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Questions tagged [consumer-theory]

the study of consumer choice and its fundamental underpinnings in preferences and constraints.

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2answers
568 views

Fast way to write out the utility optimization problem for a Cobb-Douglas function?

In my last problem set, I had to solve both the Utility Maximization Problem (UMP) and Expenditure Minimization Problem (EMP) for a Cobb Douglas utility function. Recall, Cobb Douglas is defined as $$...
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0answers
28 views

Shortcuts for elasticity of substitution

How can I find the elasticity of substitution (I know the definition) if I know the utility function $u(x,y)$? I know its increasing in $x$ and $y$, etcetera, and has everything else you want from a ...
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27 views

On shapes of indifference curves

I encountered this question in Microeconomics by Pindyck and Rubinfeld. The question says that "Suppose Jones and Smith have each decided to allocate $1000 per year to an entertainment budget in the ...
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1answer
24 views

Budget Constraint in Utility Maximisation Problem with Lagrange Multipliers

Lets say we have a utility function $U: \mathbb{R}^{2} \to \mathbb{R}$ given by $U(x,y)$ and a binding budget constraint $p_{x} x + p_{y} y = m$, where $p_{x}, p_{y}$ are prices of goods $x,y$ and $m$ ...
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1answer
19 views

Optimizing Lagrangian Function Subject to 4 Input/Output Constraints:

The objective function: $$\text{utility}=U\left(x_{c}, y_{c}\right)$$ subject to, $x_{o}=f\left(y_{i}\right)$ $y_{o}=g\left(x_{i}, x_{o}\right)$ $x_{c}+x_{i}=x_{o}+x^{*}$ $y_{c}+y_{i}=y_{o}+y^{*}$ ...
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1answer
88 views

Consumer Utility Maximization equivalent of economies of scope

Economies of scope captures the idea of having efficiency in variety. I've come across this idea only in producer theory to capture the idea that companies may benefit from their ability to reduce ...
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1answer
776 views

Intertemporal consumption question

This question is driving me nuts. Suppose, an individual lives for two periods. In each period she consumes only one good,which is rice. In period 2, she can costlessly produce 1 unit of rice, but ...
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0answers
197 views

MWG Example 3.E.1

I do not understand how Mas-Collel, Whinston, and Green derive the Hicksian demand functions in Example 3.E.1 in their textbook. Allow me to give further background regarding the problem: The ...
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1answer
45 views

How to find Marshallian demand of $u(x,y,z)=x+y^2+2z^2$?

Consider the utility function $u(x)=x+y^2+2z^2$. How to derive Marshallian demand for a consumer with these preferences?
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157 views

Derive demand function $x(p,w)$ from utility function $u(x) = \min\{x1, x2\} + x3$

I know how to solve the two-good case with $u(x) = \min\{x1, x2\}$, but the addition of $x3$ confuses me. Problem Derive the demand function $x(p,w)$ from $u(x) = \min\{x1, x2\} + x3$ What I did ...
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21 views

weakly preferred consumer bundles

I am currently studying consumer choice and saw that weak preference refers to when an individual prefers or is indifferent to two bundles (such as bundle A and bundle B). I was wondering what is ...
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1answer
32 views

Is Buy Nothing Day a classist protest of Black Friday?

I hope this isn't off topic, it seems specifically economic to me even though it probably intersects with other fields of study. Black Friday is seen as an iconic hallmark of consumerism, and Buy ...
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1answer
41 views

Why is the marginal utility of money assumed to be constant in Marshallian Theory of Consumer Behaviour

While studying the Marshallian Theory of Consumer Behaviour, I came across the assumption that the marginal utility of money is assumed to be constant. Can someone please explain why is this so?
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1answer
29 views

Is there any evidence for consumer utility-maximising behaviour, at individual or market level?

