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Research and Development
Part 2: Competition and R&D
R&D as a Race If firms can patent a new process or
product, R&D can be seen as a “winner-take-all” race. Coming in first is all that matters, not
how much you win by. What are the consequences of such races
in terms of the level of R&D and thus innovation?
How does market structure affect the race?
Patent Race Model Assume there are two firms that are
potential entrants in a race to develop the cure for cancer.
The R&D effort will require the firm to set up a special research unit at a cost of K which is non-recoverable.
The probability of discovering a cure within a year if the research unit is established is .
Patent Race Model, con’t
If both firms discover the cure this year, assume that they will split the market as Cournot competitors and each get C.
If only one firm discovers the cure, it will get monopoly profits of M.
Patent Race Model, con’t
If only one firm innovates, that firm’s expected profit is M - K.
If both firms innovate, each firm’s expected profit is: (1- ) M + 2 C + (1-)0 - K.
If a firm does not innovate, its profit is 0.
No R&D R&D
No R&D 0
0
0
M - K
R&D M - K
0
(1-)M+2C-K
(1-)M+2C-K
The Patent Race as a Game
So what is the NE of this game?
No R&D R&D
No R&D 0
0
0
M - K
R&D M - K
0
(1-)M+2C-K
(1-)M+2C-K
For No R&D for either firm to be a NE:
M - K < 0 or (rewritten) < K/ M, which means that the probability of discovering the cure is relatively unlikely.
No R&D R&D
No R&D 0
0
0
M - K
R&D M - K
0
(1-)M+2C-K
(1-)M+2C-K
For R&D for one firm but not the other firm to be a NE:
M - K > 0 or (rewritten) > K/ M and
(1-)M+2C-K < 0.
No R&D R&D
No R&D 0
0
0
M - K
R&D M - K
0
(1-)M+2C-K
(1-)M+2C-K
For R&D for both firms to be a NE:
(1-)M+2C-K > 0.
We can graph the relationship between and K/M to show how these variable affect the amount of R&D.
K/M
K/M =
No R&D
(1-)M+2C = K
One Firm Does R&D
Two Firms Do R&D
Optimality of R&D Investment
There will be no R&D in this model if <K/M.
If >K/(M + consumer surplus), then R&D by one firm would be socially optimal, so there is too little R&D investment.
Optimality of R&D Investment, con’t
Both firms will undertake R&D if (1-)M+2C-K > 0.
But this may be too much R&D This occurs when the joint profit
from both firms investing is less than that if only one invests:
2[(1-)M+2C-K] < M-K or (rewritten) (1-2)M+22C < K.
K/M
K/M =
No R&D
(1-)M+2C = K
One Firm Does R&D
Two Firms Do R&D
Too much investment
Too little investment
Optimal investment
Optimal investment
K/(M+CS) =
(1-2)M+22C = K
Risk and Patent Races
Patent races can encourage firms to undertake “risky” strategies.
Assume firms have two R&D options: “Safe” option: Invest $100 million in
“durable” equipment. Probability of discovery is 33% each year.
“Risky” option: Invest $100 million in “perishable” equipment. Probability of discovery is 75% this year, 0% in the future.
Risk and Patent Races, con’t
Assume that everything else is the same for the two scenarios: benefit from innovation (B), costs of production, etc.
Further, for computational simplicity assume that this discount rate is 0.9 (which corresponds with an interest rate of 10%).
Then we can compare the expected value of the two options.
Risk and Patent Races, con’t
If only one firm invests in R&D: Expected Value of the “safe” strategy is:
1/3B+ 2/3*1/3*0.9B+ (2/3)2*1/3*0.92B+…=B*1/3[1/(1-2/3*0.9)] = B*5/6
Expected Value of the “risky” strategy is:3/4B+ 0 = B*3/4
So the “safe” strategy is better if only one firm invests.
Risk and Patent Races, con’t
If both firms invest in R&D, the firm must win the race to get the benefit: Both firms using the “safe” strategy has the
highest value of actually getting the innovation and is socially optimal.
Each period, 1/3*1/3 chance both discover, 1/3*2/3 chance firm 1 discovers not firm 2, 1/3*2/3 chance firm 2 discovers not firm 1, 2/3*2/3 chance no one discovers.5/9*B1+ 4/9*5/9*0.9B+ (4/9)2*5/9*0.92B+…
=B*5/9[1/(1-4/9*0.9)] = B*25/27
Risk and Patent Races, con’t
If both use safe strategy there is a 50% chance that firm 1 innovates first and a 50% chance firm 2 innovates first.
