## Recoupmment

As we’ve discussed, a firm would only price below cost if they expected to recoup their losses in the future

• Traditional theory of predatory pricing envisions two stages in carrying out the predation strategy:
1. The Predation Stage The predator prices its product below some measure of economic cost with the intent of driving its prey from the market

2. The Recoupment Stage The predator leverages the absence of competition to price its product at above-competitive levels, thereby recovering the losses incurred during the predation stage and earning monopoly profits thereafter

From the firm’s perspective, the predation can be viewed as an investment whose Net Present Value (NPV) can be calculated

• $$L_t$$ : the losses incurred per period from selling below cost during the predation stage
• $$\pi_t$$ : monopoly profit earned per period during the recoupment stage
• $$r$$ : the discount rate
• $$\tau$$ : the number of periods where the firm experiences losses
• $$T$$ : number of periods the firm is in the market

$NPV=-\sum_{t=1}^{\tau} \frac{L_t}{(1+r)^t} + \sum_{\tau+1}^{T} \frac{\pi_t}{(1+r)^t}$

If NPV is positive, the firm will find it profitable to engage in predatory pricing.

### Example

Suppose a firm is considering engaging in predatory pricing and knows the following information:

• $$r$$ = 0.05
• 2 periods of losses of $20,000 per period • 8 periods of gains of$10,000 per period

Will the firm engage in predatory pricing?

First step in solving any of these problems is to extract the relevant information.

This tells us:

• $$r = 0.05$$
• $$L_t=20,000$$
• $$T=10$$
• $$\pi_t=10,000$$
• $$\tau=2$$

\begin{aligned} NPV &= -\sum_{t=1}^{\tau} \frac{L_t}{(1+r)^t} + \sum_{\tau+1}^{T} \frac{\pi_t}{(1+r)^t} \\ &= -\sum_{t=1}^{2} \frac{20000}{(1+0.05)^t} + \sum_{t=2+1}^{10} \frac{10000}{(1+0.05)^t} \\ &= -\left( \frac{20000}{(1+0.05)^1}+\frac{20000}{(1+0.05)^2} \right) + \left( \frac{10000}{(1+0.05)^3} + \frac{10000}{(1+0.05)^4} + \cdot + \frac{10000}{(1+0.05)^{10}} \right) &= \21,435.04 > 0 \end{aligned}

• Positive NPV → the firm will participate in predatory pricing because they gain positive profit in the long run by predatory pricing in the short run