Even though utility maximisation is ubiquitous in economic textbooks to model consumer behaviour, its usefulness is rarely demonstrated by evidence. Is there any evidence that some consumers do ...
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2answers
174 views

Corner solution of the maximization problem

Answer Hello, I upload the actual question with my 8-pages answer. Please can you check it. Is there a corner dissolution for $c=\gamma$. Please share your ideas. Thanks.
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2answers
1k views

Utility function used to indicate bliss point

How does one create a utility function to indicate existence of a bliss point? what do the goods marshillian demands look like in such a situation?
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44 views

Special case for wealth allocation with quasilinear utility functions

Building on this question, regarding the answer from Bkay: Is it a general statement that when $m < \frac{p_y^2}{4 p_x}$, all income will be allocated to $x_M$? What about the case when the ...
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22 views

Change in Consumer Surplus with two goods

Suppose we have two goods, price changes in the two are independent; having seen this question I am considering why the change in total Consumer Surplus is the sum of the change in Consumer Surplus ...
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1answer
123 views

Are there any other rational preference relations without utility function representations, besides Lexicographic?

It seems like lexicographic isn't that "special". Like yes it is special in that supposing it has a utility function gives you a bijection from the rationals to the reals, but I mean unique in some ...
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3answers
4k views

Optimal decision for perfect substitutes utility function ?

Given $u(x_1,x_2)=4x_1+14x_2$ and $m=\frac{1}{2}x_1+\frac{3}{2}x_2$, I shall choose the optimal decision among: $a)(2m,\frac{2m}{3})$ $b)(2m,0)$ $c)(\frac{m}{2},0)$ $d)(0,\frac{2m}{...
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2answers
253 views

Finding demand functions for an unusual utility function

I have a utility function: $U = x + \min\{x,y\}$ I want to draw the indifference curve and find the demand functions. Will it be the case of the usual perfect complements? Also, what preferences ...
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20 views

Would households rather live in a world with or without the unemployment insurance?

Would households rather live in a world with or without the unemployment insurance? What is a good example of world in which unemployment insurance is seen as a benefit, and not a hindrance?
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1answer
59 views

Consumer Theory question [closed]

You plan to use the following specification for an empirical study: $$e_i = \alpha_i + \sum_{j=1}^{n} \beta_{ij}p_i + \gamma_iy +\delta_i, i=1,...,n$$ where $e_i$ is the consumer's expenditure on ...
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1answer
62 views

Log Utiliy Function Trick

I am watching Lecture 3 of Yale's Financial Theory Lecture (by John). At about minute 50 he explains something along this line (with reference to log utility functions). MUx/Px=MUy/Py And ...
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1answer
76 views

Identifying utility function

I recently came across a utility function with min written at the start. I assumed that it was a case of a leontief utility function, and only after going ahead with the problem I found out that it is ...
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Index Theorem for Regular Infinite-Agent Economies

A formulation of the Index theorem states that for a regular economy: $\sum_{p | z(p) = 0, p_L = 1} index p = +1$ Does this hold for models with uncountably many agents?
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1answer
35 views

Prove that $h(p,u) = \nabla_p e(p,u)$ is implied by Roy's identity

I am struggling a bit with the math in my first graduate microeconomics course. I'm not sure if this belongs here. If it doesn't, please direct me to a more appropriate place. Below is one question ...
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15 views

CPI Bias with consumers using computers extensively

I was studying Microeconomics from Microeconomics by Pindyck and Rubinfeld where it was written that CPI calculated on Laspeyres index has overstated the cost of living for consumers who use computers ...
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2answers
62 views

Indifference Curves and Preferences

Why are averages preferred to extremes on the same indifference curve? Doesn't everything along an indifference curve have the same preference?
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2answers
309 views

Difference between Engel curve and income expansion path

I was scrolling through many questions on this site about income offer path and it appeared to me that income offer path, income expansion path, engel curve all are different terms with same meaning, ...
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2answers
96 views

Set Theory Properties of the Budget Constraint

In Microeconomic theory, the budget constraint is defined by 4 distinct properties: It is Bounded Closed Convex Non-empty The 1. 2. and 4. are very straight forward and the benefits in terms of ...
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0answers
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Difficulty Understanding CPI (Consumer Price Index)

Here's a question about CPI in my microeconomics text (Pindyck), which I don't seem to understand: The price of computers has fallen substantially over the past two decades. Use this drop in price ...
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1answer
39 views

Opportunity Cost effect on benefits

My question is the following: Let's say a person has two career choices. He would be succesful in both, but in one of them he is slightly better and thus he will do better. So let's say career A will ...
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2answers
98 views

Assumption of sufficient wealth in quasi-linear preferences

Whenever we talk about quasi-linear preferences, we assume that the consumer is sufficiently wealthy. As far as I understand is that we need that assumption in order to obtain an interior solution. ...
2
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1answer
3k views

Are Cobb-Douglas preferences homothetic?

