EconS Pricing and Advertising - Part 2

Transcription

1 EconS Pricing and Advertising - Part 2 Eric Dunaway Washington State University eric.dunaway@wsu.edu November 2, 2015 Eric Dunaway (WSU) EconS Lecture 27 November 2, / 47

2 Introduction Today, we will nish up our unit on price discrimination and advertising. There is one more type of price discrimination to cover: second-degree price discrimination. Eric Dunaway (WSU) EconS Lecture 27 November 2, / 47

3 Second Degree Price Discrimination Second-degree price discrimination is probably the most di cult of the three to understand. Rather than guring out how their consumers are di erent, in second-degree price discrimination the monopolist creates a menu of di erent options designed for di erent types of people and then lets the consumers self-select into their best bundle. Most of the math involved is too complicated for this course. We will be focusing on intuition. In essence, it can be broken down into four di erent types. Quantity Discounting Block pricing Two-part tari s Bundling Eric Dunaway (WSU) EconS Lecture 27 November 2, / 47

4 Quantity Discounting With quantity discounting, a monopolist gives a discount with every additional unit purchased. We see this all the time at the grocery store. A two liter bottle of soda typically costs much less per ounce than a twenty ounce bottle of the same soda. Eric Dunaway (WSU) EconS Lecture 27 November 2, / 47

5 Quantity Discounting To implement this, the monopolist uses a pricing schedule. The monopolist creates a menu of quantities and their respective prices. The consumers then can observe the menu of quantities and prices, then self-select into whichever bundle gives them the highest utility, subject to their own budget constraints. The non-linear aspect of this type of price discrimination comes from the fact the expenditure function (the amount the consumer pays) is now curved as we increase price, as opposed to straight (as it was before). Eric Dunaway (WSU) EconS Lecture 27 November 2, / 47

6 Quantity Discounting pq Total Expenditure q Eric Dunaway (WSU) EconS Lecture 27 November 2, / 47

7 Quantity Discounting pq Total Expenditure q Eric Dunaway (WSU) EconS Lecture 27 November 2, / 47

8 Quantity Discounting Under quantity discounting, the consumer will eventually pay less at a higher quantity than they will under traditional linear pricing. At the same time, the monopolist can take advantage of the consumer and raise prices for small quantities to encourage their customers to buy more of the good. This type of pricing is very similar to our next type of second degree price discrimination: block pricing. Eric Dunaway (WSU) EconS Lecture 27 November 2, / 47

9 Block Pricing With block pricing, a monopolist charges an initial price for the rst few units of a good, then a lower price for the next few units, then an even lower price for the next few and so on. Avista uses this kind on pricing for electricity, and the US Income tax system works similarly (although it is not a form of price discrimination). Basically, if we looked at the producer and consumer surpluses, the monopolist prices such that it takes blocks out of the consumer surplus. This could actually be welfare improving. Eric Dunaway (WSU) EconS Lecture 27 November 2, / 47

10 Block Pricing Here s an example. Consider a monopolist facing a linear inverse demand curve of p = 45 q and constant marginal costs of MC = 5. Our marginal revenue will be MR = 45 2q Eric Dunaway (WSU) EconS Lecture 27 November 2, / 47

11 Block Pricing Setting up our optimal marginal revenue equals marginal cost equation MR = MC 45 2q = 5 and from the inverse demand curve Putting it all together, 2q = 40 q = 20 p = = 25 TR = p q = 20(25) = 500 TC = 5q = 5(20) = 100 π = TR TC = 400 Eric Dunaway (WSU) EconS Lecture 27 November 2, / 47

12 Block Pricing 45 p D MR S 45 q Eric Dunaway (WSU) EconS Lecture 27 November 2, / 47

13 Block Pricing 45 p D 25 CS PS 20 DWL MR S 45 q Eric Dunaway (WSU) EconS Lecture 27 November 2, / 47

14 Block Pricing Now, let s have the monopolist use block pricing. Arbitrarily picking quantity breakpoints, the monopolist can charge the corresponding inverse demand curve price for all units under that breakpoint. Sounds complicated. Basically, pick a breakpoint, plug it in to the inverse demand function, and charge that price up to the breakpoint. Using breakpoints of 10 units Breakpoint Price First 10 units p 1 = = 35 Second 10 units p 2 = 45 2(10) = 25 Third 10 units p 3 = 45 3(10) = 15 Eric Dunaway (WSU) EconS Lecture 27 November 2, / 47

15 Block Pricing In this case, our total revenue, total costs, and pro ts will be TR = p 1 q 1 + p 2 q 2 + p 3 q 3 = 35(10) + 25(10) + 15(10) = 750 TC = 5q 1 + 5q 2 + 5q 3 = 5(10) + 5(10) + 5(10) = 150 π = TR TC = 600 Clearly, pro ts rise signi cantly under block pricing. Let s see what happens to surplus. Eric Dunaway (WSU) EconS Lecture 27 November 2, / 47

