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  • 1.  expected value - without perfect information ?

    Posted 10-04-2013 07:49 AM
    Correct answer is D.

    I cant understand how without perfect information, the expected value is 30,40.
    Could you please explain?
    Thanks


    Fact Pattern: Stan Berry is considering selling peanuts at the Keefer High School football games. The peanuts would cost $.50 per bag and could be sold for $1.50 per bag. No other costs would be incurred to sell the peanuts. All unsold bags can be returned to the supplier for $.30 each. Berry estimated the demand for peanuts at each football game and constructed the payoff table that follows.
    Action (Bags to Stock)
    Demand
    Probability
    (Bags)
    of Demand
    20
    30
    40
    50
    20
    .2
    $20
    $18
    $16
    $14
    30
    .4
    $20
    $30
    $28
    $26
    40
    .3
    $20
    $30
    $40
    $38
    50
    .1
    $20
    $30
    $40
    $50
    Question: 10 The maximum that Stan Berry should pay for perfect information so that he could always stock the correct number of bags of peanuts is


  • 2.  RE:expected value - without perfect information ?

    Posted 10-04-2013 12:28 PM
    The best case is to know the exact demand (perfect information). In this way Stan Berry can stock the correct number of bags. The expected value with perfect info can be calculated as:

    Demand    Stock Level    Probability    Contribution                 Expected Value
    20                20                .2                1$ (1.5-0.5)                20x1x.2=4$
    30                30                .4                1$ (1.5-0.5)                30x1x.4=12$ 
    40                40                .3                1$ (1.5-0.5)                40x1x.3=12$
    50                50                .1                1$ (1.5-0.5)                50x1x.1=5$
                                                                                                   Total=33$

    So, with perfect info exp. value is 33$. Without perfect info, our expected value is the greatest of all expected values. The distribution of expected values under each and every case is given in the question. For example, if demand is 30 bags, and Stan Berry stocks 40 bags, it will sell 30 bags with 1$ contribution (30$), and sell back remaining 10 bags to supplier with -0.2$ contribution (-2$), total value will be 28$ (highlighted as bold below).

    Demand
    Probability
    (Bags)
    of Demand
    20
    30
    40
    50
    20
    .2
    $20
    $18
    $16
    $14
    30
    .4
    $20
    $30
    $28
    $26
    40
    .3
    $20
    $30
    $40
    $38
    50
    .1
    $20
    $30
    $40
    $50

    We need to calculate expected value for each stock scenario:

    Stock Level        Expected Value
    20                        20x0.2+20x.4+20x.3+20x.1=20
    30                        18x.2+30x.4+30x.3+30x.1=27.6
    40                        16x.2+28x.4+40x.3+40x.1=30.4
    50                        14x.2+26x.4+38x.3+50x.1=29.6

    To sum up, without perfect info the company can expectedly earn 30.4$ by choosing stock level of 40 bags. Since with perfect info expected value is 33$, it will give up only 2.6$ (33-30.4) for perfect info.

    BR.


    -------------------------------------------
    Yasin Duran CPA
    Director/Manager
    Istanbul
    Turkeyyasinduran@...
    -------------------------------------------






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