An individual has a nice project of a new product, but needs money for that.
She can only produce if she raises the amount of money required (noted "K")
She has the possibility of raising K if she participates on a given program (let's say, a government program).
The probability of raising K through this money is p.
However, to participate on this program, she needs to incur some costs c < K.

The problem is that there is a probability (1 - p) that she does not raise the money, but only incurs c.

Summing up:

positive payoff = (K - c) with probability p
negative payoff = (-c) with probability (1-p)


In order to try to reduce the costs c, she can ask for some professional help.
The costs for this professional help are sunk (for example, it can be a government agency that provides advice for free to inventors and entrepreneurs). With the help, the costs become c.a with 0 < a < 1.

Therefore:

positive payoff = (K - ca) with probability p
negative payoff = (-ca) with probability (1-p)

I want to calculate:

. What is the minimum p in the first case for the individual to participate on the program?
. What is the minimum p in the second case for the individual to participate on the program?
. What would be the correct notation for EU = p(K-c) + (1-p)c?
. What is the variable I should set as the one I am interested in, i.e., the variable which she will maximize for? For me it was "c", but when I change the setting, the result is the same and it makes no sense!

Answer rating: 100% (QA)

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