16 Block Pricing 45 p D 25 CS PS 20 DWL MR S 45 q Eric Dunaway (WSU) EconS Lecture 27 November 2, / 47

17 Block Pricing 45 p D 35 CS PS DWL S 45 q Eric Dunaway (WSU) EconS Lecture 27 November 2, / 47

18 Block Pricing As we can see, the producer surplus clearly goes up, while the consumer surplus does go down a bit. The most impressive part is that the dead weight loss has almost completely disappeared. If the monopolist used more "blocks," it could reduce the dead weight loss even more, with an in nite amount of blocks eliminating it completely. That would actually just turn in to rst degree price discrimination, though. Let s look at the expenditure function. Eric Dunaway (WSU) EconS Lecture 27 November 2, / 47

19 Block Pricing pq Total Expenditure q Eric Dunaway (WSU) EconS Lecture 27 November 2, / 47

20 Block Pricing pq Total Expenditure q Eric Dunaway (WSU) EconS Lecture 27 November 2, / 47

21 Block Pricing This expenditure function is similar to its quantity discrimination counterpart. The only di erence is that this curve is not smooth, but rather a set of kinked lines. Eric Dunaway (WSU) EconS Lecture 27 November 2, / 47

22 Two-Part Tari Our next type of second-degree price discrimination is a two-part tari. Perlo calls this two-part pricing. Finally, the Costco example! In a two-part tari, the monopolist charges an access fee, then only charges the marginal cost per unit purchased. Essentially, the monopolist makes the consumers pay for the right to purchase the good. Eric Dunaway (WSU) EconS Lecture 27 November 2, / 47

23 Two-Part Tari Let s break that down a bit. Having the price be equal to marginal cost actually gives the monopolist zero pro ts for each unit sold. They key is the access fee. The monopolist can charge an access fee equal to the entire consumer surplus and take it all for themself. Let s see it graphically when the monopolist prices at marginal cost. Eric Dunaway (WSU) EconS Lecture 27 November 2, / 47

24 Two-Part Tari 45 p D 25 CS 5 20 S 45 q Eric Dunaway (WSU) EconS Lecture 27 November 2, / 47

25 Two-Part Tari In this situation, all of the welfare is in the form of consumer surplus. To optimize with a two-part tari, the monopolist needs to gure out what the consumer surplus is, and charge that as a fee. In our example, CS = 1 (45 5)40 = and thus, the monopolist s optimal two-part tari would be to charge an access price of 800, and then a price of 5 per unit sold. The monopolist s pro ts are equal to 800 in this case. Eric Dunaway (WSU) EconS Lecture 27 November 2, / 47

26 Two-Part Tari 45 p D 25 PS 5 20 S 45 q Eric Dunaway (WSU) EconS Lecture 27 November 2, / 47

27 Two-Part Tari Now, the entirety of welfare is in the form of producer surplus. At the same time, there is no dead weight loss. If designed well, and all consumers are identical, two-part tari s are e cient. If consumers are di erent, there are many di erent kinds of access fees that are possible. All of them will yield dead weight loss. Eric Dunaway (WSU) EconS Lecture 27 November 2, / 47

28 Two-Part Tari This is the pricing model used by both Costco and local bars. At Costco, you pay a yearly membership fee. This is where all of Costco s pro ts come from. Costco only breaks even (covering all its operation costs), but doesn t make any pro ts from the sale of its goods. At the local bar (typically on weekends), you pay a cover charge. This results in the drinks being cheaper (in theory). The bar already extracted all of your estimated surplus for the night in the cover charge. As a note, these two-part tari s are not perfect since all consumers are di erent. Eric Dunaway (WSU) EconS Lecture 27 November 2, / 47

29 Two-Part Tari pq Total Expenditure q Eric Dunaway (WSU) EconS Lecture 27 November 2, / 47

30 Two-Part Tari pq Total Expenditure q Eric Dunaway (WSU) EconS Lecture 27 November 2, / 47

31 Two-Part Tari In this case, the expenditure function jumps from zero to the higher point, and then grows very slowly. It is non-linear just because of this discontinuity. Eric Dunaway (WSU) EconS Lecture 27 November 2, / 47

32 Bundling The last case of second-degree price discrimination I wanted to cover is bundling. This can be either mandatory bundling, or nonmandatory. The monopolist groups multiple products together and sells them for less than the sum of their individual parts. Eric Dunaway (WSU) EconS Lecture 27 November 2, / 47

33 Bundling Bundling happens all the time. They even call it by name. Cable companies want to bundle cable, phone and internet. Printers come bundled with ink cartridges. I nd it interesting that it is often cheaper to buy a new printer than it is to replace the ink. Razors with replacement blades. Etc. Eric Dunaway (WSU) EconS Lecture 27 November 2, / 47

