Questions tagged [consumer-theory]

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

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What are Giffen Goods?

What exactly are Giffen goods and are they of purely theoretical interest or has there been empirical evidence of their existence?
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3answers
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Are monotonic and continuous preferences necessarily rational?

Let $\succsim$ be a strictly monotonic and continuous preference relation, and let $X=\mathbb{R}^{n}$ be the consumption set. Is rationality of $\succsim$ implied by these conditions? I think ...
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3answers
159 views

Current knowledge about the empirics of consumer theory

I would like to get up to speed on the current state of empirical work done to test the assumptions and predictions of consumer theory (think Chapters 1, 2, 3, and 6 of Mas-Colell et al.). Can anyone ...
12
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2answers
10k views

The relationship between the expenditure function and many others!

I dont understand the relationships between Hicksian demand, walrasian demand (marshallian), the expenditure function and the indirect utility function (including the value function V(b)). I have ...
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3answers
4k views

Is scalping tickets harmful?

IMHO, scalping tickets is no different from legitimate arbitrage unless manipulative. Iirc, arbitrage increases surplus and hindering scalping is setting a price ceiling which leads to deadweight ...
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2answers
24k views

Marshallian Demand for Cobb-Douglas

When trying maximize the utility having a cobb-douglas utility function $u=x_1^ax_2^b$, with $a+b = 1$, I found the following formulas (Wikipedia: Marshallian Demand): $x_1 = \frac{am}{p_1}\\ x_2 = \...
10
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1answer
503 views

Is it possible to derive indifference curves given marshallian demand function?

In a two good world, will a marshallian demand function the likes of D(p,m) where p is the price of one good and m the income yield a utility function or ...
9
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6answers
871 views

Piracy/File sharing - Why aren't songs, movies or books given for free?

Why aren't songs, movies or books given for free (+ads)? i. Every minute, people are pirating and there is no stopping that. If people see 0.99 for a song on iTunes and 0.00 for a song on a torrent ...
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2answers
798 views

Thin indifference curves

If a consumer follows the rationality axiom of continuity (i.e. no jumps in his preferences), the indifference curves of a utility function are said to be thin. Why does continuity ($x \succeq y \...
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1answer
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Homogenous of degree one in utility function.

Question My solution is as follows. Please check my solution. If I make a mistake, please tell. I am really not sure about my solution. Thank you U(x) is homogenous of degree one i.e. u(...
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3answers
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Why does Slutsky compensation “overcompensate” the consumer?

Suppose I have a Marshallian demand function $x_M(p_x^0,p_y,m^0)$. As I understand it, Slutsky compensation is defined as $$T_S = \Delta p_x \cdot x_M(p_x^0,p_y,m^0)$$ Can someone explain why this ...
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2answers
861 views

When can one safely talk about decreasing marginal utility?

One thing I hear a lot is talk of decreasing marginal utility—the idea being that additional units of a good become progressively less attractive the more units of that good one has already. However, ...
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1answer
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Leontief preferences

I can solve most utility maximization problems using my mathematical knowledge .... but not when it comes to Leontief preferences. I do not have a book to lean on (am self-studying), so would really ...
8
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1answer
466 views

Competitive equilibrium in Leontief economies

Consider an economy in which all consumers have, possibly different, Leontief utilities. Since preferences are not strictly convex, it is not guaranteed that a competitive equilibrium exists. I found ...
8
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2answers
317 views

Log-normality assumption in consumption based asset pricing

Consider a very basic discrete time representative consumer maximization problem with CRRA utility. There exist a risky asset with time $t$ price $p_t$ that pays time $t+1$ dividend $d_{t+1}$ , and a ...
8
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0answers
433 views

Calculus and Indifference Curves in an Urban Economics Example

I am reading the paper 'The Structure of Urban Equilibria' by Jan Brueckner. It uses a monocentric city model, where all consumers earn income $y$ at the centre of the city. They buy $q$ housing for ...
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2answers
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What is an example application of a quasilinear utility function?

I am told a quasilinear utility function is a function like $$U(x,y) = \sqrt{x}+y$$ My Question: Can someone provide a real world example of a quasilinear utility function?
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1answer
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Do perfect complements have to be normal goods? If so, why?

