Managerial Economics: Topic 9 Commitments and their effect on short-run competition Commitments that change the game from Bertrand to … Soft commitments in Bertrand Tough commitments in Cournot The Bigger Game We viewed the process of reaching a price through bargaining as part of a bigger game Bargaining Firm 1 makes Firm 2 makes commitment commitment Bargaining Bargaining Now: view the process of reaching a price in competition as part of a bigger game Price/Quantity Competition Firm 2 makes Firm 1 makes commitment Price/Quantity Competition commitment or takes action Price/Quantity Competition Bertrand competition = price war! Extreme result: P = MC, even with only 2 competitors. Competitors are likely to try and change the game: Limit their capacity = part A Differentiate their products = part B Merge (then they’d earn monopoly profits) Collude (illegal) or tacitly collude = ethically dubious, Topic 10! A. Commitments that change the game from Bertrand to … 1. Limited stock 2. Limited capacity What if firms have limited capacity to meet demand? = a credible commitment 1. Limited stock: Shell and Mobil have pumped oil & shipped it to market. Galleria and Travelite are competing in the market for (identical) Melbourne souvenir Tee-shirts. There is limited stock in the store on any given day. 2. Limited productive capacity: Brunetti’s and the MBS coffee-shop have 1 espresso machine each there is a limit to how many coffees they can produce in an hour (as we know!) Turbine generators: they can be ordered before they’re produced, but there is a backlog--only so many in a month. Case 1. Limited stock Galleria and Travelite are competing in the market for sheepskin coats; the coats are identical, from the point of view of a tourist. The demand curve is Q=1000 – P per day Both companies face a marginal cost of $200 to produce the coats Once the coats are produced, they can be sold on the secondary market for $200 What happens today if Galleria stocks 400 coats and Travelite stocks 200 coats? (no re-stocking today) Case 1. Limited stock Price If the firms charged P=MC=$200, $1000 customers would demand 800 coats = more than stock! $700 $400 Q MC= $200 300 600 800 1000 The game with limited stock: Galleria stocks 400 coats and Travelite stocks 200 coats today. Suppose the firms are currently charging $700, and selling 150 each: is that a Nash equilibrium? No, each firm has a incentive to undercut the price and thereby sell more Price falls lower Suppose the market price falls to $400: Each firm could sell 300, if they had the stock In fact, Travelite doesn’t have the stock some of its customers go to Galleria Travelite sells 200 and Galleria sells the rest (400) Is $400 a Nash equilibrium? Or does price fall to $200? Does the price fall lower? The new game with limited stock: When the total stock is 600 = 400 + 200 The price will not fall below $400, because at $400 there is no incentive for either firm to cut its price further Cutting price at that point doesn’t increase your sales, it just lowers the price paid by customers Firms set the price to clear all the stock: P = $400 $400 is the Nash equilibrium price Q: How do they decide how much to stock? Galleria is trying to choose the amount that it will stock, while Travelite is simultaneously choosing the amount that it will stock If their total quantity is above 800, the amount they stock is the amount they will sell, at the price that clears their shelves They sell their whole stock, at the market-clearing price Does this sound familiar? It’s the Cournot game! Choose how much to supply to the market, at the same time as your competitor is choosing how much to supply. your stock = the quantity you will supply to the market This explains why you end up in Cournot competition, if you have to choose your output before getting to market: Galleria & Travelite stock the Cournot quantity. Application: in-class exercise Donnini’s and Ginevra’s both sell identical fresh pasta products on Lygon St They produce pasta early in the morning. Demand for fresh pasta is Q=80 - P per day (where quantities are measured in pounds) Marginal cost of each firm is $20 Pasta is perishable, so they cannot sell it the following day. But they can sell any leftovers to an (undiscriminating) restaurant wholesaler that night, for $10 per pound. 1) What price do they charge? 2) Suppose that this Monday, after they produced, they realise that demand is unusually low: based on the first hour, they determine demand will be Q=55 - P that day. What price do they charge? 