1. the analytics of constrained optimal decisions microeco nomics spring 2016 the perfectly competitive market ………….1the monopolist problem ………….2 the pricing problem session four ………….3revenue analysis ………….5 revenue, cost and profit analysis ………….8standard/uniform pricing ………….9 user fee pricing ………10bundling menu pricing ……….11 pricing intermediation ………17consolidation

2. microeconomic s the analytics of constrained optimal decisions lecture 4 the monopoly model (I): standard pricing and consolidation  2016 Kellogg School of Management lecture 4 page |1 the monopolist problem ► We discussed so far models in which there were (at least a few if not) several producers competing with each other to sell a non-differentiated good (commodity markets) ► The equilibrium emerged at the intersection of demand and supply : - demand curve shows the willingness to pay (or how many units are demanded at each price level) - supply curve shows the willingness to produce (or how many units are offered at each price level) ► We move now to a new market setup characterized by: - several consumers, therefore the demand curve definition and analysis remains valid - there is only one producer (monopolist) serving the market ► The challenge is to determine how the monopolist behaves, i.e. what price it will charge, what quantity it will offer, etc. In other words we have to study the profit maximization problem for a monopolist. ► Conceptually, the equilibrium is defined in a similar way: a pair of price and quantity such that given that price level consumers are willing to buy the quantity offered and the monopolist maximizes its profit by offering exactly the quantity demanded. competition the monopolist

3. microeconomic s the analytics of constrained optimal decisions lecture 4 the monopoly model (I): standard pricing and consolidation  2016 Kellogg School of Management lecture 4 page |2 standard pricing I am an airline with a monopoly on the Atlanta-Los Angeles route I have market power : I can set the price ! But how high should I go? Or how low should I go? I currently price tickets at P = $760, and expect a volume Q = 100 passengers per trip, which is less than my plane’s capacity. Questions to consider: ► If I lower the price can I get more paying passengers ? ► How much revenue does an additional passenger add ? ► Is the extra revenue worth the extra cost ? If I am to answer these questions what information do I need? ► Demand sensitivity to change in price ► Sensitivity ( a lot of/far fewer additional passengers ) not enough for second question ► Demand equation, i.e. Q = a – b∙P ► Cost of adding an additional passenger ( marginal cost ) the pricing problem

4. microeconomic s the analytics of constrained optimal decisions lecture 4 the monopoly model (I): standard pricing and consolidation  2016 Kellogg School of Management lecture 4 page |3 standard pricing revenue analysis P Q 960 480 760 758 100 101 (0) (1) lost revenue by lowering the price extra revenue by increasing number of passengers Let’s assume that we know the demand equation as Q = 480 – 0.5 P and the constant marginal cost for accommodating each additional passenger as MC = $160. ► At current price P 0 = $760 → Q 0 = 480 – 0.5∙760 = 100 passengers for a total revenue TR 0 = P 0 Q 0 = $760∙100 = $76,000 ► I would like to add an extra passenger… what should be the price for that to happen ? to get Q 1 = 101 → 101 = 480 – 0.5 P 1 → P 1 = $758 The total revenue is now TR 1 = P 1 Q 1 = $758∙101 = $76,558 The change in total revenue is TR 1 – TR 0 = $558 ► Should I add this one extra passenger ? marginal revenue = $558 vs. marginal cost = $160 I get an extra profit of $398 for this extra passenger…

5. microeconomic s the analytics of constrained optimal decisions lecture 4 the monopoly model (I): standard pricing and consolidation  2016 Kellogg School of Management lecture 4 page |4 standard pricing revenue analysis ► Total revenue : revenue obtained for all units sold; TR = P ∙ Q ► Marginal revenue : change in revenue due to the last unit sold ; MR = ∆ TR /∆ Q ► Marginal cost : cost for the last unit produces (sold) ; MC = ∆ TC /∆ Q P Q a a/b ► The general definition for the marginal revenue is “ the change in total revenue when quantity changes ” ► For a linear demand function P = a – b ∙ Q we get a very nice result: (Step 1): TR ( Q ) = P ∙ Q = ( a – b ∙ Q )∙ Q = a ∙ Q – b ∙ Q 2 (Step 2): MR ( Q ) = dTR ( Q ) /dQ = a – 2b ∙ Q ► Conclusion: for a linear demand function P = a – b ∙ Q the marginal revenue is also a linear function MR ( Q ) = a – 2b ∙ Q demand, P ( Q ) a/ (2 b ) MR ( Q )

