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

Question

BlackTom AI · Accepted Answer

Question restatement: The problem gives p1 = 11, p2 = 3, and M = 63, and asks for the quantity of good 2 that Qin will demand.

Key point to start with: to determine a demand for good 2, we need Qin's preferences (the form of the utility function or the underlying demand system). Without specifying how Qin values goods 1 and 2 relative to each other, there is no unique solution for x2.

Reasoning under common benchmark models:
- If Qin faces a Cobb-Douglas utility u(x1, x2) = x1^a x2^b with a + b = 1 (a and b are the expenditure shares on goods 1 and 2), the demand for good 2 is x2 = (b * M) / p2. If we assume a = b = 0.5 (equal shares), then x2 = (0.5 * 63) / 3 = 31.5 / 3 = 10.5. In this benchmark, Qin would demand 10.5 units of good 2.
- If Qin has preferences of perfect substitutes with u = x1 or u = x2 (i.e., the agent cares only about one good and the cheaper good dominates), Qin would spend all income on the cheaper good 2 since p2 = 3 < p1 = 11. Then x2 = M / p2 = 63 / 3 = 21, a clearly different outcome from 10.5 or any other particular value.
- If Qin has perfect complements, such as u = min{x1, x2}, the optimal bundle under a linear budget constraint 11x1 + 3x2 ≤ 63 would typically satisfy x1 = x2, giving 11x + 3x = 63 → 14x = 63 → x = 4.5, so x2 = 4.5 in that case.

Observations:
- In each of these standard specifications, the resulting x2 is 10.5, 21, or 4.5 depending on the assumed utility form. None of these straightforward benchmark cases yield x2 = 6.
- The absence of Qin’s utility function or any additional constraints means the exact quantity of good 2 cannot be uniquely determined from p1, p2, and M alone.

Potential reasons for the reported answer (6):
- It is possible the dataset assumes a specific utility specification not stated in the prompt (for example, a nonstandard Cobb-Douglas with a particular share b that yields x2 = (b * 63) / 3 = 6, which would require b = 18/63 ≈ 0.2857, an unusual but possible preference weight).
- Alternatively, there could be a misprint or mismatch between the question data and the provided answer.

Summary in plain terms: Without knowing Qin’s utility function or preference structure, the quantity of good 2 demanded cannot be uniquely determined from p1, p2, and M alone. Under common models, the predicted x2 values would vary (e.g., 10.5 under equal Cobb-Douglas shares, 21 under pure substitution favoring good 2, or 4.5 under a perfect-complements setup). The fact that the listed answer is 6 suggests either a nonstandard or unstated preference specification, or a data error. The key lesson is that demand quantities hinge critically on the assumed preferences, not just prices and income.

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

Similar Questions

The income and substitution effects explain which of the following?

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)

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