Luke Froeb ; 5 Nov, 2010.
CH 6 Script
OUTLINE
1.
2.
3.
4.
Intro
Demand curves
Price elasticity
Marginal Analysis of pricing in practice
INTRO:
This is Luke Froeb at Vanderbilt University. I am the author, along with Brian McCann, of the
textbook “Managerial Economics: A Problem Solving Approach.” This lecture is designed to
supplement Chapter 6, “Simple Pricing.”
When the Soviet Union fell and embraced capitalism, Mars decided to begin selling its popular
Snickers candy bar in Russia. They priced it at the same price in rubles as it sold for in England,
adjusted for the exchange rate.
This was a huge mistake. Since it was the first western-style candy bar sold in Russia, it had no
competitors, and there was a huge demand for the product. Distributors purchased all the
candy bars for themselves, and then re-sold the candy bar at 2-3 times the recommended
retail price. It took Snickers a long time to recognize their mistake, because distributors were
reporting sales at the price that Snickers had originally set.
Obviously, Mars could have benefited from a better understanding about how to set profitable
prices, the topic of this chapter. We begin with the simple case of a firm that owns a single
product and sets a single price. Later we will talk about setting prices on multiple, commonly
owned products, and about selling a single product at different prices, called “price
discrimination.” But before we get there, we have to understand how to price in this simpler
case.
When choosing price, a firm faces a tradeoff: a higher price means fewer goods sold, but
higher margin earned on each sale; while a lower price means more goods sold, but a lower
margin on each sale.
<<CAN YOU ILLUSTRATE THIS WITH A FIGURE?>>
This is an extent decision, and we know from Chapter 4 that marginal analysis tells us how to
choose the optimal price.
Luke Froeb ; 5 Nov, 2010.
There are two big ideas in this chapter. The first is that we use a demand curve to turn a
difficult price decision into easy quantity decision. The question “what price should I charge?”
is equivalent to the question “how much quantity should I sell?”
Fortunately, we already know how to use marginal analysis to figure this out: If the marginal
revenue is bigger than the marginal cost, then sell more. And we do that by reducing price.
<<Maybe some kind of moving figures showing that MR>MC means that you should Raise
price, and MR<MC means that you should reduce price>>
The second big idea of the chapter is that the biggest problem with marginal analysis is
measurement. You may have some idea of what your marginal cost is, but figuring out what
your marginal revenue is is much more difficult. If you get any information about marginal
revenue, it is likely to come in the form of a price elasticity. The more price elastic your
demand curve is, the lower the price you should charge.
DEMAND CURVES
To construct a demand curve, imagine that we have ten consumers, each of whom wants to
purchase one unit of a good. We arrange them by their values, by what they are willing to pay
for the item. Imagine that the first consumer is willing to pay $10, the second consumer $9,
the third consumer $8, and so on. The tenth consumer is willing to pay only $1.
So if we charge a price of $10, only one consumer buys; but if we reduce the price to $9, two
consumers buy (both the consumer with the $10 value and the consumer with the $9 value).
If we lower price all the way down to $1, all ten consumers purchase. This is a demand curve.
It describes the behavior of this group of consumers, and tells you how much you will sell if
you charge a particular price.
Now let’s show you how to use the demand curve to turn the pricing decision into a quantity
decision. In the Table below, we show the demand curve in the first two columns. For each
price, the demand curve tells us how much we will sell.
Luke Froeb ; 5 Nov, 2010.
Price
Quantiity Revenue MR
MC
Profit
$10
1
$10
$10
$3.50
$6.50
$9
2
$18
$8
$3.50
$11.00
$8
3
$24
$6
$3.50
$13.50
$7
4
$28
$4
$3.50
$14.00
$6
5
$30
$2
$3.50
$12.50
$5
6
$30
$0
$3.50
$9.00
$4
7
$28
($2)
$3.50
$3.50
$3
8
$24
($4)
$3.50
-$4.00
$2
9
$18
($6)
$3.50
-$13.50
$1
10
$10
($8)
$3.50
-$25.00
<<IN THE TEXT THAT FOLLOWS, CAN YOU HIGHLIGHT THE CELLS IN THE TABLE THAT
CORRESPOND TO THE FIGURES AS I SAY THEM.>>
At a price of $10, we sell only one unit, for a revenue of $10. The “extra” or marginal revenue
we get from selling the first unit is $10, which is bigger than the marginal cost of $3.50, so we
sell the first unit.
Then we ask, “should we sell another unit?” We do this by reducing the price to $9. The
revenue is $18, and the marginal or extra revenue from selling the second unit is $8. This is
still greater than the marginal cost, so we sell the second unit.
To sell the third unit, we have to reduce price to $8, for a revenue of $24 and a marginal
revenue of $6. This is still bigger than the marginal cost of producing the third unit, so we
make the sale.
To sell the fourth unit, we have to reduce price to $7, for a revenue of $28 and a marginal
revenue of $4. This is still bigger than the marginal cost of $3.50, so we sell the fourth unit.
To sell the fifth unit, we have to reduce price to $6, for a revenue of $30 and a marginal
revenue of only $2. This is below the marginal cost of $3.50, so we do NOT sell the fifth unit.
The optimal price is $7, and in the last column, we see that profit is maximized at this price.
There are three things to take away from this analysis. First, the demand curve allowed us to
turn a difficult pricing problem into a simple quantity problem that we know how to solve
using marginal analysis.