6. microeconomic s the analytics of constrained optimal decisions lecture 4 the monopoly model (I): standard pricing and consolidation  2016 Kellogg School of Management lecture 4 page |5 standard pricing revenue, cost and profit analysis The demand equation P ( Q ) is P = 960 – 2 Q giving a marginal revenue function MR ( Q ) = 960 – 4 Q. We saw above that increasing the number of passengers from 100 to 101 gave a marginal revenue of $558 and we decided that this is profitable to do since … the marginal revenue is greater than the marginal cost… P Q demand, P ( Q ) MR ( Q ) MC ( Q ) ► Should we continue to increase the number of passengers (by decreasing the price)? How many more? ► As long as MR ( Q ) > MC ( Q ) it is profitable to add more passengers because each will bring a positive net profit… ► If MR ( Q ) < MC ( Q ) we added too many passengers… the net profit for the last added is negative → better off to decrease the number of passengers ► Profit is maximized for Q m such that MR ( Q m ) = MC ( Q m ) ► The corresponding monopoly price P m is found through the demand function: P m = P ( Q m ) QmQm this gives market output this gives market price PmPm

7. microeconomic s the analytics of constrained optimal decisions lecture 4 the monopoly model (I): standard pricing and consolidation  2016 Kellogg School of Management lecture 4 page |6 standard pricing revenue, cost and profit analysis P Q demand, P ( Q ) MR ( Q ) MC ( Q ) Q m =200 P m =560 this gives market output this gives market price 960 480240 For our initial example: ► the “marginal” functions: MR ( Q ) = 960 – 4 Q and MC = 160 ► profit maximization condition: MR ( Q ) = MC ► optimal output: 960 – 4 Q = 160 Q m = 200 ► the demand function: P ( Q ) = 960 – 2 Q ► optimal price: P m = P ( Q m ) = 960 – 2 Q m = 560 ► Profit is maximized for Q m such that MR ( Q m ) = MC ( Q m ) ► The corresponding monopoly price P m is found through the demand function: P m = P ( Q m )

8. microeconomic s the analytics of constrained optimal decisions lecture 4 the monopoly model (I): standard pricing and consolidation  2016 Kellogg School of Management lecture 4 page |7 standard pricing revenue, cost and profit analysis The benchmark is the perfect competition. ► perfect competition equilibrium : demand = supply (left diagram) - consumer surplus is shown in the diagram as the light gray area (producer surplus = 0, deadweight loss = 0) ► monopolistic competition equilibrium : MR = MC (right diagram) - consumer surplus the light gray area, producer surplus the dark gray area, deadweight loss the orange area P Q demand, P ( Q ) MR ( Q ) MC ( Q ) QmQm PmPm PcPc QcQc (c)(c) (m)(m) P Q demand, P ( Q ) MR ( Q ) MC ( Q ) QmQm PmPm PcPc QcQc (c)(c) (m)(m) deadweight loss

9. microeconomic s the analytics of constrained optimal decisions lecture 4 the monopoly model (I): standard pricing and consolidation  2016 Kellogg School of Management lecture 4 page |8 price discrimination standard/uniform pricing ► The pricing method we studied so far is called uniform pricing because it assumes that all units are sold to all consumers at the same price P m (this is the $0.99 per song price that iTunes charges) ► We saw how the monopolist is determining the optimal price to maximize its profit. The outcome is shown in the diagram (the dark gray area is the profit for the monopolist) ► Notice that the consumer still gets some surplus, i.e. the price is still below his/her willingness to pay… is there any way for the monopolist to “capture” this remaining surplus and leave the consumer with no surplus? P Q demand, P ( Q ) MR ( Q ) MC ( Q ) Q m =15 P m =0.75 (m)(m) 1.20 0.30 ► Before advancing let’s calculate ( demand function P ( Q ) = 1.20 – 0.03 Q, marginal revenue MR ( Q ) = 1.20 – 0.06 Q and marginal cost MC = 0.30 ): - consumer surplus = 1/2∙(1.20 – 0.75)∙15 = 3.375 - monopolist profit = (0.75 – 0.30)∙15 = 6.750 ► First suggestion: charge a “user fee” of $3.375 (to use iTunes) and then charge $0.75 per song ► Second suggestion: offer a “bundling” menu such as - any 1 song for a total of $1.185 - any 2 songs for a total of $2.34 … - any 15 songs for a total of $14.625 4020

