Suppose that a consumer had a utility function given by: U=X2Y4. This consumer has a budget of $12.Fill in the value of this consumer's demand function. X = Answer Question 3[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: a utility function U = X^2 Y^4 with a budget I = 12 and prices Px and Py. For a Cobb-Douglas utility of the form U = X^m Y^n, the optimal expenditure shares on each good depend on the exponents m and n. Specifically, the share of income spent on good X is m/(m+n). Here, m = 2 and n = 4, so the share allocated to X is 2/(2+4) = 2/6 = 1/3.

Thus, the optimal quantity of X satisfies: X = (share of income on X) * (I / Px) = (1/3) * (12 / Px).

Compute the product: (1/3) * 12 = 4, so X = 4 / Px.

Therefore, the expression for X in terms of Px is 4 * (1/Px). This matches the prescribed format where X is given as [input]*(1/Px) with the input value equal to 4.

If one wanted to verify using the budget constraint, the demand for Y would similarly be Y = (n/(m+n)) * (I / Py) = (4/6) * (12 / Py) = 8 / Py, which confirms the remaining budget allocation to Y under Cobb-Douglas preferences with the given exponents.

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

Suppose that a consumer had a utility function given by: U=X2Y4. This consumer has a budget of $12.Fill in the value of this consumer's demand function. X = Answer Question 3[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 image above shows which demand curve?

Suppose the demand equation for a product is given by: Qd = 50 - 12\frac{1}{2}P b) Calculate the price at which consumers would demand 10 units of the product. Price: $ [Fill in the blank],

Suppose the demand function for Good X was given by: QDx = 58 - 4Px.Calculate the reservation price for the 38th unit.(Do not include a $ sign in your response.)

Suppose the demand for a good was given by the function: QD = 230 - 0.1 P.Calculate the choke price of this demand function.(Do not include a $ sign in your response.)

The demand function for this good is given by: QD= 225 -0.5P. Find quantity demanded when price is $300.

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