Ex. 1 Value of Information A venture capital (VC) is deciding whether to invest firm 1....

 

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Ex. 1 Value of Information A venture capital (VC) is deciding whether to invest firm 1. The investment cost is 1 and upon investment, the VC gets 2 if the firm has a success and 0 if the firm has a failure. If the VC does not invest, the payoff is 0. The probability of success depends on the state s € {G, B) and the ability of manager 1,0₁ € {H, L}. The probability of success is given by: 0 H L $8 G 1 B 1/2 1/2 0 The above matrix implies that if both the state is G and the ability is H, the firm will succeed with probability 1; if either the state is G or the ability is H, the firm will succeed with probability 1/2; if neither the state is G nor the ability is H, the firm will succeed with probability 0. Suppose the VC can acquire an information about whether another firm, firm 2, has a success. The probability of success in firm 2 depends on s and the ability of manager 2, 0₂ € {H, L}. The probability is also given by the above matrix. The random variables s, 01, 02 are independently distributed with probabilities Pr(s = G) = 1/2, Pr(0₁ = H) = x and Pr(02 = H) = y. As a consultant to the VC, you are asked to calculate the value of information from observing the performance of firm 2. 1. Calculate the value of information when x=y= 1/2. 2. Keep x = 1/2. How does the value of information change with y? Explain your result. 1 3. Keep y = 1/2. How does the value of information change with a? Explain your result. 1 Ex. 1 Value of Information A venture capital (VC) is deciding whether to invest firm 1. The investment cost is 1 and upon investment, the VC gets 2 if the firm has a success and 0 if the firm has a failure. If the VC does not invest, the payoff is 0. The probability of success depends on the state s € {G, B) and the ability of manager 1,0₁ € {H, L}. The probability of success is given by: 0 H L $8 G 1 B 1/2 1/2 0 The above matrix implies that if both the state is G and the ability is H, the firm will succeed with probability 1; if either the state is G or the ability is H, the firm will succeed with probability 1/2; if neither the state is G nor the ability is H, the firm will succeed with probability 0. Suppose the VC can acquire an information about whether another firm, firm 2, has a success. The probability of success in firm 2 depends on s and the ability of manager 2, 0₂ € {H, L}. The probability is also given by the above matrix. The random variables s, 01, 02 are independently distributed with probabilities Pr(s = G) = 1/2, Pr(0₁ = H) = x and Pr(02 = H) = y. As a consultant to the VC, you are asked to calculate the value of information from observing the performance of firm 2. 1. Calculate the value of information when x=y= 1/2. 2. Keep x = 1/2. How does the value of information change with y? Explain your result. 1 3. Keep y = 1/2. How does the value of information change with a? Explain your result. 1

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Given L 1 O s 0 0 independent variables PS G 1 Pr 1A H X ... View the full answer