Download Slides 3

Section 5 Section Notes
EWMBA201A
Eva Vivalt
September 26, 2009
Section 5 Section Notes
1
Administrative Stuff
1.
2.
Problems from the textbook are posted – these are good for
general understanding and it would definitely help you to do
them, but they’re not the most time-efficient way of studying
for the final. I would still recommend going through them,
perhaps in your pricing project groups since there are no
solutions to post. (You can ask me if you have any questions.)
Old exams will be circulated. Next session – the last one!! –
I’ll go through the last problem set and summarize what I feel
are the highlights of the course.
September 26, 2009
Section 5 Section Notes
2
Review of Pricing: Marginal Cost
•
•
•
•
TC = C(Q)  MC = dC(Q)/dQ
In competitive markets, MC curve is the supply curve. Set
P=MC, so long as P>minATC.
For monopoly, set MR=MC, so long as P>minATC.
See following graph…
September 26, 2009
Section 5 Section Notes
3
Monopolist with Linear Demand Curve
and P<minATC
P, C
MC
ATC
C(Q*)
P*
Notice that Total Costs are
Greater than Total Revenues
Q*
September 26, 2009
MR
D
Section 5 Section Notes
Q
4
Price Discrimination: Overview
•
•
•
•
Price discrimination allows the firm to achieve higher profits.
1st degree PD achieves the highest profits (charge every
consumer her maximum willingness to pay).
3rd degree PD depends on some observable trait of the
consumers (e.g.: student id).
2nd degree PD induces consumers to self select into groups
(e.g.: quantity discounts, versioning, etc).
September 26, 2009
Section 5 Section Notes
5
2nd Degree Price Discrimination
•
Present consumers with menu of options and let them self
select into groups.
In the optimal 2nd degree PD price scheme, the lowest
valuation consumer group gets zero consumer surplus.
The pricing scheme should be such that every group of
consumers buys the option intended for them, and not the
option intended for another group.
•
•
–
High valuation consumers should not prefer the option for the low
valuation consumers. (This is why high valuation customers usually
get some “rent” in the PD scheme – to “pay” them not to take the low
valuation option!)
September 26, 2009
Section 5 Section Notes
6
Tips for 2nd Degree PD Problems
1.
2.
Set up strategies or a “menu of options” and methodically
calculate the prices which get customers to do what you want
them to do. Pick the option that maximizes profit.
Some options to try:
1.
2.
3.
3.
Sell one product, only to high valuation group.
Sell one product to everyone (note high valuation group will get rent).
Set up a 2nd degree PD scheme (setting prices so people self-select).
General rules for setting up 2nd degree PD scheme:
1.
2.
Always charge low WTP group its maximum WTP for low quality
product.
Make sure that high WTP group buys high quality product by giving
more than CS from choosing low quality product.
September 26, 2009
Section 5 Section Notes
7
Extra Thought Exercises – Pricing
•
What would a perfectly competitive firm want to do if
–
–
•
•
•
the market price were below its marginal costs?
the market price were above its marginal costs?
What tradeoffs does the monopolist face as it lowers its price?
Why is it that when the absolute value of demand elasticity is
less than one, marginal revenue is less than zero?
What does the marginal revenue curve faced by a perfectly
competitive firm look like?
September 26, 2009
Section 5 Section Notes
8
Extra Thought Exercises – Pricing
•
What would a perfectly competitive firm want to do if
–
–
•
the market price were below its marginal costs?
• It would want to reduce output until its marginal cost equaled the
market price. If the market price is below the firm’s minimum
average cost, it would shut down.
the market price were above its marginal costs?
• If this price is above its minimum average costs, it would expand
production until its marginal cost equaled the market price.
What tradeoffs does the monopolist face as it lowers price?
–
Although quantity demanded increases at lower prices, the average
revenue from each unit sold decreases (for all units sold).
September 26, 2009
Section 5 Section Notes
9
Extra Thought Exercises – Pricing
•
Why is it that when the absolute value of demand elasticity is
less than one, marginal revenue is less than zero?
–
–
–
•
R=P(Q)*Q
MR= P + Q*dP/dQ = P + P (1/Ed) = P (1+ 1/Ed) <0 if |Ed|<1 where Ed is
always negative.
