Question

State of Nature Alternative Favorable Market Unfavorable Market Large Plant 4 Small Plant 5 Do Nothing $150,000.00] -$180,000.00 $100,000.00 -$33,000.00 $0.00 $0.00

Answer 1

The payoffs for each of the boxes are being written in order when the MARKET SURVEY IS CONDUCTED

A) Survey Results Favourable (Probability 0.45)

i) Large Plant Built

a) Market is Good (Probability 0.8) : 0.45 * 0.8 * 150000 = 54000

b) Market is Bad (Probability 0.2) : 0.45 * 0.2 * (-180,000) = -16200

ii) Small Plant Built

  a) Market is Good (Probability 0.8) : 0.45 * 0.8 * 100000 = 36000

b) Market is Bad (Probability 0.2) : 0.45 * 0.2 * (-33,000) = -2970

iii) No Plant Built

a) Market is Good (Probability 0.8) : 0.45 * 0.8 * 0 = 0

b) Market is Bad (Probability 0.2) : 0.45 * 0.2 * 0 = 0

B) Survey Results Unfavourable (Probability 0.55)

i) Large Plant Built

a) Market is Good (Probability 0.3) : 0.55 * 0.3 * 150000 = 24750

b) Market is Bad (Probability 0.7) : 0.55 * 0.7 * (-180,000) = -69300

ii) Small Plant Built

  a) Market is Good (Probability 0.3) : 0.55 * 0.3 * 100000 = 16500

b) Market is Bad (Probability 0.7) : 0.55 * 0.7 * (-33,000) = -12075

iii) No Plant Built

a) Market is Good (Probability 0.3) : 0.55 * 0.3 * 0 = 0

b) Market is Bad (Probability 0.7) : 0.55 * 0.7 * 0 = 0

Total Expected value after conducting Survey = (54000 - 16200 + 36000 - 2970 + 24750 - 69300 + 16500 - 12075) - Cost of Survey

Expected Value = 30705 - 10000 = 20705

If the survey is not conducted, expected payout = 0.6 * 150000 + 0.4 * (-180000) + 0.6 ( 100000) + 0.4 * (-33000)

= 90000 - 72000 + 60000 - 13200 = 64800.

The expected payout by not doing the survey is more the payout after doing the survey and deducting its costs. So it is better to not do the survey.

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