If firm 2 uses safe strategy, firm 1 can improve chance by using risky strategy: 3/4*2/3 firm 1 discovers not firm 2, 3/4*1/3
both discover. Assume tie breaker is both discover:
3/4*2/3 +3/4*1/3*1/2 = 5/8>1/2 So the risky strategy is dominant.
Monopoly and Sleeping Patents
A sleeping patent is a patent on a product or process that is not being used.
Why would firms keep sleeping patents? Keep others from inventing around a patent. Keep others from adopting the technology.
Can be profitable to patent technology so potential entrants cannot use it even if you have a superior technology.
Potential entrants will have to invest in R&D to discover their own technology.
Patent Licensing Allows others to use a patented process or
sell a patented product for a fee. Similar to trademark and copyright licensing.
Moves society away from a monopoly, so positive in terms of social welfare.
When will a firm license its technology? Increases profits through the payment of
royalties. Decreases profits through increased
competition (“cannibalization” of demand).
Patent Licensing, con‘t Ideal situation is to license in markets in
which you don’t currently compete (perhaps geographically separate markets). Potential drawback: gives other firms more
experience with process/product which many help them develop their own innovations.
In a Bertrand market licensing is generally not profitable. Increase profits from royalties is less than the
decreased profit from competition.
Patent Licensing, con‘t Example: 2 firms, Firm A has MC=$15, Firm B
has patented technology with MC=$12. Without licensing:
Firm B prices at $14.99 and sells to whole market. Profit = $2.99 per unit.
With licensing: The maximum royalty Firm B can charge Firm A
is $2.99. At this royalty level, both firms price at $14.99 and split the market. Firm b continues to make Profit = $2.99 on each unit sold. No improvement in profit.
Patent Licensing, con‘t
In a Cournot market, licensing can be profitable, however.
Assume P = 100 - Q. As before Firm A has MC=$15, Firm B has patented technology with MC=$12.
In a Cournot market with different MCs: q1 = (a + c1 - 2c2)/3b; 1 = (a + c1 -
2c2)2/9b
Patent Licensing, con‘t Without licensing:
qB = (100 + 15 - 24)/3 = 91/3
B = (100 + 15 - 24)2/9 = 8281/9 920. With licensing:
B licenses to A for $3 and decreases quantity produced to 85/3. At this quantity, A’s best response is also 85/3. Market price will be $43.33.
On each unit B produces, B earns $31.33. On each unit A produces, B earns $3.
B = $31.33*85/3+ $3*85/3 973.
R&D and Spillovers
R&D spillovers: My R&D directly benefits me and indirectly benefits you, i.e. there is a positive externality.
How do the existence of spillovers affect the incentives for R&D?
What are the impact of spillovers on the economy?
Should we encourage joint R&D?
R&D and Spillovers, con’t
Let X be the R&D level of a firm. Assume that c1 = c - X1 - X2.
If = 1, “perfect spillovers” i.e. there is no way to patent any new innovations.
If = 0, no spillovers. Assume that research exhibits
diseconomies of scale, i.e. diminishing returns to R&D spending. For example, let the cost of R&D = X2/2.
R&D and Spillovers, con’t
For simplicity, assume that the market is a Cournot duopoly with demand P = a-bQ.
If firms do not cooperate on R&D: q1 = (a-2c1 + c2 )/3b
1 = (a-2c1 + c2 )2/9b - X1
2/2
Since c1 = c - X1 - X2: q1 = (a-c + X1(2-) + X2(2-1))/3b
1 = (a-c + X1(2-) + X2(2-1))2/9b - X12/2
q1 and 1 are increasing in X1, and increasing in X2 if > 0.5.
R&D and Spillovers, con’t
The other firm’s R&D benefits you by decreasing your costs, however, since it decreases the other firm’s costs by a larger amount it also increases competition.
When is low, the spillover is small. An increase in X by one firm causes the
other firm to decrease X. When is high, the spillover is large.
An increase in X by one firm causes the other firm to increase X.
When is low, R&D levels are strategic substitutes. An increase in the other firms’ R&D makes their costs decrease significantly compared to yours, increasing competition and decreasing your profits, so you cut back on your own R&D.
BR1
X2
X1
BR2
When is high, R&D levels are strategic complements. An increase in the other firms’ R&D makes their costs decrease but not that much more than yours, so overall your profits also increase, so you can increase your R&D level.
BR1X2
X1
BR2
R&D and Spillovers, con’t
If firms cooperate on R&D to maximize joint profits, but continue to compete in the output market: If is low, joint R&D will be low. If is high, joint R&D will be high, since
there is a higher benefit relative to cost.
