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.

ECON 302 AL1 SP25: Inter Microeconomic Theory (Buckley, B)

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)

View Explanation

Log in for full answers

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?

In a consumer society, many adults channel creativity into buying things

Economic stress and unpredictable times have resulted in a booming industry for self-help products

People born without creativity never can develop it

A product has a selling price of $20, a contribution margin ratio of 40% and fixed cost of $120,000. To make a profit of $30,000. The number of units that must be sold is: Type the number without $ and a comma. Eg: 20000

Which of the following statement regarding cost is correct:

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