Question

Nick and Rosa are going to a music festival and are debating whether they should buy food at the festival or bring sandwiches. They only have $7 each to spend on food but would prefer the convenience of buying sandwiches at the festival to the task of preparing them beforehand. If they bring sandwiches, they will eat them regardless of how much food costs at the festival (having already expended the effort of preparing the sandwiches), and will get a utility of 10. Alternatively, if they don't bring sandwiches and are able to buy food for $7 or less, they will get utility of 20. However, if food at the festival costs more than $7 and they don't get to eat, they will get a utility of 0. The numbers in the following table reflect the utility Nick and Rosa get under each of the described outcomes.

Food Price
Options More than $7 $7 or less
Try to buy food 0 20
Bring sandwithces 10 10

If the probability that food costs more than $7 is 50%, then the expected value of utility from not preparing food is ________ , and the expected
value of utility from bringing sandwiches is___________ .

NoW, suppose Nick and Rosa a third if food at festival Costs more than $7, buy sandwiches less $7 at a deli and bring them back to the festival. If Nia and Rosa Can Choose to try to buy food at the festival, knowing they have the to buy at the deli, they now get either a utility Of 10 (if food costs more than $7 and they have to leave the festival to go to the deli) or a utility of 20 (if costs $7 or less and they can buy it at festival).

Assuming the same probabilities as before, the expected value of utility from not preparing food (with the option to convert to buying sandwiches at the deli) is ____________ therefore, the value Of the real option is ___________

Answer 1

10, 10

15, 20

Step-by-step explanation:

p (food > $7) = 50% = 0.5

p (food < $7) = 0.5

= 0.5 (0) + 0.5 (20)

=10

=0.5 (10) + 0.5(10)

= 5+5=10

2. 0.5 (10) + 0.5 (20)

= 5+10 = 15

=20

Answer 2

1) 10 , 10

2) 15 , 20

Step-by-step explanation:

1) P( food > $7 ) = 50% = 0.5

P ( food < $7 ) = 0.5

Expected value of utility for not preparing food

= 0.5( 0 ) + 0.5(20 )

= 10

Expected value of utility from bring sandwiches

= 0.5( 10 ) + 0.5(10)

= 5 + 5 = 10

2) Considering the third option

Value of utility from not preparing food with option to convert to buying sandwiches at deli

= 0.5 ( 10 ) + 0.5(20 )

= 5 + 10 = 15

The Value of the real Option = 20