Question

6. Consider old McDonald, who must carry a dozen eggs from the barn to the house. The ground between the barn and the house is slippery, so there is a 50 percent chance that McDonald will slip on a given trip and break all the eggs in his basket. Consider two strategies: a one-basket strategy (a single trip with all 12 eggs) and a two-basket strategy (two trips, with 6 eggs per trip). McDonald can sell each egg for 10 cents. 0 3 List all of the possible outcomes under each of the strategies. What is the expected number of delivered (unbroken) eggs under each strategy? What is his expected revenue under each strategy? What strategy is better? o o o o

Answer 1

Strategy 1: Single basket

Possible Outcomes	Probability	Payoff
Fall and all eggs break	0.5	0 x 10 x 0.5 = 0
Doesn't fall and no eggs break	0.5	12 x 10 x 0.5 = 60
Total	1	0+60=60

• Under strategy 1 there are two possible outcomes, 1 that he falls and all eggs break, 2 that he doesn't fall and no eggs break. Each outcome is equally likely so the probability of each is 0.5 or 50%
• As calculated above, there is 50% chance that 12 eggs will be delivered unbroken, so the expected value is 0.5 x 12 = 6 eggs
• Expected revenue as shown above will be 60 cents

Strategy 2: Two baskets

Possible Outcomes	Probability	Payoff
Fall and all eggs from both the baskets break	1/4	0 x 10 x 1/3 = 0
Fall and all eggs from one the baskets break	2/4=1/2	2 x 6 x 10 x 1/2 = 60
Doesn't fall and no eggs break	1/4	12 x 10 x 1/4 = 30
Total	1	0+60+30=90

• Under strategy 2 there are 4 possible outcomes, 1 that he falls and all eggs break, 2 that he doesn't fall and no eggs break, 3 that he falls and eggs in one basket break, 4 he falls and eggs in other basket break. Each outcome is equally likely so the probability of each is 0.25 or 25%
• As calculated above, there is 25% chance that 12 eggs will be delivered unbroken, and there is 50% chance that 6 eggs will be delivered unbroken, so the expected value is 0.25 x 12 = 3 eggs + 0.25 x 6 + 0.25 x 6 = 3 eggs so total expected value = 6 eggs
• Expected revenue as shown above will be 90 cents
• As the second strategy leads to higher expected revenue that the first strategy, second one is better.