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1 Predatory Conduct

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2 Predatory conduct is the implementation of a strategy designed specifically to deter rival firms from competing in a market. To be predatory, it must be the case that the firm’s action is profitable only if it causes a rival firm to exit, or deters a potential rival from entering.

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3 John McGee in 1958 said that predatory pricing only makes sense when 1. the increase in post-predatory profit is sufficient to compensate the predator for the loss incurred during the predatory pricing phase, 2. there is no other strategy that achieves the same result with more profit. Here we show an example, and we try to spell out the details more. First I show the Cournot duopoly case just for practice. The context of our work here is really the Stackelberg model.

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4 Say the demand in the market as expressed by consumers is P = 5 - Q and here let’s say the TC = 1Q for each seller so that MC = 1. The Cournot Duopoly Here the two sellers think about making a quantity based on what the other will do. Let’s make this more concrete by thinking about how firm 1 views things. Firm 1 sees the demand as P = 5 - q2 - q1, where I split Q up into q1 and q2 (the amount firm 1 and firm 2 will make, respectively) and list q2 first because firm 1 sees q2 much like the number 5, out of its control. Similarly, firm 2 sees the demand as P = 5 - q1 - q2.

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5 Now, firms sell the output where MR = MC, so we have for firm 1for firm 2 P = 5 - q2 - q1P = 5 - q1 - q2 and therefore MR = 5 - q2 - 2q1MR = 5 - q1 - 2q2, and MR = MC means 5 - q2 - 2q1 = 15 - q1 - 2q2 = 1 for each, so q1 = (4 - q2)/2q2 = (4 - q1)/2. q1 and q2 are called the best response functions for firm 1 and firm 2, respectively. They indicate what each will sell, given the amount of the other. Imagine a table with many rows and columns, where each row is a different output amount of firm 1 and each column is a different output amount for firm 2.

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6 The table I have you envision is a game between the two players. You have only seen two rows and two columns. But in the context of the current problem there are many rows and many columns. We could proceed as before to find any dominant strategies and see if we have a Nash equilibrium. Without proof, I tell you a Nash equilibrium exists and we can find it by setting firm 2 reaction function into firm ones and solve for q1. Then we take the result and put it back into firm 2’s reaction to find q2. When we have q1 and q2 we plug them both back into the demand curve to find the price. Let’s do this next.

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7 We had q1 = (4 - q2)/2q2 = (4 - q1)/2 = 2 -.5q1 make this substitution q1 = (4 - 2 +.5q1)/2 or multiplying both sides by 2 2q1 = 2 +.5q1 or 1.5q1 = 2 or q1 = 4/3. Now put this back into q2 to get q2 = 2 -.5(4/3) = 4/3. The price is then P = 5 - (4/3 + 4/3) = 7/3 and the profit of each is 7/3(4/3) - 1(4/3) = 8

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8 Now we turn to the main part of this section. We have the same demand and costs as before. Firm 1 is the leader and firm 2 is the follower. Initially we have firm 1 take the reaction of firm 2 (as in the Cournot case) into the demand curve directly, like so P = 5 - Q = 5 - q1 - (2 -.5q1) = 3 -.5q1 and so MR for the leader is MR = 3 - q1 and with MR = MC we see 3 - q1 = 1 or q1 = 2. Firm 2 then takes this into the reaction function to set q2 = (4 - 2)/2 = 1. The P = 5 - (2 + 1) = 2. Firm 1 profit = 2(2) - 1(2) = 2. Firm 2 profit = 2(1) - 1(1) = 1.

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9 So here we see the leader has a larger profit than the follower. But maybe the leader will want to have more profit. The leader may try to drive out the follower. Let’s look back at the follower’s reaction function again: q2 = (4 - q1)/2. If the leader sets q1 = 4 the follower will make q2 = 0. P = 5 - 4 = 1 and the profit for the leader will be 1(4) - 1(4) = 0 So the leader will take zero profit to drive the follower out. Then in the future the leader will be a monopoly and because P = 5 - Q means MR = 5 -2Q = 1 = MC and Q = 2. So P = 3 and Q = 2 for the leader and Profit = 3(2) - 1(2) = 4.

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10 Summary of predation so far: no predation leader profit = 2 follower profit = 1. These profits would occur every period. predation leader profit = 0 in period 1 and 4 in period 2 follower profit = 0 in each period. The leader has to ask if it is better to be a predator and we evaluate the answer by the taking the option with the highest present value of profit.

