Problem

At a consumer optimum involving goods $A$ and $B$, the marginal utility of good $A$ is three times the marginal utility of good B.
The price of $\operatorname{good} B$ is $\$ 4.00$. The price of $\operatorname{good} A$ is
A. $\$ 20.00$.
B. $\$ 12.00$.
C. $\$ 3.00$,
D. There is not enough information.

Answer

Expert–verified
Hide Steps
Answer

Final Answer: The price of good A is \(\boxed{\$ 12.00}\)

Steps

Step 1 :Given that at a consumer optimum, the marginal utility of good A is three times the marginal utility of good B.

Step 2 :We also know that the price of good B is \(\$ 4.00\). We are asked to find the price of good A.

Step 3 :The consumer optimum is achieved when the ratio of the marginal utility of good A to its price is equal to the ratio of the marginal utility of good B to its price. This is also known as the law of equi-marginal utility.

Step 4 :Given that the marginal utility of good A is three times the marginal utility of good B, we can set up the following equation: \(\frac{MU_A}{Price_A} = \frac{MU_B}{Price_B}\)

Step 5 :We know that \(MU_A = 3* MU_B\) and \(Price_B = \$4.00\). We can substitute these values into the equation and solve for \(Price_A\).

Step 6 :By substituting the values, we get \(Price_A = 12\)

Step 7 :Final Answer: The price of good A is \(\boxed{\$ 12.00}\)

link_gpt