Question

Harry enjoys dark roast coffee because he thinks drinking it makes him look quite sophisticated. In order to stomach it, however, he puts three containers of creamer into every cup of coffee so it is not too bitter. Harry only enjoys coffee in this combination. With less creamer the coffee is too bitter and he won't drink it; with more creamer the coffee is too sweet and also undrinkable. With coffee and creamer in the right proportions, however, Harry is always happy to have more coffee and creamer. His utility function can be written as follows: u(x,y) = min(3x,y), where x is cups of coffee y is containers of creamer.

Required:
Suppose that Harry drinks one cup of coffee with his preferred three packs of creamer every day for seven days. What is his utility for that week?

Answer 1

Answer is explained in the explanation section below.

Step-by-step explanation:

Function given:

u(x,y) = min(3x,y)

Where, x = cups of coffee

y = containers of creamer.

From the above equation, we know that:

3x = y

For a week, Harry consumes 7 cups of coffee with 21 containers of creamers.

Thus,

u(x,y) = min (3x,y)

u(x,y) = min (3x7,21)

u(x,y) = min (21,21)

u(x,y) = 21

Now, if Harry 21 containers, he will get 28 (21 +7)

Thus,

u(x,y) = min(3x,y)

u(x,y) = min(3x7,28)

u(x,y) = min(21,28)

u(x,y) = 21

Additional 7 containers are useless cup of coffee and 3 containers of creamer are used together. Thus, for 7 cups of coffee Harry only needs 21 containers of creamer.