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11 Remember P = F[1/(1 + r)] = FR, where r is the interest rate, F is the future value and P is the present value. Note R < 1 Leader present value of profit - no predation = 2 +2R present value of profit with predation = 0 + 4R Now 2 + 2R > 4R so no predation is better for the leader. How do you know 2 + 2R > 4R? Assume it isn’t and look for an untruth - is untruth a word? 2 + 2R < 4R would mean 2 < 2R would mean 1 R, so we have what we said.

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12 So, in this example we see predation by the leader is not the most profitable solution, so why would the leader do it? Is another solution even better for the leader? Say the leader could bribe the follower to not produce in any period. The leader would be a monopoly in both periods and the present value of profits would be 4 + 4R. Now, it has to pay off the follower. If the follower produced it would have profit 1 + 1R. So if leader paid off the follower the leader would have 3 + 3R. This is even better than no predation. Instead of a bribe, maybe it just buys the firm for 1 + 1R. So, predation is not better for the leader because the future profit does not make up for the lost profit the first period. Plus there is a better way to be a monopoly than predation.

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13 Predatory Conduct Here is just a different example of what we just did.

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14 Predatory conduct is the implementation of a strategy designed specifically to deter rival firms from competing in a market. To be predatory, it must be the case that the firm’s action is profitable only if it causes a rival firm to exit, or deters a potential rival from entering. Here we will work through a simple Stackelberg leader/follower model. We will see if it would make sense for the leader to try to get rid of the follower firm. In the example we assume demand is P = 1 - Q and the MC = 0 for both firms. First, let’s do the leader/follower solution.

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15 The follower firm’s best response function is found from MR = MC. MR is found from the demand: demand P = 1 - q 1 - q 2, MR = 1 - q 1 - 2q 2 = 0 = MC, q 2 =.5 -.5q 1. The leader will take this amount and plug it into its view of the demand curve to get its MR and then will make the amount where MR = MC = 0 here: P = 1 - q 2 - q 1 = 1 -.5 +.5q 1 - q 1. =.5 -.5q 1. So MR =.5 - q 1 = 0 = MC means q 1 =.5 and then q 2 =.25. Putting these both back into the demand curve shows price =.25 Profits for each are: leader.25(.5) =.125, follower.25(.25) =.0625

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16 Digress: Present value F = P(1 + r), or the future value of P dollars today is the P dollars times the amount of 1 plus the interest rate. This formula can also be used to tell us P = [1/(1 + r)]F = RF, where R = [1/(1 + r)]. In other words, the formula assists us in finding the present value of a future sum of money. R is often called the discount factor. If we use these ideas in the Stackelberg model, assume the model works for 2 periods, and discount the second period profits back one period to the first period we would find the present value of profits for each to be: leader:.125 + R(.125), follower:.0625 + R(.0625)

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17 Say the leader acts as a predator and tries to drive the follower out in the first period and then will act as a monopolist in the second period. Let’s see how this might be done. Remember the followers best response function is q 2 =.5 -.5q 1, so if the leader makes 1 unit the follower will make 0 units, or exit the market. The price in the first period from the demand curve is zero when the output level is 1. The leader would have a profit of zero in the first period. In the second period the leader will be a monopolist. The monopoly solution is found on the next screen.

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18 Demand for the monopoly is P = 1 - q, so MR = 1 - 2q, and MR = MC means 1 - 2q = 0, or q =.5, then back in the demand curve we see P =.5. Monopoly profit in a period is then.5(.5) =.25. Under this predation strategy we find the present value of profits for each to be: leader: 0 + R(.25), follower: 0 + R(0) = 0

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19 Summary so far in terms of profit: leader/follower model leader:.125 + R(.125), follower:.0625 + R(.0625) Predation model leader: 0 + R(.25), follower: 0 + R(0) = 0. For the leader predation only makes sense if.25R >.125 +.125R, but this means.25R -.125R >.125, or.125R >.125, or R > 1. But, clearly R < 1, so predation is not a better strategy here for the leader. The typical argument against predators is that they drive out firms and then the future profits make up for the lost profit while predation was occurring.

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20 So, although predation leaves the follower with nothing, it is not the best strategy for the leader. Say the leader pays off the follower to not produce in either period. Then the leader gets monopoly profit in both periods, minus the payoff in the first. Let’s say the payoff is the present value of profits the follower would have under the Stackelberg situation, so the follower is the same whether it operates or not. The present value of profits for the leader is then.25 -.0625 -.0625R +.25R =.1875 +.1875R. So the leader making some sort of payoff, a merger payment perhaps, is clearly better for the predator leader.

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