Expected Value Exercise 7
Aline and Sarah decide to go into business together as
economic consultants. Aline believes they have a 50-50 chance of earning
$200,000 a year, and that if they don't, they'll earn $0. Sarah believes they
have a 75% chance of earning $100,000 and a 25% chance of earning $10,000.
What is the expected value for Aline and Sarah?
aline= (50%x200,000)+(50%x0)= 100,000
ReplyDeletethen, sarah= (75%x100,000)+(25%x10,000)= 77,500
so, the EU for aline is higher than the EU of sarah.
Known:
ReplyDeleteAline and Sarah are both economic consultants. These are both from their own believes :
Aline
Probability Success 50 % = 0.5
Earn if success = $ 200,000
Probability Unsuccess 50 % = 0.5
Earn if unsuccess = $ 0
Solution:
Aline’s Expected Value = (Success Income) (Probability Success) + (Unsuccess Income) (Probability Unsuccess)
= ( $ 200,000 x 0.5 ) + ( $ 0 x 0.5 )
= $ 100,000
Sarah
Probability Success 75 % = 0.75
Earn if success 75 % = $ 100,000
Probability success 25 % = 0.25
Earn if success 25 % = $ 10,000
Solution:
Sarah’s Expected Value = (Success 75% Income) (Probability Success 75%) + (Success 25% Income) (Probability Success 25 %)
= ( $ 100,000 x 0.75 ) + ( $ 10,000 x 0.25 )
= ( $ 75,000 + $ 2500 )
= $ 77,500
Aline believes :
ReplyDelete50% (0.5) on earning $200,000 a year
or
0% (0) on earning $0 a year
EU = (probability of success) x (success) + (probability of failure) x (failure)
(0.5 x 200,000) + (0.5 x 0) = 100,000 + 0 = $100,000
Sarah believes :
75% (0.75) on earning $100,000
or
25% (0.25) on earning $ 10,000
EU = (probability of success) x (success) + (probability of failure) x (failure)
(0.75 x 100,000 ) ( 0.25 x 10,000) =75,000 + 2,500 = $77,500
ALINE
ReplyDeleteAline with 50% (0.5) to earn $200.000 and 50%(0.5) to earn $0
Expected income/EV : (0.5)($200.000) + (0.5) ($0) = 100.000 + 0 = $100.000
so, Aline expected value is $100.000
SARAH
Sarah with 75%(0.75) to earn $100.000 and 25%(0.25) to earn $10.000
Expected income/EV : (0.75)($100.000) + (0.25) ($10.000) = 75.000+2500 = $77.500
and Sarah expected value is $77.500
expected value Aline
ReplyDeleteE(v) = (P1 x X1) + (P2 x X2)
=(50% x200,000)+(50% x 0)
= (0,5 x 200,000) + (0,5 x 0)
= $ 100,000
Expected value Sarah
E(v)= (P1 x X1) + (P2 x X2)
=(75%x100,000)+(25%x10,000)
= (0.75)(100.000) + (0.25) (10.000)
= $ 77,500
so the expected value from Aline is $ 100,000 and Expected value from Aline is $ 77,500.ALine is greater than sarah.
Aline
ReplyDeleteE(v) = (P1)(X1) + (P2)(X2)
= (50%)(200000)+(50%)(0)
= (0.5)(200000)+(0.5)(0)
= $ 100.000
Sarah
E(v) = (P1)(X1)+ (P2)(X2)
= (75%)(100000)+(25%)(10000)
= (0.75)(100000)+(0.25)(10000)
= $ 77.500
Aline's expected value is higher than sarah's expected value
ANSWER:
ReplyDeleteAline = 50% x 200,000 + 50% x 0 = 100,000
Sarah = 75% x 100,000 + 25% x 10,000 = 77,500