Question

Brad Smith has done some analysis about the profitability of the bicycle shop. If Brad builds...

Brad Smith has done some analysis about the profitability of the bicycle shop. If Brad builds the large bicycle shop, he will earn $60,000 if the market is favorable, but he will lose $40,000 if the market is unfavorable. The small shop will return a $30,000 profit in a favorable market and a $10,000 loss in an unfavorable market. At the present time, he believes that there is a 50-50 chance that the market will be favorable. His former marketing professor will charge him $5,000 for the marketing research. Furthermore, there is a 0.9 probability that the market will be favorable given a favorable outcome from the study.

What is the highest Expected Monetary Value for Brad’s decision?

Homework Answers

Answer #1

Answer:

Given,
E(favorable | large shop) = 60,000
E(unfavorable | large shop) = -40,000

E(favorable | small shop) = 30,000
E(unfavorable | small shop) = -10,000

Current expected value of the decision given that no market research is used:

  • For Large Shop:
  • = P(favorable)E(favorable | large shop) +P(unfavourable)E(unfavorable | large shop)
  • = 0.5*(60,000 - 40,000)
  • = 10,000
  • For Small Shop:
  • = P(favorable)E(favorable | Small shop) +P(unfavourable)E(unfavorable | Small shop)
  • = 0.5*(30,000 - 10,000)
  • = 10,000

Now if Market Resarch is used:

  • Given:
  • P(favourable | favourable predicted ) = 0.9
    Therefore, expected value if favourable predicted
    = 0.9*60,000 - 0.1*40,000 - 5000 = 45000
  • Expected value if unfavourable = Market research cost = -5000
    Therefore, total expected value:
    = 0.5*(-5000 + 45000) = 20,000

Therefore 20,000 is the required expected value of the decision here.

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