Suppose that a consumer had a utility function given by: U=XY3. This consumer has a budget of $48.Fill in the value of this consumer's demand function. X = Answer Question 6[input]*(1/Px).(For instance, if X = 4/Px, then X = 4 * (1/Px) and enter 4)

Question

BlackTom AI · Accepted Answer

We start by identifying the consumer's problem and the given utility function: U = X * Y^3 with a budget of 48 and prices Px and Py for goods X and Y, respectively. To find X as a function of Px (holding Py and income constant), we solve the utility maximization with a Lagrangian: L = X Y^3 + λ (48 - Px X - Py Y).

First-order conditions:
- ∂L/∂X = Y^3 - λ Px = 0 → λ = Y^3 / Px.
- ∂L/∂Y = 3 X Y^2 - λ Py = 0 → λ = 3 X Y^2 / Py.
Equating the expressions for λ gives Y^3 / Px = 3 X Y^2 / Py. Assuming Y > 0, divide both sides by Y^2 to get Y / Px = 3 X / Py, which leads to Y = (3 X Px) / Py.

Next, substitute Y back into the budget constraint: Px X + Py Y = 48. Replacing Y with (3 X Px) / Py yields
Px X + Py * (3 X Px / Py) = 48.
The Py terms cancel in the second term, giving Px X + 3 Px X = 48 → 4 Px X = 48.
Solve for X: X = 48 / (4 Px) = 12 / Px.

Thus X can be written as X = 12 * (1 / Px). In the requested format, this is X = 12 * (1/Px). So the numeric coefficient is 12, which aligns with plugging in the given structure. The result 12 is the appropriate coefficient multiplying (1/Px) to express X as a demand function of Px.

Suppose that a consumer had a utility function given by: U=XY3. This consumer has a budget of $48.Fill in the value of this consumer's demand function. X = Answer Question 6[input](1/Px).(For instance, if X = 4/Px, then X = 4 (1/Px) and enter 4)Numerical

Similar Questions

The income and substitution effects explain which of the following?

Suppose p1 = 11, p2 = 3 and M = 63. What quantity of good 2 will Qin demand?

The history of the Nation of Islam (NOI) reveals that they seek recruits from prison.

Malcolm was president of his 6th grade class, he was one of several Blacks students in his school; a straight “A” student, and well like by his peers.

E.D. Nixon graduated from Howard University, majoring in political science.

Sharon Collins links the rise of Black professions to market efficiency. In other words, the labor market success of the Black professional elite is tied to market efficiency.

Regarding the role of race and class in structing the Black community, for those who saw race as a dominant factor --- discrimination was a key obstacle to Black economic development and attainment.

More Practical Tools for Students Powered by AI Study Helper

Homework AI Solver

Stylized AI Paper Writer

Plagiarism Checker Assistant

Citation AI Academic Writing Tool

In-Class Translation Assistant

AI Note Generator

AI Quiz Answers

Past Exam Questions from University Test Bank

Smart Practice Assistant

Adaptive Practice

Making Your Study Simpler

Suppose that a consumer had a utility function given by: U=XY3. This consumer has a budget of $48.Fill in the value of this consumer's demand function. X = Answer Question 6[input]*(1/Px).(For instance, if X = 4/Px, then X = 4 * (1/Px) and enter 4)Numerical