         PERSONAL UTILITY FUNCTION

UTILITY THEORY HAS TO DO WITH ONE'S PREFERENCE FOR VARIOUS
DECISION ALTERNATIVES. SUPPOSE EVERY DECISION ONE CAN MAKE
LEADS TO A KNOWN MONETARY PAYOFF. THEN THAT PERSON WILL
CHOOSE THE DECISION WITH THE HIGHEST PAYOFF. HOWEVER, IF THERE
IS SOME UNCERTAINTY IN THE RESULT OF A DECISION THE CORRECT
DECISION IS NOT SO OBVIOUS. UTILITY THEORY PERMITS US TO
ASSIGN A NUMBER TO EACH PAYOFF, ITS 'UTILITY'. HIGHER PAYOFFS
LEAD TO HIGHER UTILITIES BUT A UTILITY OF 2  FOR $5000 DOES
DOES NOT NECESSARILY MEAN A UTILITY OF 4 FOR $10000. ONCE
UTILITIES ARE DETERMINED DECISIONS ARE MADE BASED UPON HIGHEST
EXPECTED UTILITY.

PRESS ENTER TO CONTINUE? 
UTILITIES ARE DETERMINED IN THE FOLLOWING WAY: THE POSSIBLE
PAYOFFS ARE RANKED FROM HIGHEST TO LOWEST. THE HIGHEST PAYOFF
IS ASSIGNED SOME ARBITRARY UTILITY, SAY 1. THE LOWEST PAYOFF
IS ASSIGNED SOME LOWER ARBITRARY UTILITY, SAY 0. WE DETERMINE
THE UTILITIES OF THE OTHER PAYOFFS BY SETTING UP A GAMBLE
WE ARE GIVEN THE CHOICE OF HAVING THIS PAYOFF FOR SURE OR OF
GETTING THE HIGHEST PAYOFF WITH PROBABILITY P AND THE LOWEST
WITH PROBABILITY 1-P. WITH P BEING DETERMINED THE UTILITY OF
THIS MIDDLE PAYOFF IS COMPUTED. AS THE PAYOFFS GO UP SO MUST P.
WE LOOK FOR THE P SO THAT WE ARE INDIFFERENT BETWEEN THE SURE
THING AND THE GAMBLE. UTILITY THEORY SAYS THERE IS SUCH A P.

PRESS ENTER TO CONTINUE? 
FOR EXAMPLE IF THE LOWEST PAYOFF WAS $0 AND THE HIGHEST WAS
$100000 THEN FOR AN INTERMEDIATE PAYOFF OF $50000 WE WOULD ASK
WOULD WE PREFER $50000 FOR SURE OR $100000 WITH PROBABILITY P
AND $0 WITH PROBABILITY 1-P. KEEP ADJUSTING P UNTIL WE ARE
INDIFFERENT TO THE SURE THING AND THE BET. THIS IS P.

DIFFERENT PEOPLE HAVE DIFFERENT UTILITY FUNCTIONS. THUS UNDER
IDENTICAL CIRCUMSTANCES DIFFERENT PEOPLE MAY MAKE DIFFERENT
DECISIONS AND BOTH STILL MAXIMIZE EXPECTED UTILITY. THE
PROGRAM WILL ASSIGN UTILITIES TO DOLLAR AMOUNTS BETWEEN
$0 AND $100000 WITH THE UTILITY OF $0 BEING SET TO 0 AND THAT
OF $100000 BEING SET TO 10.

PRESS ENTER TO BEGIN? 

WITH WHAT PROBAILITY(P) WOULD YOU BE INDIFFERENT TO $ 100 FOR
SURE OR $ 100000 WITH PROBABILITY P AND 0 WITH PROBABILITY
1 - P. THIS PROBABILITY MUST BE AT LEAST EQUAL TO 0 

ENTER THE PROBABILITY? 0.1

WITH WHAT PROBAILITY(P) WOULD YOU BE INDIFFERENT TO $ 1000 FOR
SURE OR $ 100000 WITH PROBABILITY P AND 0 WITH PROBABILITY
1 - P. THIS PROBABILITY MUST BE AT LEAST EQUAL TO .1 

ENTER THE PROBABILITY? 0.2

WITH WHAT PROBAILITY(P) WOULD YOU BE INDIFFERENT TO $ 3000 FOR
SURE OR $ 100000 WITH PROBABILITY P AND 0 WITH PROBABILITY
1 - P. THIS PROBABILITY MUST BE AT LEAST EQUAL TO .2 