This means a monopolist will always set a price that corresponds to an
elastic portion of the demand curve.
What does the marginal revenue curve faced by a perfectly
competitive firm look like?
–
–
It is the market price.
Can you see this from the MR equation above?
September 26, 2009
Section 5 Section Notes
10
Extra Thought Exercises – Price
Discrimination
•
•
•
Why can’t a firm price discriminate if it is operating in a
perfectly competitive environment?
Why can’t a firm price discriminate if its consumers can resell
the product?
Would you as a buyer ever want a supplier to price
discriminate?
September 26, 2009
Section 5 Section Notes
11
Extra Thought Exercises – Price
Discrimination
•
Why can’t a firm price discriminate if it is operating in a
perfectly competitive environment?
–
•
Consumers have the option of buying from other suppliers at the
market price. If a perfectly competitive firm tries to offer a price above
the market price, it will result in zero sales.
Why can’t a firm price discriminate if its consumers can resell
the product?
–
Arbitrage would prevent the firm from selling to different consumers at
different prices. A low valuation person can buy the good for a low
price from the firm, and resell to high valuation consumers.
September 26, 2009
Section 5 Section Notes
12
Extra Thought Exercises – Price
Discrimination
•
Would you as a buyer ever want a supplier to price
discriminate?
–
If you are a low valuation consumer, who otherwise would not get
served, then yes. A uniform price may be higher than your valuation,
whereas price discrimination allows the firm to charge higher prices to
other consumers who are willing to pay, and still profitably lower its
price to you.
September 26, 2009
Section 5 Section Notes
13
Question 1 from Problem Set 4
• A) How to start this kind of question:
• 1) Find the minimum P at which any quantity
will be sold for any kind of buyer.
• 2) Write down the ranges and what the demand
will be in each range.
 For P below 7, demand is 60000-7500P
For P between 7 and 10, demand is 25,0002500P
For P above 10, demand is 0
September 26, 2009
Section 5 Section Notes
14
• 3) Then find in which range does MC=MR or
MC=P.
TC=2QMC=2. Where does MR=2?
At P=7, only Marin buys: Q=25,000-2,500*7
= 7,500
TR=10Q-Q2/2500  MR = 10 – Q/1250
At Q=7,500, MR = 10-6=4
At P>7, MR only increases.  MC will not
equal MR in this range.  Produce to sell in
both areas.
September 26, 2009
Section 5 Section Notes
15
• For P<7, TR=8Q-Q2/7,500  MR=8-Q/3,750
• MR=MC  8-Q/3,750=2  Q=22,500  P=5
• Don’t forget to calculate profits if the question
asks! (You probably want to even if it doesn’t,
in case they’re negative.)
• Profits=P*Q-TC(Q)=5*22,5002*22,500=67,500.
September 26, 2009
Section 5 Section Notes
16
• B) Now we just have two pricing problems.
Set MC=MR in each case.
• Thought question: Why are the profits higher?
2) A) Recall the three possibilities we must
definitely check:
- Sell to both at the same price
- Sell to the higher one and exclude the lower by
pricing too high for it
- Sell to both and price-discriminate
September 26, 2009
Section 5 Section Notes
17
• Here we have an extra quirk: 2-litre vs. 1-litre bottles. Nobody
should buy a 2-litre bottle when two 1-litre bottles are cheaper,
and nobody should buy two 1-litre bottles when a 2-litre bottle
is cheaper.
• Let us call the prices we have to set P1 and P2.
• Identify the critical prices at which someone will start/stop
buying:
• What’s the most a vegan would pay for a 1-litre bottle? $3.25.
What’s the most a meat-eater would pay for a 1-litre bottle?
$4.
• What’s the most a vegan would pay for a 2-litre bottle? NOT
$6.50 (2 times $3.25) – but $5 (see their demand function).
What’s the most a meat-eater would pay for a 2-litre bottle?
$7.
• What’s the most a vegan would pay for a 3-litre bottle? $5.
What’s the most a meat-eater would pay for a 3-litre bottle?
$8.
