Transcript Section_4_2009 - Faculty Directory | Berkeley-Haas

MBA 201A
Section 4 - Pricing
Overview
 Review of Pricing Strategies
 Review of Pricing Problem from Class
 Review PS3
 Questions on Midterm
 Q&A
Overview of Pricing - back to the basics…
 Knowledge of costs give you information on how firms should price
 To maximize profits set MR=MC by adjusting Q
 To solve you need to know Revenues and Costs
Overview of Pricing - back to the basics…
 Monopolist can affect market price, ie changing Q will change P so we
write P(Q)
 In competitive markets, firms are price takers, so firm cannot affect P by
changing Q (we just have P) so MR = P
 Remember the solution concept:
 Find MR (take derivative of Revenue function)
 Find MC (might have to take derivative of Total Cost function)
 Set MC = MR for the monopolist
 Find Q and P using original equations
 Does it make sense to stay in business?
Price Discrimination
 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).
Review of Class Problem
Willingness to pay for ticket
Type of Consumer
# of cons
(unrestricted)
(Saturday-night-stay)
Tourist
10
$300
$300
Businessperson
10
$800
$400
Strategy 1: Offer all tickets at price $300
 Total revenue = $30010 + $30010 = $6,000
Strategy 2: Offer only unrestricted tickets at price $800
 Total revenue = $80010 = $8,000
Strategy 3: Offer Saturday-night-stay at price $300, unrestricted at
price $800
Will the businessperson buy the unrestricted ticket?
Review of Class Problem (cont’d)
Willingness to pay for ticket
Type of Consumer
# of cons
(unrestricted)
(Saturday-night-stay)
Tourist
10
$300
$300
Businessperson
10
$800
$400
Strategy 3: Offer Saturday-night-stay at price $300, unrestricted at price
$800
Question: Will the businessperson buy the unrestricted ticket?
Answer: No.
•
If she purchases unrestricted ticket she receives consumer surplus
(CS) = $800 (her WTP) - $800 (the amount she pays) = $0.
•
If instead she purchases Sat-night-stay ticket she receives CS = $400
(her WTP) - $300 (the amount she pays) = $100.
•
She will choose option that gives her more CS. Here, it is Sat-nightstay.
Review of Class Problem (cont’d)
Willingness to pay for ticket
Type of Consumer
# of cons
(unrestricted)
(Saturday-night-stay)
Tourist
10
$300
$300
Business person
10
$800
$400
Strategy 3, revised: Offer Sat-night-stay at price $300, unrestricted at price
$699.
Question: Will the business person buy the unrestricted ticket?
Answer: Yes.
•
If she purchases unrestricted ticket she receives consumer surplus
(CS) = $800 (her WTP) - $699 (the amount she pays) = $101.
•
If instead she purchases Sat-night-stay ticket she receives CS = $400
(her WTP) - $300 (the amount she pays) = $100.
•
She will choose option that gives her more CS. Here, it is unrestricted.
•
Notice that Tourist receives zero surplus, the but the business person
receives positive surplus ($101). This is an example of the “rent” that
the high willingness to pay group receives
Review of Class problem (cont’d)
 You may find it useful to keep track of strategies and prices in a table
 Describe which options you want each group to buy and then decide
how to set prices to get the groups to do what you want
 Example:
Groups
Prices ($)
Strategy Tourist Business
Unrestricted
(U)
Sat. Night Stay
(S)
Profits
($)
1
U
U
300
300
6,000
2
0
U
800
>400
8,000
3
S
U
699
300
9,990
Tips for 2nd degree PD problems
 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:
 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
 General rules for setting up 2nd degree PD scheme:
 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.
PS3 / #3 (a)
 Big Picture: we need to see where MC crosses MR – does it just cross
one market or does it cross both? (Third Degree PD)
 There are a couple of ways to look at this problem
 Graphically (see that MC crosses the joint MR schedule)
 Algebraically (through seeing that P < 7)
 If you solve for the Marin market only, you will find that P=6, which
implies that you will be selling to the SF market (will explain later)
 The Graphical solution is outlined in the answer key
 First the MR of the Marin market is graphed
 Then the joint MR for the two markets is graphed
 Plotting MC = 2, you can see that MC crosses the joint MR line
 Conclusion: need to add the demand curves together and solve, we are in
the joint market world
PS3 / #3 (a) cont’d
 Algebraic solution requires you to think about where MR “jumps”
 Qm = 25,000 – 2,500P
 Set Qm = 0, then 25,000 = 2,500P / P = 10
 So Marin will start buying ice cream at P = 10. Lower values of P mean
they will buy more Q (check by putting in e.g. P = 9)
 QSF = 35,000 – 5,000P
 Set QSF = 0, then 35,000 = 5,000P / P = 7
 And SF will start buying ice cream at P = 7
 And naturally, NO ONE buys ice cream when P > 10
 So demand looks like this:
SF & Marin Buys
Price
Marin Buys
7
No One Buys
10
PS3 / #3 (a) cont’d
 Now that we have the “cut points” where Marin and SF start buying ice
cream, let’s see what demand looks like:
 Let’s plug in P = 7 b/c this where the markets turn from Marin buying
only to SF & Marin buying
 Qm = 25,000 – 2,500P  Qm = 25,000 – 2,500 * 7  Qm = 7,500
 Now should we stop producing at 7,500 units? We need to look at MR…
 MR = 10 – (Qm / 1,250) (I got this from the standard way)
 Plug in 7,500  MRMarin = 10 – (7,500/1,250) = 4
 Recall, if MC = 2 and MR = 4 that means we should continue producing ice
cream past 7,500 units b/c MR > MC, so we are making money on the next
incremental unit of ice cream
 But what happens to P when we push past 7,500? If P = 7 when Q = 7,500
then P falls below 7 when we make more than 7,500. You can see for
yourself by plugging in say 7,501 into Qm = 25,000 – 2,500P
PS3 / #3 (a) cont’d
 So…we have shown that P is going be less than 7. Now if we refer back
to our line:
SF & Marin Buys
Price
Marin Buys
7
No One Buys
10
 So we are in the market where SF & Marin are buying ice cream.
Therefore, to find the optimal price / quantity we add the demand
curves for Marin & SF and solve per usual
PS3 / #3 (a) cont’d
 Finally, what if we had decided to solve for the Marin County market to
begin with?
 Set MR = MC  10 – (Qm / 1,250) = 2  Qm = 10,000
 And P = 6 when you plug 10,000 into the Marin demand equation
 With P = 6, we are already pass the threshold of just selling to Marin (P = 7)
so that implies we are also selling to SF. This can also be seen on the graph in
the answer key. The MR curve for Marin ends at Q = 7,500. When we go
past this, we jump up to the joint MR curve. And we just found that Q =
10,000 if only sell to Marin.
 Bottom line, we need to add the demand curves together and then solve
 MC only crosses the MR curve once, at the joint MR curve