3) What about if the unusually low demand were Q=45 - P? What is the relevant Marginal Cost? Once they’re in the market, the amount they spent to make the pasta is irrelevant = it’s a sunk cost. the $20 per pound to make the pasta does not affect market behaviour. But they will never price below $10 a pound. Why not? If they were selling for $8 a pound, they would be making an economic loss They’re worse off than if they sold to the wholesaler. $10 per pound is the relevant marginal cost. Case 2. Limited productive capacity Suppose there are only two coffee shops in Parkville, and they are next door to each other on Royal Parade: Grinders’ and Trilussa. They face a daily demand curve for coffees of Q=1000 – 250P Marginal cost of each firm (the cost of coffee, milk, and labour) is $0.80 Suppose Grinders’ has one espresso machine, which can produce 200 coffees per day Trilussa has two espresso machines, and so can produce 400 coffees per day What is the equilibrium price? Case 2. Limited productive capacity Price If the firms charged P=MC=$0.80, $4 customers would demand 800 coffees a day. $2.80 $1.60 MC= $0.80 300 600 800 1000 Q The new capacity game: Grinders’ has capacity of 200, Trilussa has capacity 400 Suppose the firms are currently charging $2.80, and selling 150 each: is that a Nash equilibrium? No, each firm has a incentive to undercut the price and thereby sell more Price falls lower Suppose the market price falls to $1.60: Each firm could sell 300, if they had the capacity In fact, Trilussa doesn’t have the capacity Trilussa sells 200 and Grinders’ sells the rest (400) Is $2.80 a Nash equilibrium? Or does price fall to $1.60? Does the price fall lower? The new capacity game: The price will not fall below $1.60, because at $1.60 there is no incentive for either firm to cut its price further They price to use up their full capacity Now suppose total capacity is more than 800 (800 is the quantity demanded when P=MC) Then it’s Bertrand equilibrium, again. The new capacity game: If total capacity is less than demand at P=MC: Firms will produce up to full capacity, and charge the market-clearing price = no incentive to under-cut each other, if they cannot sell more by doing so They want to restrict capacity Remaining question: how do they choose their capacities? Summary: What is the source of “Cournot” competition? Case 1. Quantity decisions have to be made a long time before sale Firms choose the quantity they want to produce without knowledge of others’ choices (or, equivalently, firms choose the amount they stock without knowledge of others’ choices of stock levels; all stock is sold) They will choose to produce/stock the Cournot quantity, and price so that both firms sell their whole stock. (Case 2. Production on demand but limited capacities) = closely related situation, not identical Once they see each others’ capacities, they each charge the price at which they’re producing to full capacity. NO SELF CONTROL! If firms are focused on maximising short term profits: When they get to the market, they behave as if they have no self- control. They can’t resist under-cutting each other to steal customers. = Bertrand behaviour ALL MARKETS are inherently Bertrand The only thing that stops the undercutting if is there is no way to steal any more customers: Firms keep undercutting until Capacity of both firms completely used up (otherwise the one with extra capacity would undercut, and the other would be wary) or Stock of both firms completely used up (otherwise the one with extra capacity would undercut, and the other would be wary) or The firm has hit P=MC in its process of undercutting stops. Win-win commitments Both firms are aware that once they get to the market, their behaviour will be Bertrand. Both make commitments that (taken together) restrict their ability to undercut: Limit stock Limit capacity Galleria commits before the market: brings 267 coats Higher profits in the market, even though market behaviour is Bertrand Travelite commits before the market: brings 267 coats B. More win-win commitments: Soft commitments in Bertrand No maths in this section! Product differentiation Another way firms avoid the P = MC price war of Bertrand = differentiating their products—adding different features, etc. ex: Breakfast cereal! Extremely unusual for firms to sell exactly the same product! Differentiating your product: eases competition, because some customers prefer your product to the other one, even if it’s a little more expensive creates more surplus, because now there’s more chance that a product corresponds to what a customer wants: if she doesn’t like product A, there’s always product B! How do we represent the effect of product differentiation? West Milk Bar Central Milk Bar East Milk Bar $2.00 $2.20 $2.00 Suppose your town has just one street with shops and residences. You want to buy milk, but some shops are closer to you than others. There are three milk bars, each two blocks apart. You live halfway between the Central and East Milk bars. You only care about price and distance from where you live you go to the East Milk Bar. If everyone has a disutility of walking of $0.20 per block: People that are half a block from Central Milk Bar go there; the rest go to West or East. West Milk Bar Central East Milk Bar $2.00 $2.20 $2.00 Product differentiation, graphically Imagine a one-dimensional product characteristic distributed along a line (you could have more dimensions): Example: Breakfast cereals, going from less sweet to very sweet Imagine customers distributed along the same line: a line—every point on the line is someone’s ideal product Think of yourself as “residing” at your ideal product If you’re under 10, you probably prefer sweeter cereal this isn’t differentiation in quality (like horsepower in a car): no one direction is better for everyone A product that is not your ideal gives you less utility your WTP is higher, the closer a product is to your ideal. (one way to think of it is as a “transportation cost”) “Grape-Nuts” “Just