10. microeconomic s the analytics of constrained optimal decisions lecture 4 the monopoly model (I): standard pricing and consolidation  2016 Kellogg School of Management lecture 4 page |9 price discrimination user fee pricing P Q demand, P ( Q ) MR ( Q ) MC ( Q ) Q m =15 P m =0.75 (m)(m) 1.20 0.30 4020 ► Demand function P ( Q ) = 1.20 – 0.03 Q, marginal revenue MR ( Q ) = 1.20 – 0.06 Q and marginal cost MC = 0.30 : - consumer surplus = 1/2∙(1.20 – 0.75)∙15 = 3.375 - monopolist profit = (0.75 – 0.30)∙15 = 6.750 ► What is the buyer doing? If the buyer pays $3.375 it basically gives up the surplus but he/she still buys the 15 songs (since his demand is not changed, i.e. he’s willingness to pay is not changed) What’s the resulting outcome? The monopolist gets the whole surplus available, making a total profit of $3.375 + $6.750 = $10.125 ► The total profit is now the sum of what was consumer surplus before and the initial producer surplus (it basically “absorbed” the consumer surplus) First suggestion : charge a “user fee” of $3.375 (to use iTunes) and then charge $0.75 per song

11. microeconomic s the analytics of constrained optimal decisions lecture 4 the monopoly model (I): standard pricing and consolidation  2016 Kellogg School of Management lecture 4 page |10 price discrimination bundling menu pricing ► Demand function P ( Q ) = 1.20 – 0.03 Q, marginal revenue MR ( Q ) = 1.20 – 0.06 Q and marginal cost MC = 0.30 : - consumer surplus = 1/2∙(1.20 – 0.75)∙15 = 3.375 - monopolist profit = (0.75 – 0.30)∙15 = 6.750 P Q demand, P ( Q ) 1.17 40 1.14 0.75 0.78 1.20 1 21415 Second suggestion : offer a “bundling” menu… If the monopolist chooses this suggestion how does he/she calculates the “bundling” prices? - any 1 song for a total of $1.185 - any 2 songs for a total of $2.34 … - any 15 songs for a total of $14.625 ► Consumer surplus: CS (1 st ) = ½(1.20 – 1.17)1 + 1.17 = 1.185 CS (2 nd ) = ½(1.17 – 1.14)1 + 1.14 = 1.155 In total for two songs = 1.185 + 1.155 = 2.34 ► …and so on … for a given number of songs just ask a “bundle” price equal to the area under demand line up to that number of songs (this is the total amount the consumer is willing to give up for that number of songs). For 15 songs you’ll get the total amount consumer is willing to give up for those songs, namely 14.625.

12. microeconomic s the analytics of constrained optimal decisions lecture 4 the monopoly model (I): standard pricing and consolidation  2016 Kellogg School of Management lecture 4 page |11 pricing intermediation free market equilibrium - demand D ( P ) = 10 – P - supply S ( P ) = P The equilibrium is very easy to find by setting demand equal to supply 10 – P = P P * = $5 ($) Q demand supply Buyers and seller can transact with each other directly and to keep algebra simple let’s assume:

