Ambrose's brother Francis has an income of $60 and a utility function U(x₁, x₂) = . The price of good 1(nuts) is $5 and the price of good 2(berries) is $1. How many units of berries will Augustine demand?

Question

Quizplus · Accepted Answer

To maximize utility, the consumer should allocate their budget such that the marginal utility per dollar spent on each good is equal. 
MU1/P1 = MU2/P2
The marginal utility of good 2 from the given utility function is:
MU2 = 6x^-0.5*y^0.5
where x is the quantity of nuts and y is the quantity of berries.
Substituting the values given:
MU2 = 6x^-0.5*(60/5)^0.5
MU2 = 6x^-0.5*12
MU2 = 72x^-0.5
The marginal utility of good 1 is:
MU1 = 2x^0.5*y^-0.5
Setting the two marginal utilities equal and solving for y:
MU1/P1 = MU2/P2
2x^0.5*y^-0.5 / 5 = 72x^-0.5 / 1
y = 4x
Substituting the budget constraint:
5x + y = 60
5x + 4x = 60
x = 8
y = 32
Therefore, the consumer will demand 32 units of berries.

Ambrose's Brother Francis Has an Income of $60 and a Utility