ECON 330 Lecture 25 Monday, December 23

R&D races and the evolution of market structure Last week’s lecture….

The R&D race: winner takes all! There are two firms … one incumbent and one potential entrant. A (cost reducing) innovation is already discovered and patented by an R&D lab. The innovation will be sold to the highest bidder.

The greatest story ever told … The Entrant enters only if she can acquire the new technology. In which case … the market becomes a duopoly, Each firm earns πD. If … the Incumbent acquires the the new technology: He remains a monopoly, and earns πM, and the Entrant earns 0.

Who has a stronger incentive to innovate? Which firm bids more?

The rule is… The maximum a firm will bid (pay) for an innovation is … the difference in its profit between getting and not getting the innovation. profit with the innovation profit without the innovation

Variation II: gradual vs. drastic innovation Drastic innovation: If the Entrant acquires the patent and enters, the Incumbent’s profit will be 0, the Entrant will earn monopoly profit.

Who wins the race for the drastic innovation? The monopoly acquires the patent: profits: πM If it doesn’t bid: profits: ρπM + (1–ρ)0. The monopolist is not sure about the threat of entry: He thinks that with some probability ρ there is no threat. The monopoly’s maximum bid πM – ρπM = (1–ρ)πM

The entrant acquires the patent: profits: πM Without the patent there is no entry so profits are 0. Entrant’s maximum bid πM

Who wins? The entrant wins if πM > (1–ρ)πM. If there is some uncertainty about the threat of entry, the monopolist is willing to pay less for a drastic innovation than the new firm.

Let’s see how this works out as an exam question

Question #5, final exam, Fall 2012 (last year) The inverse demand is P = 21 – Q. There is one incumbent firm with TC(q) = 5q. There is also a potential entrant. The new technology lowers costs to TC(q) = 3q. The entrant will enter, only if she acquires the new technology, in which case the two firms will compete in the style of Bertrand. a. Which firm will acquire the new technology? b. If the incumbent assumes that with probability 0.5 the entrant is NOT interested in entry at all, then which firm will acquire the new technology?

Solutions, Part A Incumbent wins: Incumbent becomes a monopoly with TC(q) = 3q. Monopoly P = 12, Q = 9. Incumbent’s profit is 81 Entrant wins: Sets P = 5 – 0.001 profit ≈ (5 - 3)x16 = 32. Incumbent’s maximum bid is 81, Entrant’s max bid is 32. Incumbent wins and remains a lower cost monopoly.

Solutions, Part B Incumbent wins: same as PART A, Incumbent’s profit is 81. Incumbent doesn’t bid. With probability 0.5 Incumbent remains a monopoly with cost c = 5, (P = 13, Q = 8, profit = 64) With probability 0.5 the entrant wins and enters. In that case the incumbent gets 0. Incumbent’s expected profit is 0.5x64 = 32. Entrant wins: Sets P = 5 – 0.001 profit ≈ (5 - 3)x16 = 32. Incumbent’s maximum bid is 81 – 32 = 49, Entrant’s max bid is 32. Incumbent wins again

Summary

Summary Incumbent firms have a greater incentive than the entrants to perform R&D for a gradual innovation. If there is uncertainty about the threat of entry or if the innovation is sufficiently drastic, then the outsiders may have a greater incentive to perform R&D than the incumbents.

Now a slightly different story

Multiple rounds of innovation - Bertrand competition Initially … At the pre-innovation stage both firms have TC(q) = cHxq MC = cH

Initially MC – cH. There are two rounds of innovation firms bid for the exclusive rights to a technology that lowers the cost to co. The winner of round 1 will have MC = co, while the other firm will have MC = cH. _______________________________________________ Round 2 … firms bid for the exclusive rights to a technology that lowers the cost to cL. The winner of round 2 will have MC = cL. cH > co > cL

The R&D race in round 1 The high-cost firm (loser of R&D race) can’t price below cH. The low-cost firm (winner of R&D race) will set P = cH – 0.001, and sell Q units. Profit = (cH –co )xQ; the blue area. cH co

Both firms have an equal chance of winning the R&D race in round 1 Pre-innovation profit is 0 for both firms. Post-innovation profit for the winner: (cH–co)Q Both firms can win. Say firm A wins in round 1.

R&D race in round 2 cH > co > cL The winner of round 2 will have the lowest cost cL. The winner will set P = the other firm’s cost – 0.01.

If A wins (again) in round 2 … cH > co > cL Firm A had been successful in round 1. Firm B fell behind: now has cH. A has cL B has cH Price is P = cH – 0.001 A’s profits ≈ (cH –cL)xq(cH). Blue + Green cH co cL

If B wins round 2 … B has cL A has co Price is P = co – 0.001 cH > co > cL Firm A had been successful in round 1: has co. Firm B fell behind: mc = cH B has cL A has co Price is P = co – 0.001 B’s profits ≈ (co –cL)xq(co). Green + Pink cH co cL

Summary: Early success in R&D gives a permanent advantage cH > co > cL The winner of round 2 will have the lowest cost cL. The winner will set P = the other firm’s cost – 0.01. If A wins again in round 2, Profit = Blue + green if B wins in round 2, Profit = pink + green cH co cL

SUMMARY Multiple innovations with Bertrand competition The round 1 winner has a greater incentive to win in round 2. This leads to “persistence”. If a firm gains an early cost advantage it will maintain the advantage at later stages. cH co cL

Now it is your turn Things can be very different when firms compete in the style of Cournot

Cournot competition: Leapfrogging or Persistence? Inverse demand: p = 20 – Q cH = 3, co = 2, cL = 1. Profits in the Nash equilibrium (Cournot competition) Firm A has MC = cA, Firm B has MC = cB πA = (20–2cA+cB)2/9 πB = (20–2cB+cA)2/9

Suppose A has won the R&D race in round 1 Suppose A has won the R&D race in round 1. Which firm will win the R&D race in round 2? Is there persistence under Cournot competition? Please explain. cA 3 2 1 cB profit A 32 40 49 profit B 28 25 44

End of the lecture