For this question, ignore time value of money and discounting.

You and your competitor are simultaneously developing a product and hoping that it will be the industry standard. It is possible that your product may be accepted, partially accepted or not accepted by the industry with 40%,40%, and 20% chance respectively. You will get a chance to invest 14 units after you know your acceptance status. Only after you invest, you will know the competitors acceptance probabilities.

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The rivals acceptance probabilities depend on your status and they are given as follows:

Given your standard is accepted, your rivals standard will be also accepted or partially accepted or not accepted with probabilities 60%, 25%,and 15% respectively.

Given your standard is partially accepted, your rivals standard will be also accepted or partially accepted or not accepted with probabilities 35%, 40%,and 25% respectively.

Given your standard is not accepted, your rivals standard will be also accepted or partially accepted or not accepted with probabilities p%, q%,and (1-p-q)% respectively.

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You will make money only when your product is accepted or partially accepted.

If your standard is accepted, you will make 25, 40, or 50 units if the rivals standard is accepted, partially accepted or not accepted respectively.

If your standard is partially accepted, you will make 8, 20, or 40 units if the rivals standard is accepted, partially accepted or not accepted respectively.

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a) What is your expected gain at the initial node?

b) If the investment decision were to be done before knowing whether your product (or your competitors product) is accepted, partially accepted, or not accepted, with what probability would you lose all the money you invested?

c) Consider the situation in part (b). How much would you pay for a test that would reveal whether your product is accepted, partially accepted or not accepted?