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 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? Willingness to pay for ticket Type of Consumer# of cons(unrestricted)(Saturday-night-stay) Tourist 10 $300 Businessperson 10 $800 $400

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. Willingness to pay for ticket Type of Consumer# of cons(unrestricted)(Saturday-night-stay) Tourist 10 $300 Businessperson 10 $800 $400

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 Willingness to pay for ticket Type of Consumer# of cons(unrestricted)(Saturday-night-stay) Tourist 10 $300 Business person 10 $800 $400

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: GroupsPrices ($) StrategyTouristBusinessUnrestricted (U) Sat. Night Stay (S) Profits ($) 1UU300 6,000 20U800>4008,000 3SU ,990

Tips for 2 nd 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”  Q m = 25,000 – 2,500P  Set Q m = 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)  Q SF = 35,000 – 5,000P  Set Q SF = 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: 107 Price No One BuysMarin BuysSF & Marin Buys

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  Q m = 25,000 – 2,500P  Q m = 25,000 – 2,500 * 7  Q m = 7,500  Now should we stop producing at 7,500 units? We need to look at MR…  MR = 10 – (Q m / 1,250) (I got this from the standard way)  Plug in 7,500  MR Marin = 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 Q m = 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:  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 107 Price No One BuysMarin BuysSF & Marin Buys

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 – (Q m / 1,250) = 2  Q m = 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