Two goods $x,y$ are perfect complements if they have the utility function $$U(x,y) = \min \lbrace ax,by \rbrace $$ $$a,b \in \Bbb{Q}^+$$ My professor said $x,y$ have to be normal goods but didn't ...
6
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1answer
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Gross substitutes vs. net substitutes

Wikipedia explains the difference between products that are "gross substitutes" and products that are "net substitutes". However, the mathematical explanation doesn't give much intuition about these ...
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3answers
6k views

What is a rational consumer?

There is a lot of debate on whether or not consumers and investors are rational. Unfortunately, I haven't seen much qualification for what is called a rational consumer. What are the requirements ...
6
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1answer
2k views

Prove the budget correspondence is upper hemi-continuous

Let $p \in \mathbb{R}_+^L$ be price vector and let $w \in \mathbb{R}_+$ be wealth of the consumer. Define the Budget correspondence $B(p,w) =\{x \in \mathbb{R}_+^L : p\cdot x\le w \}$ . How to prove ...
6
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1answer
689 views

Does a monotonic transformation of a homothetic utility function imply the preference relation on the set of consumption bundles is still homothetic?

Does a monotonic transformation of a homothetic utility function imply the preference relation on the set of consumption bundles is still homothetic? Obviously, if a utility function on a set of ...
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3answers
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What is the point of the indirect utility function?

Where does this have application? I understand how the demand function may be arrived at using the utility maximization problem but I don't understand where the indirect utility function is used and I ...
6
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1answer
1k views

If the Engel Curve of a Cobb-Douglas utility function is positive and linear, than does that mean it is neither a necessity nor a luxury good?

Since the concavity of the Engel Curve determines whether it is a necessity or luxury (i.e. how fast quantity demand changes in relation to changes in income), and since the second derivative of a ...
6
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1answer
185 views

Shopping example in Kőszegi / Rabin (2006)

In "Section IV Shopping" of Kőszegi / Rabin (A model of reference-dependent preferences, QJE 2006), the example of consumer buying a pair of shoes is given. They claim that "her disutility from ...
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3answers
16k views

Quasilinear Utility Functions

We know if the utility function is quasilinear (QL) w.r.t good 1, then the demand for other goods is independent of income (no income effect for goods $(2,\dots, N)$). But is the reverse implication ...
6
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1answer
13k views

Differences between Hicksian and Slutskian approaches

When deriving the substitution effect for both Slutskian and Hicksian definitions, a 'phantom' budget line is drawn.However, for a Slutskian definition, the 'phantom' budget line is drawn parallel to ...
6
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3answers
2k views

Which utility function yields a constant price elasticity of demand function?

How do I know which utility function I can use to find an isoelastic demand function, e.g., $x(p)=Ap^a$? And similarly, which cost function can I use to find an isoelastic supply function? Does it ...
6
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1answer
415 views

Prove that a continuous $\succsim$ is quasilinear

This question is closely related to Mas-colell, Whinston, Green: Microeconomic Theory, Question 3.C.5b Let $\succsim$ be a strictly monotone, continuous, and rational preference relation on $(-\...
6
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1answer
912 views

Weak Axiom of Revealed Preference

Maybe this is a well-known fact that I have somehow overlooked or forgotten etc., but I found myself curious recently if there are any conclusions about WARP holding over different dimensions for a ...
6
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1answer
718 views

Intuition for why $EV>CV$ for a normal good

I understand the mathematical proof and the graphical illustration behind this property ($EV>CV$ for the variation in the price of a normal good), but I still do not understand the economic ...
6
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1answer
815 views

Usefulness of the Convexity Axiom

I'm asked to write an essay supporting the statement which says the convexity axiom has little economic content and should be eliminated from the economic models of consumer theory. I'm supposed to ...
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2answers
754 views

Why do so many models assume homothetic preferences?

...when Engels Law, backed by a good amount empirical evidence, demonstrates that overall consumer preferences are not homothetic. See for example, Jorgenson (1997)
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2answers
343 views

Does consumer theory assume that utility functions are consistent overtime?