Our lecture defined a preference to be homothetic, if the following is true: $$(x_1, x_2) \thicksim (y_1, y_2) \Leftrightarrow (kx_1, kx_2) \thicksim (ky_1, ky_2)$$ Cobb-Douglas preferences can be ...
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2answers
290 views

If the (direct) utility is concave in all goods, is the indirect utility necessarily concave in wealth?

Suppose that the direct utility $u(x_1,...,x_n)$ is concave in each of its arguments. Does this imply that the indirect utility $U(w,p)$ is concave with respect to $w$? If all goods are normal than ...
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2answers
73 views

The mathematical proof of a monotonic utility transformation does not restrict the use of strictly decreasing monotonic functions. Why bar them?

I understand from an intuitive sense that decreasing monotonic transformations will skew the choices and ordinality. But mathematically the $F'(U(x,y))$ just cancels out each other out in numerator ...
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1answer
122 views

Is there a proof for composite commodity theorem?

I have been reading Economics and Consumer Behavior by Angus Deaton and John Muellbauer, specifically reading up on Composite Commodity Theorem, which states: if prices move in parallel to each ...
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1answer
44 views

Asymmetric (in sign) cross-price derivatives in consumer-theory problem

I'm puzzled why, in the following optimal-choice problem, good $x$ depends on price $p_y$ but the opposite is not true. Should not the sign of $\frac{\partial x}{\partial p_y}$ be the same of $\frac{\...
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4answers
4k views

Can someone explain graphically why MRS is invariant under monotonic transformation?

Let $U(x,y)$ be a utility function. Suppose I have an indifference curve for which $U(x,y) = \bar{U}$. Then $dU = 0$ along the curve and I can rearrange to find the MRS. Suppose I have a monotonic ...
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2answers
113 views

Why do housing and parking cost more in urban than in rural areas, but road access doesn't?

In city centres, land is more expensive than in suburban or rural areas, as land is scarce. Consequentially, housing and parking in cities cost more. However, the same is not true for using the road ...
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1answer
53 views

A weaker definition of local non-satiation can also imply indifference “curve”

Let $u$ be a continuous utility function on $\mathbb R^2_+\setminus\{0\}$. Consider the following three conditions: Local non satiation says that for any $x \in X$ and $\epsilon > 0$, there exists ...
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1answer
68 views

What is the iff condition for a preference with linear Engel curves (all Engal curves are linear)?

If we restrict the consumption at $\mathbb R_+^n$, then it seems like we are implicitly assuming that the Engel curve pass through the origin, so the iff condition would be homothetic preference. ...
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38 views

Household utility functions

In basic consumer theory, there is an individual consumer who has a utility function, this function induces the individual's demand (given budget and prices), and this in turn determines the ...
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0answers
42 views

Finding the optimal consumption bundle given the strictly concave utility function $v(x,y) = U(x) +y$?

I am also finding it difficult to understand what are the fundamental differences between analysing optimal bundles between concave and convex functions ? Does it also happen that the optimal bundle ...
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1answer
28 views

How can i determine the homogeneity degree of Stone Gaery function? [closed]

I dont know how to demonstrate homogeneity degree of this function $(X-\alpha)^{\beta}(Y)^{1-\beta}$ Any idea? Thanks.
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Do you know any paper that discuss the effect of the deterrence of fines of individuals' behaviours? What is the difference between a fine a fee?

According to Gneezy and Rustichini the presence of an extrinsic reward in activities with a level of intrinsic motivation (e.g. volunteering) reduces intrinsic motivation, thus it may determine ...
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2answers
59 views

Market baskets: cross-border comparisons

The concept of a market or consumer basket is quite intuitive. I assume a market basket for a given country tells for which goods an average person spends how much of her money. To be able to compare ...
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3answers
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Is the price-quantity diagram fundamentally wrong?

I have wondered about the following diagram: which shows a relationship between Price (Preis) and quantity (Menge). The supply (Angebot) curve is rising with the amount; the demand (Nachfrage) is ...
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1answer
25 views

Substitution effect when price of both goods change by the same percentage

I am trying to grasp the concept of income- and substitution effects. The way, I've understood it, the decomposition bundle is found, at the original indifference curve, where the slope equals that ...