Section 5 Section Notes

September 26, 2009 Section 5 Section Notes 1

Section 5 Section Notes

EWMBA201A

Eva Vivalt


Administrative Stuff

1. 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.)

2. 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.


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…


Monopolist with Linear Demand Curve and P<minATC

QQ*

P*

MR D

MCP, C

ATC

C(Q*)

Notice that Total Costs are Greater than Total Revenues


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).


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!)


Tips for 2nd Degree PD Problems

1. 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.

2. Some options to try:1. Sell one product, only to high valuation group.

2. Sell one product to everyone (note high valuation group will get rent).

3. Set up a 2nd degree PD scheme (setting prices so people self-select).

3. General rules for setting up 2nd degree PD scheme:1. Always charge low WTP group its maximum WTP for low quality

product.

2. Make sure that high WTP group buys high quality product by giving more than CS from choosing low quality product.


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?



• 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).



• 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?


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?



• 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.



• 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.


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 60000-7500PFor P between 7 and 10, demand is 25,000-

2500PFor P above 10, demand is 0


• 3) Then find in which range does MC=MR or MC=P.

TC=2QMC=2. Where does MR=2?At P=7, only Marin buys: Q=25,000-2,500*7

= 7,500TR=10Q-Q2/2500 MR = 10 – Q/1250At Q=7,500, MR = 10-6=4At P>7, MR only increases. MC will not

equal MR in this range. Produce to sell in both areas.


• 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*22,500-2*22,500=67,500.


• 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


• 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.


• 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.


• 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.)


• IF P1>$3.25 AND P2>$5, no Vegans buy. Meat-eaters 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 profit-maximizing.


• Now compare profits:

• P1=3.25, P2=6.25 Profits=1000x(3.25-1)+1200(6.25-2)=7350

• P1=3.25, P2>6.25 Profits=1000x(3.25-1)+1200x(3.25-1)=4950

• P1=3.25, P2=5 Profits=1000x(5-2)+1200x(5-2)=6600

• P1>4, P2=7 Profits=1200x(7-2)=6000

Go with the option that yields the highest profits.


• 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.


• 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.


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?

Section 5 Section Notes

Documents

section notesextra

section notestips

section notesmonopolist

degree pd scheme

degree pd price scheme

high valuation group

group of consumers

high valuation consumers