34 Bundling Mathematically, the rm will have one product that depends on another product for success. For example, printers are useless without a compatible ink cartridge. By grouping them together, rms can get higher sales of both, and don t have to worry about their competitors selling knock o s. They sacri ce pro ts on the printer itself, making it up with a higher price of ink. Eric Dunaway (WSU) EconS Lecture 27 November 2, / 47

35 Advertising Advertising is a method for a monopolist to increase the demand of its product. It can be murky though, as advertising is useless under perfect competition. A dead giveaway that a market isn t perfectly competitive is if the rms in it advertise. Furthermore, advertising amongst competitors is only e cient if its purpose is to increase knowledge of the product. Advertising to compare your product to another with the intent of poaching sales causes dead weight loss. We are not going to cover this type of advertising. Eric Dunaway (WSU) EconS Lecture 27 November 2, / 47

36 Advertising As said before, the goal of advertising is to increase the demand for the product. This would shift the demand curve to the right. When this happens, both the equilibrium price and quantity sold for the monopolist will increase, causing a gain in pro ts. Eric Dunaway (WSU) EconS Lecture 27 November 2, / 47

37 Advertising 45 p 35 D Profit 15 MR S 45 q Eric Dunaway (WSU) EconS Lecture 27 November 2, / 47

38 Advertising p 45 D Profit MR 35 S 45 q Eric Dunaway (WSU) EconS Lecture 27 November 2, / 47

39 Advertising Like in almost everything else we do, the decision of whether to advertise or not will come down to the margin. We would want to be able to determine the marginal bene t of advertising (how much extra revenue we get from an additional unit of advertising) as well as the marginal cost of advertising (how much one more unit of advertising costs). The rm will advertise at the level where marginal bene t equals marginal cost of advertising. Let s look at an example. Don t worry about the math. Eric Dunaway (WSU) EconS Lecture 27 November 2, / 47

40 Example Let s return to our earlier example where our monopolist faced a linear inverse demand curve of p = 45 q and constant marginal costs of MC q = 5. Recall that our equilibrium under the standard monopoly model is q = 20 p = 25 π = 400 Now, let s add advertising to the model. Our inverse demand function becomes p = 45 q + A 0.5 where A represents one unit of advertising (an online ad, facebook posts, etc.). The cost of each unit of advertising is constant at MC A = 2. Eric Dunaway (WSU) EconS Lecture 27 November 2, / 47

41 Example Our new total revenue function is TR = pq = (45 q + A 0.5 )q = 45q q 2 + qa 0.5 and since the monopolist needs to choose both its quantity and its advertising level, we have to get marginal revenues for both q and A MR q = 45 2q + A 0.5 MR A = 0.5qA 0.5 Next, we set the marginal revenues equal to their respective marginal costs MR q = MC q 45 2q + A 0.5 = 5 MR A = MC A 0.5qA 0.5 = 2 Eric Dunaway (WSU) EconS Lecture 27 November 2, / 47

42 Example 45 2q + A 0.5 = 5 0.5qA 0.5 = 2 This is just a system of two equations and two unknowns, which we can solve! A bit tougher than what we usually see, though. Rearranging the second equation, we get A 0.5 = 0.25q which we can substitute into the rst equation to get 45 2q q = q = 40 q = Eric Dunaway (WSU) EconS Lecture 27 November 2, / 47

43 Example Plugging this back into our second equation, A 0.5 = 0.25q = 0.25(22.86) = 5.71 A = = and we can nd our price from the inverse demand curve p = 45 q + (A ) 0.5 = = Lastly, for our pro ts, TR = p q = 27.85(22.86) = TC = 5q + 2A = 5(22.86) + 2(32.65) = π = TR TC = = Eric Dunaway (WSU) EconS Lecture 27 November 2, / 47

44 Example As we can see, the quantity, price, and pro ts all increased due to the advertising. This is because the advertising increased the demand for the product, and was a ordable. Don t expect to see an advertising problem on the exam, the math is rough. Be sure to know the e ects of advertising, though. Eric Dunaway (WSU) EconS Lecture 27 November 2, / 47

45 Summary Price discrimination helps the monopolist capture surplus away from the consumer. It also brings more consumers into the market. There are many ways to price discriminate, and perform di erently depending on the situation. Advertising is a method to increase the demand for a product. Eric Dunaway (WSU) EconS Lecture 27 November 2, / 47

46 Preview for the Next Week Review Session on Wednesday. Quick exam overview from me, then we move into an AMA session. I won t be preparing questions. Exam 2 on Friday. On Monday we start Game Theory! We are going to look at how people and rms behave strategically. Yay! I love game theory. Eric Dunaway (WSU) EconS Lecture 27 November 2, / 47

47 Assignment 5-1, 5-2, and 5-3 (1 of 1) This is an open ended question designed to make you think. A single paragraph answer should be su cient. Note: For those not from the US, Black Friday occurs on the fourth Friday of November and is the largest shopping day of the year. Google "Black Friday Sales" for more information. 1. Economically, why do Black Friday sales exist? Eric Dunaway (WSU) EconS Lecture 27 November 2, / 47