Transcript ch6.slides.4e.MEAPSA.wardx

PowerPoint Slides © Michael R. Ward, UTA 2014
Econ 5313
Some Theory Background
• Lots of formulas and math with this chapter. Trust me,
there is a payoff
• Demand curves slope downward
• For two reasons:
• People value the first unit more than the second, etc.
• Different people value the product differently
Econ 5313
Demand
• A Typical
Demand
“Curve”
• Purely
hypothetical
P
Q
Econ 5313
MR from Demand
P
Q Revenue
$7.00
1
$6.00
2
$5.00
3
$4.00
4
$3.00
5
$2.00
6
$1.00
7
• Very simple demand curve
• Calculate Revenues
MR
MC
Profit
Econ 5313
MR from Demand
P
Q Revenue MR
$7.00
1
$7.00
$6.00
2 $12.00
$5.00
3 $15.00
$4.00
4 $16.00
$3.00
5 $15.00
$2.00
6 $12.00
$1.00
7
$7.00
MC
• Multiply price (P) times quantity (Q)
• Rises then falls
Profit
Econ 5313
MR from Demand
P
Q Revenue
$7.00
1
$7.00
$6.00
2 $12.00
$5.00
3 $15.00
$4.00
4 $16.00
$3.00
5 $15.00
$2.00
6 $12.00
$1.00
7
$7.00
MR
MC
Profit
$5.00
$3.00
$1.00
-$1.00
-$3.00
-$5.00
• MR is the change in revenue from selling another unit
• Falls fast
Econ 5313
MR from Demand
P
Q Revenue
$7.00
1
$7.00
$6.00
2 $12.00
$5.00
3 $15.00
$4.00
4 $16.00
$3.00
5 $15.00
$2.00
6 $12.00
$1.00
7
$7.00
MR
$5.00
$3.00
$1.00
-$1.00
-$3.00
-$5.00
MC Profit
$1.50
$1.50
$1.50
$1.50
$1.50
$1.50
$1.50
• Compare MR to a constant MC of $1.50
• How many to produce?
Econ 5313
MR from Demand
P
Q Revenue
$7.00
1
$7.00
$6.00
2 $12.00
$5.00
3 $15.00
$4.00
4 $16.00
$3.00
5 $15.00
$2.00
6 $12.00
$1.00
7
$7.00
MR
$5.00
$3.00
$1.00
-$1.00
-$3.00
-$5.00
MC
$1.50
$1.50
$1.50
$1.50
$1.50
$1.50
$1.50
• For 1, 2, & 3, MR > MC so profits rise
• For 4+, MR < MC so profits fall
Profit
$5.50
$9.00
$10.50
$10.00
$7.50
$3.00
-$3.50
Econ 5313
Why Does MR Fall So Fast?
• Current price
P* yields
quantity Q*
• What does the
blue area
represent?
• What happens
when we
reduce the
price a bit?
P
P*
Q*
Q
Econ 5313
Why Does MR Fall So Fast?
P
Q
• Reduce price
means you sell
more units.
• Revenue
increases by
the green area.
• But reduced
price means
less revenue on
each unit.
• Revenue
decreases by
red area.
• Net effect is
“Marginal
Revenue”
Econ 5313
Why Does MR Fall So Fast?
• Another hypothetical: Suppose you want to sell one more
unit. How much does your revenue go up?
• To sell that one more unit, you have to reduce the price
just a smidgeon. So it earns you something just less than
the current price.
• But, if you lower the price by even a smidgeon, you earn
slightly less on each unit you would have sold before. This
decrease in revenue is also “marginal” to your decision to
sell another unit.
Econ 5313
Why Does MR Fall So Fast?
• So there are two effects:
• Gain P-smidgeon on one more unit.
• Lose smidgeon×Q on all “infra-marginal” units.
• Both effects make MR < P because of these smidgeons.
• But how about the cotton farmer example from last time?
• He had MR = P
• There he pretty much could sell as much as he wanted without
reducing his price by even a smidgeon
• This means he does not lose any revenue on “infra-marginal”
sales
• But this is the extreme case
Econ 5313
Why Does MR Fall So Fast?
• You want to set MR = MC.
• But you have P > MR.
• So do you want to find the spot on the demand curve
where P = MC?
