$500 and there are two companies he could invest X dollars in: Dog Gone Salon,which has a payoff of 2X with 50% probability and $0 with 50% probability and Pretty Kitty Grooming,which has a payoff of 4X with 25% probability and $0 with 75% probability.Dean's expected payoff from investing $250 in both Dog Gone Salon and Pretty Kitty Grooming is:

Question

Quizplus · Accepted Answer

Dean's expected payoff from investing $X in Dog Gone Salon is:
0.5(2X) + 0.5(0) = X

His expected payoff from investing $X in Pretty Kitty Grooming is:
0.25(4X) + 0.75(0) = X

Therefore, Dean's expected payoff from investing $250 in both Dog Gone Salon and Pretty Kitty Grooming is:

0.5(2(250)) + 0.5(250) + 0.25(4(250)) + 0.75(0) = $500

This is the same as his initial investment, so he is not making any profit or loss. Since he wants to make a profit, he should not invest in either of these companies.

$500 and There Are Two Companies He Could Invest X