Question

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?

Answer 1

We are given here that:
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:

• We are given here that: 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.