Question

Doreen has a utility function U(x,y)=2x+3y. The price of good x is $3, and the price of good y is $4. If Doreen's income is $120, how many units of good x would she consume if she chose the bundle that maximizes her utility subject to her budget constraint?

a. 0
b. 10
c. 30
d. 40
e. None of the above

Answer 1

Doreen would consume 30 units of good x if she chose the bundle that maximizes her utility subject to her budget constraint.

Step-by-step explanation:

To find the number of units of good x that Doreen would consume, we need to determine the bundle that maximizes her utility subject to her budget constraint.

Doreen's utility function is U(x,y) = 2x + 3y, where x represents the quantity of good x consumed and y represents the quantity of good y consumed.

The price of good x is $3, and the price of good y is $4. Doreen's income is $120.

We can set up the budget constraint equation as: Pxx + Pyy = I, where Px is the price of good x, Py is the price of good y, and I is Doreen's income.

Plugging in the values, we have: 3x + 4y = 120.

Now, we can maximize Doreen's utility function subject to the budget constraint.

Using the Lagrange multiplier technique, we set up the following equation:

2 = 3λ

3 = 4λ

3x + 4y = 120

Solving these equations, we find that x = 30 and y = 20.

Therefore, Doreen would consume 30 units of good x if she chose the bundle that maximizes her utility subject to her budget constraint.