I'm interested in how we model a consumer with a changing utility function over time. Example: an individual's demand for candy/sweets at 10 years of age will be different when he is 20,30 or 40 ...
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3answers
2k views

intertemporal utility function usage : calculating consumption

I have encountered this a lot in my exams and can not seem to understand how to use these functions here is an easy exemple : A consumer who will only live 2 periods receives 1000€ in the first ...
5
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2answers
8k views

Why is the income effect zero for quasilinear utility functions?

Suppose I have the utility function $$U(x,y) = \sqrt{x} + y$$ subject to budget constraint $$p_x x + p_y y = m$$ Then $$x_M =\frac{p_y^2}{4 p_x^2}$$ $$y_M = \frac{m}{p_y} - \frac{p_y}{4 p_x}$$ ...
5
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2answers
187 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 ...
5
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3answers
288 views

Do claims in economics require proofs?

My professor stated four axioms in class Scarcity Rationality (aka purposive behavior) Stable Preferences Equilibrium I don't understand what these axioms are for. I am used to axioms with ...
5
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1answer
150 views

Why can't I use TMoLM for this bliss point problem?

I am having difficulty with a particular bliss point problem. The basic issue I have is my approaches seem flawed and I can't tell why. The equation is $$U(x,y) = 36x -4x^2 + 6y-2y^2$$ subject to ...
5
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2answers
290 views

CES preferences intuition

I asked this question on math.stackexchange but deleted it from there and brought it here. I had a question about Constant Elasticity of substitution type preferences of the form: $$U=\int_{0}^{1}(c(\...
5
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1answer
659 views

Does the Marshallian demand function always include prices and income?

I have the following utility function: $$U(x_i)=x_1x_2+x_3$$ with budget constraint: $$p_1x_1+p_2x_2+p_3x_3\leq I$$ I use the Kuhn-Tucker method to find the optimal choices of the Utility ...
5
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1answer
463 views

Saturation of durable goods

It seems one factor ignored (or is it?) in economic theory is saturation of durable goods. By this I mean the fulfillment of fixed need for durable goods. We can imagine income to be divided between ...
5
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1answer
646 views

Money Metric Utility Function: Budget constraints become Utility Functions?

Im currently reading up on the "money metric utility function" (also known as the minimum income function or direct compensation function). By definition it is defined as: $$m(\text{p},\text{x})\...
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1answer
6k views

Is MRS supposed to have a minus sign or not? What's there to say about convexity of preferences?

If we have a utility function $U(x_1, x_2) = x_1(x_2+1)^2$ of some consumer, then $$MRS_{x_1, x_2} = \frac{\color{red}{-}(x_2+1)}{2x_1}$$ Some books have a $\color{red}{-}$. Others and Wiki don't ...
5
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1answer
101 views

Utility Maximisation Subject to Income and Time Constraints

The consumption of economic goods often takes time. Consider, for example: Transport services, eg flights, rail journeys; Leisure goods, eg watching a film, visiting a park. I would like to explore ...
5
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1answer
2k views

Stone-Geary utility function, derivation of Marshallian demand

I am reading a paper on structural change. It has three sectors and it features non homothetic utility function, namely a CES with some thresholds for the consumption of the three goods. The UMP is as ...
5
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1answer
153 views

What are the economic benefits of SLAPP in file sharing/piracy?

Spin-off from Piracy/File sharing - Why aren't songs, movies or books given for free? What are the economic benefits of SLAPP in or out of file sharing/piracy? There's a comment in above link ...
4
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3answers
796 views

A few clarifications on Utility equations and indifference curves?

I have the utility equation $U(a,b) = a^{2}b^{3}$ How can I tell if the indifference curves are convex? I was under the impression that if: $U_{a} > 0$ and $U_{b} < 0$ then the curve would ...
4
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4answers
383 views

When a support function is found to be more profitable than the primary business

Sometimes in the course of pursuing its primary business, a company discovers an unexpected source of revenue. It is particularly interesting in cases when a humble support function is found to be ...
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2answers
1k views

Meaning of Additively Separable, Linear in X

Often I see both in micro and macro two common terminology : Additively separable. Linear in price or linear in probability. I understand exactly as they sound by looking at the functional form ...