September 26, 2009
Section 5 Section Notes
18
• Vegans here are the “low” type – they’re
willing to pay less than the meat-eaters. So we
know for sure that IF we want them to buy
either the 1-litre or 2-litre bottles, we want to
set P1 or P2 at their maximum WTP, or $3.25
for 1 litre, $5 for 2.
– We will never want to set a price lower than the
highest price the “low” type is willing to pay.
• What about meat-eaters? IF we want them to
buy either the 1-litre or 2-litre bottles, P1 or P2
would have to be less than or equal to $4 or $7,
respectively.
September 26, 2009
Section 5 Section Notes
19
• Now let’s combine them:
• IF P1=3.25 (to get the Vegans to buy), then the
highest price the Meat-eaters are willing to pay for
the 2-litre bottle is actually $6.25 ($3.25 plus their
marginal utility from the second bottle).
– IF P1=$3.25 and P2=$6.25, Vegans buy 1-litre, Meat-eaters
buy 2-litre.
– IF P1=$3.25 and P2>$6.25, Vegans buy 1-litre, Meat-eaters
buy 1-litre.
– IF P1=$3.25 and P2<$6.25 – you would not be maximizing
profits. (If P2=$6.25 you get the Meat-eaters to buy for a
higher price.)
September 26, 2009
Section 5 Section Notes
20
• IF P1>$3.25 AND P2>$5, no Vegans buy. Meateaters might buy, depending on price.
– If you want Meat-eaters to buy a 1-litre bottle, charge
Meat-eaters $4 for 1-litre, since no Vegans are buying the
1-litre anyway and $4 is the Meat-eaters’ maximum WTP
for a 1-litre bottle.
– However, since you want Meat-eaters to buy two litres in
this case, set P1>$4 and P2=$7.
• Question: why is P1 greater than or equal to $3.50 not good
enough? (Hint: CS.)
• IF P1>$3.25 and P2=$5, everyone buys a 2 litre
bottle.
• IF P1>$3.25 and P2<$5, you’re not profitmaximizing.
September 26, 2009
Section 5 Section Notes
21
• Now compare profits:
• P1=3.25, P2=6.25  Profits=1000x(3.251)+1200(6.25-2)=7350
• P1=3.25, P2>6.25  Profits=1000x(3.251)+1200x(3.25-1)=4950
• P1=3.25, P2=5  Profits=1000x(52)+1200x(5-2)=6600
• P1>4, P2=7  Profits=1200x(7-2)=6000
 Go with the option that yields the highest
profits.
September 26, 2009
Section 5 Section Notes
22
• B) The options are the same, the profits differ. Re-do
the profit equations with the new number of buyers.
•
•
•
•
•
•
3) A) Options:
$400 full version, $50 scaled-down
$400 full version, $0 scaled-down??
$100 full version, $50 scaled-down??
$100 full version, $0 scaled-down??
Clearly, these last 3 are stupid if you can get the first
one.
• Tip: when in doubt, write out the options. Then you
can go through them one by one and figure out which
is best.
September 26, 2009
Section 5 Section Notes
23
• B) You really want the professionals to buy the full version,
since production costs are zero for all versions and $400 is the
most you can get out of anyone.
• So the question really is, do you want to lure the students to
$75? Well, yes, of course you do – but be careful! Producing
the intermediate version and selling it at $75 would incentivize
the professionals to buy it instead of the full version.  IF you
were to get $75 from the students for the intermediate version,
you’d have to set the price of the full version to be $75+($400$200)=$275 to get the professionals to buy it. (Difference in
price on LHS, WTP on RHS: $X-$75=$400-$200.) Is $75 for
students and $275 for professionals better than $50 for
students and $400 for professionals? Depends on their
numbers and your costs (the latter of which are 0 here)….
• Selling the full version at $400 and the intermediate at $200
but no scaled-down version is obviously bad – the
professionals buy the full version, true, but the students don’t
buy anything.
September 26, 2009
Section 5 Section Notes
24
Extra Pricing Problem
• Costs to producing a new kind of car:
• Touring around the country showing it at car
shows: $1 million.
• Costs of the parts of the car: $500/car.
• Costs of the labour to assemble the parts:
$1000/car.
• Cost of the plant it is manufactured in: $10
million.
• Question: what is the MC? AC?
September 26, 2009
Section 5 Section Notes
25