Alcohol Consumption: Recall the example in which you needed to choose how much to drink. Imagine that your payoff function is given by θa - 4a2, where θ is a parameter that depends on your physique. Every person may have a different value of θ, and it is known that in the population
(1) the smallest θ is 0.2;
(2) the largest θ is 6; and
(3) larger people have higher θs than smaller people.
a. Can you find an amount that no person should drink?
b. How much should you drink if your θ = 1? If θ = 4?
c. Show that in general smaller people should drink less than larger people.
d. Should any person drink more than one 1-liter bottle of wine?