Firms A and B are contemplating whether or not to invest in R&D. Each has two options: “Invest” and “Abstain.” A firm that invests will invent product X with a probability of 0.5, whereas a firm that abstains is incapable of invention. Investment costs $6. If a firm doesn’t invent X, it makes $0 in revenue. If a firm invests and is the only one to invent X, it becomes a monopolist and generates $20 in revenue. If both firms invent X, each firm becomes a duopolist, and generates $8 in revenue. Revenues are gross figures (i.e. they are not net of investment costs), and there are no costs besides investments costs (i.e. no variable cost of production etc.). The firms are risk-neutral entities, and are uninformed of each other’s investment decisions.What is Firm A’s expected gross revenue (i.e., not net of investment costs) from investing, assuming Firm B invests (i.e. conditional on Firm B investing)?A) -$1B) $2C) $7D) $8E) None of the above

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Asked Oct 18, 2019
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Firms A and B are contemplating whether or not to invest in R&D. Each has two options: “Invest” and “Abstain.” A firm that invests will invent product X with a probability of 0.5, whereas a firm that abstains is incapable of invention. Investment costs $6. If a firm doesn’t invent X, it makes $0 in revenue. If a firm invests and is the only one to invent X, it becomes a monopolist and generates $20 in revenue. If both firms invent X, each firm becomes a duopolist, and generates $8 in revenue. Revenues are gross figures (i.e. they are not net of investment costs), and there are no costs besides investments costs (i.e. no variable cost of production etc.). The firms are risk-neutral entities, and are uninformed of each other’s investment decisions.

What is Firm A’s expected gross revenue (i.e., not net of investment costs) from investing, assuming Firm B invests (i.e. conditional on Firm B investing)?

A) -$1
B) $2
C) $7
D) $8
E) None of the above

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Expert Answer

Step 1

Gross revenue is calculated without deducting any type of costs from the revenue generated.

 

Step 2

Given Information:

There are two firms A and B who want to either invest or abstain in R&D. The probability of success of invention of product X is 0.5. And the cost of investment is $6. When both the firms invest, $8 is revenue generated by both the firms. And when only one firm invests revenue generated is $20.

Step 3

The expected gross revenue of firm A, when B is al...

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E(eross revenue of fim A)Hprobability of success of invention by firm A xprobability of success of invention by fim B as well xrevenue generated when bothfirms invest probability of sucess of invention by fim A xprobability of failure of invention by fim B xrevenue generated when only one firm invests] H0.5x0.5x$8]-(0.5x(1-0.5)x $20] $5+$2 $7

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