If 2 all the three rms discover simultaneously each

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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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