Answer:
There are 5 apples in the best bundle Charlie can afford
Step-by-step explanation:
If the utility function is u(xa, xb) , where xa represent the quantity of apples and xb is the quantity of bananas then we want to choose the quantity of bananas and apples that maximises the utility of Charlie for the same budget restriction ( get the most benefit for the same money).
The budget restriction is
$4* xa + $2* xb = $40
then
u(xa, xb) =xa*xb
4*xa + 2*xb = 40 → xb = (40 - 4*xa)/2 = 20 - 2*xa
replacing in the utility function
u(xa, xb) =xa* (20 - 2*xa) = 20*xa - 2*xa²
the maximum of this function is obtained when the derivative of the utility function with respect to xa is 0 . Thus
du/dxa = 20 - 4*xa = 0 → xa = 20/4 = 5
then for
xa=5 apples
xb=20 - 2*xa = 20 - 2*5 = 10 bananas
Charlie maximises his utility . Therefore there are 5 apples in the best bundle Charlie can afford
