • Summary: MR=(Revenue from “new” sales at the “new” price-revenue lost from sales to “old” customers at “old” price)/(number of “new” customers. • Obvious (but useful) insight MR will be bigger, the more new customers are attracted by the reduced price

17. Measuring the Responsiveness of Demand to Price: Elasticity of Demand • Consider how much vital information is presented by the following formula Elasticity =(% change in Quantity Demanded)/(%Change in Price) • If, for example, you were contemplating a 10% price cut, and you know the value for demand elasticity, you would immediately be able to predict how much sales would increase.

18. Formulas for Demand Elasticity and Some Observations • Since demand elasticity is expressed in terms of percentage changes (BTW, see if you can figure out why it is important to work with percentages instead of absolute changes), one way to write the formula is (ΔQ/Q)/(ΔP/P) = (ΔQ/ΔP)(P/Q) • When measuring discreet changes in any variable, the calculation of “% change” may depend on the context of the problem. (Quick, tell me the % difference between a price of $5 and $4.) • In order to eliminate any confusion, it is often useful to explicitly rely on calculus to express elasticity. If we can write the demand function as x=D(p), then elasticity is D’(p)p/x

19. More Fun Facts About Elasticity • The value of elasticity will change depending on where you are taking the measurement. That is, for different values of p and x, the value of elasticity may be different (I say “may” because there are such things as “constant elasticity” demand curves.) • Elasticity is actually a negative number (since dp/dx is always negative). It is a common, but not universal, convention to report it as an absolute value. But if that convention is not honored then “elastic” demand would describe a situation where elasticity < -1

20. Relationship between MR and Elasticity • If absolute value of elasticity>1 (defined as “elastic”), then MR>0. This means that when p goes down and q goes up, TR goes up. • If absolute value of elasticity<1 (defined as “inelastic”), then MR<0 (I.e., when p goes down and q goes up, TR goes down). • If absolute value of elasticity=1 (defined as “unit elasticity”), then MR=0 (I.e., when p goes down and q goes up, TR remains constant). • We can see from our example that this is true and a bit of clever algebra done with the exact (that is, calculus) definition of MR will also confirm that it is true. But if you really understand the intuitive definition of elasticity, it is really almost common sense. • In fact, there is an extremely useful formula that captures this entire relationship. Letting v(x) stand for elasticity

21. Elasticity > 1 means TR goes up Elasticity < 1 means TR goes down