ENTER THE PROBABILITY? 0.3

WITH WHAT PROBAILITY(P) WOULD YOU BE INDIFFERENT TO $ 5000 FOR
SURE OR $ 100000 WITH PROBABILITY P AND 0 WITH PROBABILITY
1 - P. THIS PROBABILITY MUST BE AT LEAST EQUAL TO .3 

ENTER THE PROBABILITY? 0.4

WITH WHAT PROBAILITY(P) WOULD YOU BE INDIFFERENT TO $ 10000 FOR
SURE OR $ 100000 WITH PROBABILITY P AND 0 WITH PROBABILITY
1 - P. THIS PROBABILITY MUST BE AT LEAST EQUAL TO .4 

ENTER THE PROBABILITY? 0.5

WITH WHAT PROBAILITY(P) WOULD YOU BE INDIFFERENT TO $ 20000 FOR
SURE OR $ 100000 WITH PROBABILITY P AND 0 WITH PROBABILITY
1 - P. THIS PROBABILITY MUST BE AT LEAST EQUAL TO .5 

ENTER THE PROBABILITY? 0.6

WITH WHAT PROBAILITY(P) WOULD YOU BE INDIFFERENT TO $ 30000 FOR
SURE OR $ 100000 WITH PROBABILITY P AND 0 WITH PROBABILITY
1 - P. THIS PROBABILITY MUST BE AT LEAST EQUAL TO .6 

ENTER THE PROBABILITY? 0.7

WITH WHAT PROBAILITY(P) WOULD YOU BE INDIFFERENT TO $ 40000 FOR
SURE OR $ 100000 WITH PROBABILITY P AND 0 WITH PROBABILITY
1 - P. THIS PROBABILITY MUST BE AT LEAST EQUAL TO .7 

ENTER THE PROBABILITY? 0.8

WITH WHAT PROBAILITY(P) WOULD YOU BE INDIFFERENT TO $ 50000 FOR
SURE OR $ 100000 WITH PROBABILITY P AND 0 WITH PROBABILITY
1 - P. THIS PROBABILITY MUST BE AT LEAST EQUAL TO .8 

ENTER THE PROBABILITY? 0.9

WITH WHAT PROBAILITY(P) WOULD YOU BE INDIFFERENT TO $ 60000 FOR
SURE OR $ 100000 WITH PROBABILITY P AND 0 WITH PROBABILITY
1 - P. THIS PROBABILITY MUST BE AT LEAST EQUAL TO .9 

ENTER THE PROBABILITY? 1.0

WITH WHAT PROBAILITY(P) WOULD YOU BE INDIFFERENT TO $ 70000 FOR
SURE OR $ 100000 WITH PROBABILITY P AND 0 WITH PROBABILITY
1 - P. THIS PROBABILITY MUST BE AT LEAST EQUAL TO 1 

ENTER THE PROBABILITY? 

PROBABILITY MUST BE BETWEEN 60000 AND 100000 

WITH WHAT PROBAILITY(P) WOULD YOU BE INDIFFERENT TO $ 70000 FOR
SURE OR $ 100000 WITH PROBABILITY P AND 0 WITH PROBABILITY
1 - P. THIS PROBABILITY MUST BE AT LEAST EQUAL TO 1 

ENTER THE PROBABILITY? 1

WITH WHAT PROBAILITY(P) WOULD YOU BE INDIFFERENT TO $ 80000 FOR
SURE OR $ 100000 WITH PROBABILITY P AND 0 WITH PROBABILITY
1 - P. THIS PROBABILITY MUST BE AT LEAST EQUAL TO 1 

ENTER THE PROBABILITY? 1

WITH WHAT PROBAILITY(P) WOULD YOU BE INDIFFERENT TO $ 90000 FOR
SURE OR $ 100000 WITH PROBABILITY P AND 0 WITH PROBABILITY
1 - P. THIS PROBABILITY MUST BE AT LEAST EQUAL TO 1 

ENTER THE PROBABILITY? 1
IS PRINTED OUTPUT DESIRED(Y/N)? Y
  PAYOFF        UTILITY    
       0           0.00
     100           1.00
    1000           2.00
    3000           3.00
    5000           4.00
   10000           5.00
   20000           6.00
   30000           7.00
   40000           8.00
   50000           9.00

PRESS ENTER TO CONTINUE? 
  PAYOFF        UTILITY    
   60000          10.00
   70000          10.00
   80000          10.00
   90000          10.00
  100000          10.00
