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    Decision Making with Utility Functions and Uncertainty

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    ABC Company does subcontracting on government contracts. ABC Company is a small company with limited capital with a utility function described as follows:
    U(x) = -x/100-x^2/5,000 for x < -1,000
    U(x) = x/100-170 for -1,000 ≤ x ≤ 10,000
    U(x) = √x for x > 10,000

    Part 1
    Suppose ABC Company is considering bidding on a given contract. It will cost $2,000 to prepare the bid. If the bid is lost, the $2,000 cost is also lost. If ABC Company wins the bid, it will make $40,000 and recover the $2,000 bid preparation cost. Suppose ABC Company believes the probability of winning the contract is 0.5 if a bid is submitted. What should it do?

    Part 2
    What should the probability of winning have to be before ABC Company would submit a bid?

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    Solution Preview

    See attachment.

    Part 1
    U(no bid) = U(0) = 0/100-170 = -$170
    U(bid) = 0.5* U(-2,000) + 0.5 * U(40,000) = 0.5 * ...

    Solution Summary

    The solution contains step-by-step analysis of decision making with utility functions and uncertainty by obtaining the utilities for no bid and bid scenarios.