13. microeconomic s the analytics of constrained optimal decisions lecture 4 the monopoly model (I): standard pricing and consolidation  2016 Kellogg School of Management lecture 4 page |12 pricing intermediation intermediaries But now buyers and seller can transact with each other only after paying a fee t to an intermediary (gate keeper). ► The prices paid by the buyer ( P B ) and supplier ( P S ) are different such that the difference between them is exactly the fee t : P B – P S = t ► Demand and supply curves do not change but they depend for the corresponding prices for buyers and suppliers: - demand D ( P B ) = 10 – P B - supply S ( P S ) = P S How do we find the equilibrium? Common sense? ► Prices have to satisfy P B – P S = t ► Quantity demanded given P B and quantity supplied given P S should be the same D ( P B ) = S ( P S ) Thus: P B – P S = t 10 – P B = P S We get P B = P S + t which plugged in the second equation gives 10 – ( P S + t ) = P S → P S = 5 – 0.5 t but P B = P S + t → P B = 5 + 0.5 t

14. microeconomic s the analytics of constrained optimal decisions lecture 4 the monopoly model (I): standard pricing and consolidation  2016 Kellogg School of Management lecture 4 page |13 pricing intermediation intermediaries ($) Q demand supply With P S = 5 – 0.5 t or P B = 5 + 0.5 t the corresponding quantity is Q ( t ) = 5 – 0.5 t Where do we find this graphically? The hint comes from the relation P B – P S = t The vertical difference between prices has to be exactly t. Say t = 4 … start from the maximum difference of 10 (when Q = 0) and move towards the minimum difference of 0 (when Q = 5) … somewhere in between 10 and 0 the difference has to be 4. PBPB PSPS 4 Q** P * = 5 competitive price ( t = 0)

15. microeconomic s the analytics of constrained optimal decisions lecture 4 the monopoly model (I): standard pricing and consolidation  2016 Kellogg School of Management lecture 4 page |14 pricing intermediation the monopolist ($) Q demand supply What is the revenue for gate keepers? TR(t) = t ∙ Q ( t ) Graphically TR ( t ) is the area of the rectangle between the two prices and up to the transacted quantity. What happens with the total revenue if t changes? Two opposite effects: ► a higher t → TR increases ► a lower Q ( t ) → TR decreases What is the “best” t, i.e. the value for which the total revenue is at a maximum? Q(t)Q(t) t t’ Q ( t’ )

16. microeconomic s the analytics of constrained optimal decisions lecture 4 the monopoly model (I): standard pricing and consolidation  2016 Kellogg School of Management lecture 4 page |15 pricing intermediation the monopolist ($) Q demand supply Back to our simple case, the intermediary is a monopolist that sells its services at a price t and faces a demand Q ( t ) = 5 – 0.5 t therefore its marginal revenue function is MR ( Q ) = 10 – 4 Q Since the marginal cost of providing the services is assumed to be zero, MC = 0, the intermediary maximizes it’s profit by setting MR = MC giving t ** = 5 and Q ** = 2.5 and profit = 12.5 Q **= 2.5 t **=5 PBPB PSPS

17. microeconomic s the analytics of constrained optimal decisions lecture 4 the monopoly model (I): standard pricing and consolidation  2016 Kellogg School of Management lecture 4 page |16 pricing intermediation surplus analysis ($) Q demand supply Q **= 2.5 t **=5 PBPB PSPS Winners & Losers? ► intermediaries gain is the green rectangle ► buyers’ surplus is the blue triangle ► sellers’ surplus is the red triangle ► DWL is the orange triangle

18. microeconomic s the analytics of constrained optimal decisions lecture 4 the monopoly model (I): standard pricing and consolidation  2016 Kellogg School of Management lecture 4 page |17 consolidation ► Let’s consider a stylized supply –chain model: ● manufacturer unit produces the good at a constant marginal cost MC m ● the manufacturing unit sells the good at a price P m to a distributor ● the distributor unit sells the good at a price P d to the final market ● the distributor incurs no additional costs (it only pays P m per unit of good to the manufacturer) ● demand on the final market is given by P = a – bQ ► How many units of good will be produced and what are the prices P m and P d ? manufacturer (monopolist) manufacturer (monopolist) distributor (monopolist) distributor (monopolist) final market physical good Q payment P m per unitpayment P d per unit marginal cost of producing one unit is MC m demand on the final market is given by P = a – bQ

