If Joe is currently consuming 64 nuts and 10 berries, what is the largest number of berries he would be willing to give up in exchange for 17 additional nuts?

Here is the Question again :

Joe is a rational Squirrel with the utility function( u = 4n^0.5 + b ) . If Joe is currently consuming 64 nuts and 10 berries, what is the largest number of berries he would be willing to give up in exchange for 17 additional nuts?

To find out the largest number of berries Joe would be willing to give up in exchange for 17 additional nuts, we need to compare the value Joe places on nuts and berries.

First, let us determine the value Joe places on a single berry. We can do this by dividing the number of nuts Joe would give up by the number of berries he is currently consuming.

Value of a single berry = Number of nuts Joe would give up / Number of berries Joe is currently consuming

Value of a single berry = 17 nuts / 10 berries

Now, we need to determine how many berries can be exchanged for 17 nuts. We can do this by multiplying the value of a single berry by the number of berries Joe is currently consuming.

Number of berries Joe can exchange for 17 nuts = Value of a single berry * Number of berries Joe is currently consuming

Number of berries Joe can exchange for 17 nuts = (17 nuts / 10 berries) * 10 berries

By simplifying the equation, we find that Joe can exchange a maximum of 17 berries for 17 nuts. Therefore, Joe would be willing to give up a maximum of 17 berries in exchange for 17 additional nuts.