Download Lecture 14 Notes

17 February 2006
Reading Baye, Ch 3. pp 73-86
Return Problem #4
Hand out Problem #5 (Due Monday)
Lecture 14
REVIEW___________________________________________________:
II. Chapter Market Forces: Demand and Supply
A. Price Elasticity of Demand
3. A Graphical Interpretation of Price Elasticity.
4. Some Observations about Price Elasticity of Demand
a. Most Demand curves have elastic and inelastic segments
b. Exceptions
c. Elasticity and the Slope of Demand Curves
Preview__________________________________________________________
5. Elasticity TR and MR
6. Determinants of Price elasticity
B. Other Demand Elasticities
1. Cross Price Elasticities
Lecture ______________________________________________________
5. Price Elasticity, MR and TR
a. Motivation: What can we say about the optimality of prices, given limited
information. (Say, only information about the demand schedule, and perhaps MC
information). Some important inferences can be drawn only from information about
elasticity.
Definition of Marginal Revenue (MR). Recall that on most demand curves, there
are elastic, unitary and inelastic segments. (Motivate from comparison of quantity box to
price box). Price elasticity is the ratio of the quantity box to the price box.
Marginal revenue is the difference between the quantity box and the price box.
P
E
MR
D
TR
Q
MR (at max)
TR
E
I
Q
b. Relation between MR, TR and 


>1, MR >0
<1, MR <0
=1, MR =0
Thus: TR is maximized when MR = 0.
- A monopolist with no marginal costs would price where MR = 0.
-A price-setter could never increase revenues by cutting price when |<1. (ex. Never cut
prices to sold out concerts, generally don't raise price for bus service).
d. Some examples:
Example Suppose you are a monopolist, who owns a bridge. Access doesn't
deteriorate the bridge. What price should you set? (Suppose you have no marginal costs)
Answer: The price where ||=1
Example: The elasticity of demand at Jones Co. is -.5. They are considering a
sale. What can you say about the rationality of a price cut?
Answer: No firm can maximize profit on the inelastic portion of their demand
curve. They should raise price.
Example: Suppose (inverse) demand is
P = 10 - 2Q.
If P =2, what can you say about the optimality of pricing policy?
Answer: MR = 10 - 4Q. When P = 2, Q = 4. Thus, they are on inelastic part of
demand curve (and the firm could increase profits by raising price.
6. Determinants of price elasticity of demand. Your text (p.81) lists elasticities of
demand for selected products in the U.S. ranging from Motorcycles and Bicycles (-2.30)
to Transportation (-.6). It is important for you to be able to interpret these numbers.
Some assistance may be developed by considering factors that tend to make demand
curves have more or fewer elastic points.
a. Determinants of price elasticity of demand
i.) Availability of close substitutes: Demand is more elastic, the more substitutes
that are available.
ii) Price relative to income: Demand is more inelastic, the smaller price is relative
to income.
iii) Time: Demand is more elastic, the longer the time frame (because there are
more available substitutes).
b. Applications. You should be able to make comparative statements about the
elasticity of demand for various products:
i) What is more elastic: the demand for automobiles in general, or the demand for
VW Polos?
ii) What is more elastic: Demand for salt, or the demand for an automobile?
iii) What is more elastic: Your demand for pain pills at 3 a.m. at the 7-11, or your
demand for pain pills in general for your medicine cabinet.
You should also be able to combine elasticity calculations with determinants information.
iv) Suppose that auto-seller Jim Ford at Ford city lowers the price of the popular
Focus by $2000 in honor of Spring. Suppose that in response, weekly sales at
increase from 4 per week to 8. If the normal price of a new Focus is $10,000
what is the arc price elasticity of demand?


=
=
(8-4)(18,000)/[-2,000(12)]
-3.
- Over the current price range, is Marginal Revenue positive or negative?
- Could Jim Ford expect to increase revenues by further lowering price? Would
such a move be profitable?
- What would you expect to be the response of customers to a similar percentage
mark-down on all cars in the Ford city lot?.
v) Suppose all U.S. domestic auto sales increase over last year by 5% in response
to a 10% price decrease. What is the implied price elasticity?

 = -5/10 = -.5
vi) You can say a lot about the optimality of pricing from elasticity. Consider a
firm selling plastic 3-sided rulers (inches, centimeters, and thumbs). Suppose that
price elasticity was -.2. What can you say about the optimality of the firms'
pricing decision?
B. Other Demand Elasticities. Elasticity is a sensitivity measure that may be of interest
with respect to any independent variable. Some other important elasticities can be readily
calculated from a demand function.
Here at the end of the lecture, we introduce one: Cross price elasticity
1. Cross Price Elasticity. The purpose of a cross price elasticity estimate is to capture
some sense of the responsiveness of sales for one good to a change in the price of some
related good.
a. Definition. The cross price elasticity of good x with respect to a change in the
price of a related good y is:
XY
%Qx/%Py
or, decomposing,
XY
=
(Qx/Py)(Py/Qx)
Using our point price elasticity formula, this could be calculated as:
XY = Qx Py
Py Qx
For example, with a demand function
Qx
=
98 – 10Px + 4Py
Let Px =
And Py = 3
5
Thus, Q
= 98 – 10(5) + 4(3)
= 60
The cross price elasticity of Qx w.r.t. a change in the price of Py would be
4(3)/62 = .2
Notice that cross price elasticity information can be used to distinguish substitutes from
complements. In this case, the coefficient is postitive, indicating that the products are
substitutes.