At a consumer optimum involving goods A and​ B, the marginal utility of good A is three

Question

times the marginal utility of good B.
Part 2
The price of good B is ​$4.00
.
The price of good A is
Part 3
A.
​$32.00
.
B.
​$3
.00.
C.
​$12.00
.
The answer is C. $12.00
How do I get to the answer?

Answer 1

To find the answer, we can use the concept of marginal utility and the principle of equalizing marginal utility per dollar spent.

We are given that at the consumer optimum, the marginal utility of good A is three times the marginal utility of good B.

Let's assume the marginal utility of good B is MU_B.

Then, the marginal utility of good A will be 3*MU_B.

Now, we know the price of good B is $4.00.

The principle of equalizing marginal utility per dollar spent tells us that the consumer will allocate their budget in such a way that the marginal utility per dollar spent is the same for both goods.

Since the price of good B is $4.00, the marginal utility per dollar spent for good B is MU_B/$4.00.

Now, let the price of good A be P.

The marginal utility per dollar spent for good A will be (3*MU_B)/P.

Since the marginal utility per dollar spent for both goods should be equal, we can set up the following equation:

MU_B/$4.00 = (3*MU_B)/P

Cross-multiplying, we get:

P = (12 * MU_B)/MU_B

P = 12

Therefore, the price of good A is $12.00. Hence, the answer is C. $12.00.