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MBA 201A Section 4 - Pricing

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

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MBA 201A Section 4 - Pricing

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  1. MBA 201ASection 4 - Pricing

  2. Overview • Review of Pricing Strategies • Review of Pricing Problem from Class • Review PS3 • Questions on Midterm • Q&A

  3. 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

  4. 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?

  5. 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).

  6. Review of Class Problem 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?

  7. Review of Class Problem (cont’d) • 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-night-stay.

  8. Review of Class Problem (cont’d) • 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

  9. 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:

  10. 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.

  11. 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

  12. 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 Marin Buys No One Buys Price 7 10

  13. 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

  14. 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: • 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 SF & Marin Buys Marin Buys No One Buys Price 7 10

  15. 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

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