19. microeconomic s the analytics of constrained optimal decisions lecture 4 the monopoly model (I): standard pricing and consolidation  2016 Kellogg School of Management lecture 4 page |18 consolidation ► At the final stage of the chain we analyze a standard monopolist model where: ● the demand for the good is P = a – bQ ● the firm (distributor) has a marginal cost of MC d = P m ● the firm (distributor) has a marginal revenue of MR d = a – 2 bQ ► The solution at this stage is given by the condition MR d = MC d ● this gives a – 2 bQ d = P m ● we got a relation between the price set by the manufacturer and the quantity the distributor would like to order from the manufacturer → we derived the demand curve that the manufacturer faces manufacturer (monopolist) manufacturer (monopolist) distributor (monopolist) final market physical good Q payment P m per unitpayment P d per unit marginal cost of producing one unit is MC m demand on the final market is given by P = a – bQ distribution

20. microeconomic s the analytics of constrained optimal decisions lecture 4 the monopoly model (I): standard pricing and consolidation  2016 Kellogg School of Management lecture 4 page |19 consolidation ► At the initial stage of the chain we analyze a standard monopolist model where: ● the demand for the good is P m = a – 2 bQ ● the firm (manufacturer) has a marginal cost of MC m ● the firm (manufacturer) has a marginal revenue of MR m = a – 4 bQ ► The solution at this stage is given by the condition MR m = MC m ● this gives a – 4 bQ m = MC m ● we get the optimum (profit maximization) for the manufacturer: distributor (monopolist) final market physical good Q payment P m per unitpayment P d per unit marginal cost of producing one unit is MC m demand on the final market is given by P = a – bQ manufacturer (monopolist) production

21. microeconomic s the analytics of constrained optimal decisions lecture 4 the monopoly model (I): standard pricing and consolidation  2016 Kellogg School of Management lecture 4 page |20 consolidation ► We use the results for the manufacturer to determine now the price that the distributor will set for the final market. For this remember that ● the demand for the good is P = a – bQ ● the good is produced in quantity Q m determined previously ● we get the optimum (profit maximization) for the distributor: manufacturer (monopolist) distributor (monopolist) final market physical good Q payment P m per unitpayment P d per unit marginal cost of producing one unit is MC m demand on the final market is given by P = a – bQ final market

22. microeconomic s the analytics of constrained optimal decisions lecture 4 the monopoly model (I): standard pricing and consolidation  2016 Kellogg School of Management lecture 4 page |21 consolidation manufacturer (monopolist) distributor (monopolist) final market ► Profit for manufacturer : ► Profit for distributor : ► Total profit for supply chain : supply chain profit

23. microeconomic s the analytics of constrained optimal decisions lecture 4 the monopoly model (I): standard pricing and consolidation  2016 Kellogg School of Management lecture 4 page |22 consolidation consumer’s “margin” distributor’s “margin” P d – P m manufacturer’s “margin” P m – MC m ► It is fairly straightforward to calculate the surpluses for consumers, distributor and manufacturer: consumers surplus distributor’s surplus manufacturer’s surplus double marginalization surplus analysis

24. microeconomic s the analytics of constrained optimal decisions lecture 4 the monopoly model (I): standard pricing and consolidation  2016 Kellogg School of Management lecture 4 page |23 consolidation ► Let’s consider a VERTICAL INTEGRATION of the supply –chain model: ● manufacturer unit produces the good at a constant marginal cost MC m ● the distributor unit sells the good at a price P d to the final market ● demand on the final market is given by P = a – bQ ► This is a standard monopolist model with solution ► The total profit to the firm (manufacturer plus distributor) is manufacturer (monopolist) distributor (monopolist) final market physical good Q payment P d per unit marginal cost of producing one unit is MC m demand on the final market is given by P = a – bQ vertical integration

25. microeconomic s the analytics of constrained optimal decisions lecture 4 the monopoly model (I): standard pricing and consolidation  2016 Kellogg School of Management lecture 4 page |24 consolidation SUPPLY CHAIN VERTICAL INTEGRATION ► Clearly the consumers are better off under vertical integration. ● for supply chain ● for vertical integration total profit higher under vertical integration ► Total profit