•
•
•
•
No!
Revenue = P×Q
Cost = MC×Q + FC
Profit = Revenue – Cost = P×Q – MC×Q - FC = -FC < 0
• Need P > MR = MC just to break even
• How much greater?
• Depends on flatness or steepness of demand
Econ 5313
Why Does MR Fall So Fast?
• If demand is
flatter,
reducing price
increases
quantity more
• Revenue
increases by
more
• MR is bigger
P
Q
Econ 5313
Why Does MR Fall So Fast?
• If demand is
steeper,
reducing price
increases
quantity less
• Revenue
increases by
less
• MR is smaller
P
Q
Econ 5313
Taxes imply Price Increases
• In 1980, Mayor Marion Berry raised the tax on gasoline in
Washington, DC by 6%.
• What do you think happened to gas tax revenue?
Econ 5313
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Elasticity
We measure flatness or steepness with elasticity
Why not slope?
How do you measure elasticity?
Definition: Arc (price) elasticity:
• e = [(q1-q2)/(q1+q2)]  [(p1-p2)/(p1+p2)]
• Need two points on a demand curve (1 and 2)
Econ 5313
Elasticity Experiment
• Form groups of 4-5 with neighbors
• You have five dollars that you can spend on each of four
items. You must spend all you “income.” Make your
choices under “Individual Quantities.” There will be three
treatments and all three are completely different and
unrelated.
• First Treatment: Income = $5, Price(Coke) = $1,
Price(Fritos) = $1, Price(Snickers Bar) = $1, Price(Granola
Bar) = $1
Econ 5313
Elasticity Experiment
• You have five dollars that you can spend on each of four
items. You must spend all you “income.” Make your
choices under “Individual Quantities.”
• First Treatment: Income = $5, Price(Coke) = $1,
Price(Fritos) = $1, Price(Snickers Bar) = $2, Price(Granola
Bar) = $1
Econ 5313
Elasticity Experiment
• You have five dollars that you can spend on each of four
items. You must spend all you “income.” Make your
choices under “Individual Quantities.”
• First Treatment: Income = $5, Price(Coke) = $1,
Price(Fritos) = $1, Price(Snickers Bar) = $3, Price(Granola
Bar) = $1
Econ 5313
Elasticity Experiment
• In your group, calculate the quantity demanded for each
good and each treatment.
• What is the elasticity of demand for a snickers bar for your
group when the price increased from $1 to $2?
• e = [(q1-q2)/(q1+q2)]  [(p1-p2)/(p1+p2)]
• What is the elasticity of demand for a snickers bar when
the price increased from $2 to $3?
• Report group totals to me
• For the market, what are the demand elasticities?
• For the market, what are the cross-price elasticities with
granola?
Econ 5313
The Ugly Math
• Proposition: MR = P(1-1/|e|)
• Proof(ish)
•
•
•
•
•
•
•
•
MR = DRev/DQ
≈ (DQP+DPQ)/DQ
= P(DQ/DQ)+(DPQ/PDQ)
= P[1+(DP/DQ)(Q/P)]
= P[1+(DP/P)/(DQ/Q)]
= P[1+%DP/%DQ]
= P(1+1/e)
MR = P(1-1/|e|)
• So, with cotton example, e → neg. infinity and MR → P
Econ 5313
Elastic and Inelastic
• If the demand for Nike sneakers is inelastic (|e|<1), should
Nike raise or lower price?
• Implies MR < 0
• If the demand for Amana ovens is elastic (|e|>1), should
Amana raise or lower price?
• Implies MR > 0 but we do not know relative to MC
Econ 5313
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Actual versus Desired Markup
Need to know if MR > MC
But, MR = P(1-1/|e|)
So need to know if P(1-1/|e|) > MC
But this is P-P/|e| > MC
Or, P-MC > P/|e|
Or, (P-MC)/P > 1/|e|
Or, actual markup > desired markup
• actual markup = (P-MC)/P
• desired markup = 1/|e|
Econ 5313
Using Elasticities
• Example: e= –2, p=$10, mc= $8, should you raise prices?
•
•
•
•
Actual is (10-8)/10 = 0.2
Desired is 1/|-2| = 0.5
Actual < Desired
Do you know how much to raise price?