Right” “Captain Crunch” less sweet very sweet For a given set of prices, there will be an allocation of the customers across the different products: “Just Right” $4 “Captain Crunch” $4.50 less sweet very sweet If all other products have chosen their price, you know how many customers you would get for each price you choose You can work out your best response curve Interesting difference from Cournot: best response curves are upward- sloping in differentiated Bertrand. = if Captain Crunch cuts its price by $1, Just Right will probably cut its price too, but by less than $1, because it has some loyal customers (to the left), who are not swayed by the price of Captain Crunch. Nash equilibrium = the stable outcome Just Right’s price. Captn Crunch’s best response Just Right’s best response Captn Crunch’s “Best response” for each is graphed. price. The intersection is a stable point (a Nash eq.). Product differentiation, graphically Differentiating your product from your competitor’s = moving it further away on the line from your competitor Disadvantage: = you are further away from your competitor’s customers, so you’re less attractive Advantage 1: = you’re closer to more remote customers, so their WTP goes up Advantage 2: = you compete much less intensely with your competitor. The shape of the best response curves is critical for differentiation to be profitable. “Just Right” “Captain Crunch” less sweet very sweet Differentiation = a Soft commitment Capn’ Crunch’s Just Right’s price. best response Just Right’s B best response A Capn’ Crunch’s price. A “soft” commitment means that Just Right wants to price higher, for every price of Capn’ Crunch (= a weaker position, but both benefit). Tradeoff: Current profits vs. possible entry We won’t discuss entry much in this class, but it’s obvious how you keep an entrant out in this market: = don’t leave enough “space” for her! = the reason for proliferation of varieties in cereal ? “Leaving space” between you and your competitor eases competition But it might make it easier for a new competitor to enter! = that’s the tradeoff. That’s why new entrants often enter on the edges (with very weird products): sometimes incumbents don’t realise how far out demand extends… C. The Role of Tough Commitments in Cournot competition Quantity Pre-commitments In Cournot, reaction curves are downward sloping The more Shell expects Mobil competitor to produce, the less Shell wants to produce Mobil should pre-commit to producing more than it would otherwise want to (e.g. invest in mass-production equipment) Such pre-commitments cause rivals to back off and “accommodate” by producing less Numerical Example: Suppose that Mobil buys new equipment that reduces its marginal cost: MC falls from 200 to 100. Now its best response curve is QM = 450 – ½QS (check this yourself, for practice!) (before it was QM = 400 – ½QS) Best response curve shifted up! Tough quantity competition Mobil’s output 450 B 400 Mobil’s best A response 50 Shell’s output Pre-commitments The commitment moves the equilibrium from A to B: at B, Shell is producing less than at A. CAREFUL! The commitment is only worth it if the firm earns more at B (after paying for the commitment) some commitments are too strong (you commit to producing way too much) or too expensive. you have to check that the commitment is worth it. When are quantity increases credible commitments? Reputation for high quantity Large supply or purchase contracts Cost leadership: investments in lower unit production costs Irreversible capacity investments Pre-Emption Commitments change the game: now one or the other will try to commit Either firm may commit... But what happens if you can commit first? Other firm observes your action before choosing their own: You gain a first-mover advantage Case: Memory Chips Early 1980s: market dominated by US firms mid 1980s: Japanese firms (Toshiba, NEC) increased their investment in new capacity (while US firms didn’t) late 1980s: 80% of market controlled by Japanese firms 1990s: massive investments by South Korean firms (Samsung, Hyundai) while the Japanese firms have not invested These investments are preceding market demand! Stocking games versus capacity games Q = Why are capacity games “not exactly Cournot”? No long-term commitments available, in stocking games Amount of stock I bring in is a commitment “for the day”, but no more: if I brought in more stock today, that doesn’t change the game tomorrow But capacity = a one-time choice that lasts = a commitment If I’m stuck with the amount of capacity I build today (irreversible commitment), if you choose your capacity subsequently, you’ll choose a capacity that is a best response to mine. Firms will choose to make tough commitments in capacity (as in the memory chip industry) NO TRADEOFF: Current profits vs. possible entry Tough commitments are profitable against existing entrants, in Cournot (as long as you’re first, and they’re not too tough!) BUT tough commitments also keep entrants out (Why?) Interestingly, there is no tradeoff to make, in Cournot competition: tough commitments to improve current position tough commitments deter entry Only downside is that there can be a race to be the first to make a tough commitment.
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