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Unformatted text preview: vers, it is expected to earn V = $150. If two …rms discover
simultaneously, the value of the patent is shared, so each …rm earns V = $75. If
2
all the three …rms discover simultaneously, each …rm earns V = $50.
3
The …rms are privately and separately owned. Each …rm has a probability of 1
3
developing an operating system provided that it invests an amount of I = $40 in
constructing research lab. Solve the following problems. Lecture 13: Patent race, Econ483: Econ of Innovation & Technology, Evangelia Chalioti c A ll rights reserved. Intro Rivalry (i) Compute the expected pro…t of …rm 1 assuming that …rm 1 is the only
…rm to invest in a lab.
The expected pro…t of …rm 1 when only …rm 1 invests in R&D is
π 1 (1) = Lecture 13: Patent race, 1
150
3 40 = $10 > 0 Econ483: Econ of Innovation & Technology, Evangelia Chalioti c A ll rights reserved. Intro Rivalry (ii) Compute the expected pro…t of …rm 1 assuming that only …rm 1 and
…rm 2 engage in R&D.
The expected pro…t of …rm 1 when, both, …rm 1 and …rm 2 engage in
R&D is
π 1 (2) =
 1
3 1
3
{z 1
75 +
3
}
 both …rms discover Lecture 13: Patent race, 2
3
{z 150
} 40 = 5
>0
3 only …rm 1 discovers Econ483: Econ of Innovation & Technology, Evangelia Chalioti c A ll rights reserved. Intro Rivalry (iii) Compute the expected pro…t of …rm 1 assuming that all three …rms
engage in R&D.
The expected pro…t of …rm 1 when all three …rms engage in R&D is
π 1 (3) =
 1
3 Lecture 13: Patent race, 1
3 all 3 …rms discover + = 1
3
{z  1
3 2
3
{z 1
3 1
50 +
3
} 2
3 75
} …rms 1 and 2 discover 1
75 +
3
} …rms 1 and 3 discover 130
<0
27 1
3
{z Econ483: Econ of Innovation & Technology, 2
3 {z 2
3 150
} 40 only …rm 1 discovers Evangelia Chalioti c A ll rights reserved. Intro Rivalry (iv) Conclude how many …rms will invest in a lab and engage in R&D.
In equilibrium, exactly two …rms will engage in R&D. Lecture 13: Patent race, Econ483: Econ of Innovation & Technology, Evangelia Chalioti c A ll rights reserved. Intro Rivalry (v) Compute the level of social welfare...
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 Spring '08
 Staff
 Economics

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