• Example: Markup in 3-liter coke is 2.7%, should you raise
price?
•
•
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•
•
This is (P-MC)/P = 0.027
It would be correct only if 1/|e| = 0.027
We would need e = -37
Realistic value for e?
Other reasons?
Econ 5313
What makes demand elastic?
• More complements make demand less elastic
• Ex iPod and iTunes
• Products with close substitutes are more elastic
• Ex iPhone and Android phones
• Demand for an individual brand is more elastic than
industry aggregate demand
• More close substitutes
• Products with smaller shares often have lower margins
• More likely to be “fringe” competitors
Econ 5313
Brand versus Industry Elasticities
• The individual brand demand elasticity is approximately
equal to the industry elasticity divided by the brand share
• First approximation e(brand) = e(market)/share(brand)
• Helpful because we are more likely to know industry
elasticity than individual product elasticity
• Discussion: Suppose that the elasticity of demand for
running shoes is –0.4 and the market share of a Nike
brand running shoe is 20%.
• What is the price elasticity of demand for Nike running
shoes?
Econ 5313
Linear Rule of Thumb
• Marketing Dept. estimates linear demand for you. (i.e., p =
pmax - a×q)
• Linear Demand Curve Formula, e= p / (pmax -p)
• Alternatively, e= p / (a×q)
Econ 5313
Laws of Demand
• First law of demand: e < 0 ( as price goes up, quantity goes
down)
• Do all demand curves slope downward?
• Second law of demand: in the long run, |e| increases
• Why does time matter?
• A bank experimented with increasing ATM fees. After a
month they saw a slight drop in usage but this was more
than offset by the higher fees. Should they decide to keep
the higher fees at the end of the month?
Econ 5313
Laws of Demand
• Third law of demand: as price increases, demand curves
become more price elastic, |e| increases
• Why would this be the case?
• Give an example of the third law of demand
• True in the Snickers experiment?
Econ 5313
Other Elasticities
• Own-price elasticity of demand is the most important
elasticity. But there are others.
• Income elasticity
• Cross-price elasticity
• Advertising elasticity
• These are usually used in forecasting exercises
• We are moving into a new area with 50% higher income. If the
income elasticity is 0.8, how will sales be affected?
• Our competitor raised his price 10%. If the cross-price elasticity is
2, how will our sales be affected?
• Our advertising budget doubled. If the advertising elasticity is 0.5,
how will our sales be affected?
Econ 5313
Stay-even Analysis
• Stay-even analysis tells you how many sales you need
when changing price to maintain the same profit level
• Q1×(P1-MC) - FC = Q0×(P0-MC) - FC
• Q1 = Q0×(P0-MC)/(P1-MC)
• You know Q0, P0 and MC and are considering P1. Just how
many units would you have to sell to “stay even?”
• Calculate Q1
• Is this “reasonable” given general notions about demand?
• When combined with more general information about the
elasticity of demand, the analysis gives a quick answer to
the question of whether or not changing price makes
sense.
Econ 5313
Music Survey Data
• Similar to what you might get from Marketing Dept.
• How to use?
Econ 5313
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From the Blog
Chapter 6
Uber Pricing
Turkeys are cheaper at Thanksgiving
Market Research on Meth
Estimating Demand Functions
Smart Parking Meters
Econ 5313
Main Points
• Demand is the number of units bought at different prices
• Pricing is an extent decision:
• MR > MC => increase Q and visa versa
• Elasticity = [(q1-q2)/(q1+q2)]  [(p1-p2)/(p1+p2)]
• MR>MC  (P-MC)/P > 1/|e|
• Compare “actual” markup to “desired” markup
• Factors that affect elasticity:
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Substitutes (More elastic with more close substitutes)
Complements (Less elastic with more close complements)
Product breadth (Industry versus Brand)
Time (More elastic as time elapses)
Price level (More elastic as price rises)
Econ 5313
Main Points
• Other elasticities can be used for forecasting
• Income, cross-price, advertising
• %DQuantity = Factor elasticity × %DFactor
• Stay-even analysis can be used to determine Q necessary
for a price change
• %DQuantity = %DPrice / (%DPrice + margin)
• Is predicted quantity loss less than stay-even quantity?