Second, note that the marginal revenue is always LESS than the price. At the optimum output
of four, price is bigger than marginal cost. So while it might appear that you could gain $7 by
selling one more unit, and this is bigger than the marginal cost of $3.50, that would be wrong.
Luke Froeb ; 5 Nov, 2010.
You can sell more ONLY by reducing price. The relevant benefits and costs of an extent
decision are the marginal revenue and marginal cost, NOT the price.
<<MOVING DOWN THE ROW HIGHLIGHTING THE FALLING MARGINAL REVENUE IN THE TABLE
ABOVE.>>
Third, note that marginal revenue falls as we sell more. This is a critical feature of demand
curves. It is similar to the idea that marginal costs increase as we sell more. You pick the low
hanging fruit first, and then move on to the higher hanging fruit which is more costly to
harvest. Similarly, you make the easy sales first, to the high value customers, but to sell more
you have to reduce price. This results in a falling marginal revenue curve -- as you sell more,
the extra revenue that you earn on each sale falls.
PRICE ELASTICITY OF DEMAND
After using a demand curve to show you how to price optimally, I feel a little guilty for telling
you that you will never “see” a demand curve. They are very difficult to estimate, especially
with the kind of precision that might be useful to someone facing a pricing decision. You can
see only the current price and the current quantity, but not the rest of the demand curve.
Fortunately, you don’t need to know much in order to figure out whether price is too high or
too low. All you need to know are the marginal cost and the marginal revenue at the current
output level. If MR>MC, then sell more, and you do this by reducing price. If MR<MC, then
sell less, and you do this by raising price. As in Chapter 4, marginal analysis tells you which
direction to go, but not how far to go.
Still, marginal revenue is hard to measure. If you get some information about marginal
revenue, it is likely to be in the form of a price elasticity.
Price Elasticity = e = %∆Q ÷ %∆P
Price elasticity measures how sensitive consumers are to price. The more price elastic they
are, the more they react to price changes. So for example, if price goes up by 5%, and
Quantity goes down by 10%, the price elasticity of demand is e=-2. In this case we say that
demand is “price elastic” or simply “elastic” because |e|>1. In other words, quantity changes
more than price. For an Inelastic demand, one where |e|<1, quantity changes less than price.
Marginal revenue is related to price with the simple formula, MR=P(1-1/|e|). Note that this
relationship holds only for an elastic demand.
Luke Froeb ; 5 Nov, 2010.
We can plug this formula into our marginal calculus to derive the following equivalent
relationships:
MR>MC
P(1-1/|e|)>MC
(P-MC)/P > 1/|e|
I call the left side of this equation the “actual mark-up” and the right side of the equation the
“desired markup.” MR>MC if and only if the actual markup is greater than the desired
markup. And we know from above that if MR>MC, we should sell more, and we do this by
reducing price.
A numerical example, can easily illustrate this idea. If Price is $10, MC is $8, and elasticity is -2,
then the actual markup is 80%, but the desired markup is only 50%. In this case, MR>MC, so
reduce price.
Note that this equation tells us that the price if we could somehow make our demand less
elastic, we could raise price. This makes intuitive sense. If our consumers are less sensitive to
price, then we can profitably raise price.
In chapter 10, we will show you that this is the logic behind what is called a “product
differentiation strategy.” If a firm can do something unique, creative, innovative or different
to reduce the elasticity of demand, then they can command a higher price. One example is
Whole Foods. They sell food in the “Premium, Natural, and Organic” segment, and give 5% of
their profit to socially responsible causes. This gives them a less elastic demand curve, the
consequence of which is that they can command the highest markup in the grocery industry.
MARGINAL ANALYSIS OF PRICING IN PRACTICE:
Even information on price elasticity is difficult to come by so you are probably going to have to
do something else. Here is an example of how you might use marginal analysis in practice.
Imagine that you are working for John Mackey, CEO of Whole Foods, and he asks you whether
he ought to raise price by 5% on all the products sold at Whole Foods. It is obvious that Whole
Foods sells an entire range of products, and that the elasticity for the demand curve facing the
entire store would be very difficult to estimate.
Luke Froeb ; 5 Nov, 2010.
But let’s imagine that everyone who comes to Whole foods buys a similar “basket” of goods,
and let’s try to figure out if a 5% price increase on the basket would be profitable. To do this
we can use a version of “break even” analysis. We could ask “how much quantity could we
afford to lose and still break even?”
This is sometimes called the ‘stay even” quantity or “critical loss.” It can be computed as
Critical Loss= %∆Q = %∆P/(%∆P+Markup) where the Markup=(P-MC)/P.
If we lose less than the critical loss, then the price increase is profitable, but if we lose more,
then it is not. For example, if the markup at Whole Foods is 40%, then the
Critical Loss= 5%/(5%+40%)=11.1%.
So how do we determine whether Whole Foods would lose more than the critical loss?
An economist working on behalf of Whole Foods read marketing studies and found that most
people who shop at Whole Foods also shop at another grocery store, like Kroger or Safeway.
Since these stories carry many of the same items that Whole Foods does, the economist
concluded that the shoppers could easily many of their purchases if Whole Foods raised price.
He concluded that the price increase would not be profitable because demand for Whole
Foods is very elastic. This is equivalent to the marginal analysis of pricing mentioned above,
but it is done with two simple steps. First you calculate the break even quantity, and second,
you study demand to determine whether you would lose more than the break even quantity.