Stack Exchange Network

Stack Exchange network consists of 174 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers.

Visit Stack Exchange

Questions tagged [consumer-theory]

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

6
votes
1answer
596 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 ...
2
votes
0answers
384 views

What are cross price effects for the case of perfect substitutes?

U$(x_1,x_2)$ = $x_1 +x_2$ in the case of perfect substitutes If $p_1 < p_2$ then $(x_1^*,x_2^*)$ = $(m/p_1,0)$, if $p_1 > p_2$ then $(x_1^*,x_2^*)$ = $(0,m/p_2)$ Trying to figure out how a ...
5
votes
1answer
402 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 ...
4
votes
1answer
318 views

Strict preference relations and utility representations

Suppose I have a rational preference relation $\succsim$ on some consumption set $X$. Suppose also that there is a utility function $u:X \to \mathbb{R}$ representing $\succsim$. Definition: A ...
3
votes
0answers
53 views

Competitive Equilibrium in Securities Market: First Welfare Theorem

I'm working through Kerry Back's "Asset Pricing and Portfolio Choice Theory" book. Trying to work through the proof of the First Welfare Theorem in the context of securities markets on page 58. Back ...
5
votes
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 ...
6
votes
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
votes
1answer
11k 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 ...
2
votes
1answer
90 views

How can you tell if any given preference structure is continuous or not?

From a given preference structure (not the utility function), how can one tell if it satisfies the continuity axiom of preferences?
5
votes
1answer
561 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 ...
6
votes
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 ...
8
votes
2answers
257 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 ...
15
votes
3answers
1k views

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 ...
6
votes
1answer
375 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 $(-\...
3
votes
2answers
1k views

Why doesn't Costco simply raise prices and nix the membership fee?

I know little about the field of economics. I realize this question may be too rudimentary for this forum but I am sure someone here can explain this. My question concerns Costco, which is a ...
2
votes
2answers
1k views

Intermediate macroeconomics: optimal bundle for quasilinear utility?

How would I go about solving this question: Assuming consumer's utility function is $U(C,L)=c+2l^{0.5}$, consumer earns a wage of 0.5/hour, $h=24$ and there is no real dividend and tax is $T=11$. ...
4
votes
3answers
562 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 ...
2
votes
1answer
430 views

Equivalence of inada conditions and non-negativity constraints?

In a standard constrained utility maximization problem with an agent's preferences defined over good(s), does the imposition of Inada conditions on the utility function preclude us from adding non-...
4
votes
4answers
355 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 ...
2
votes
0answers
79 views

Net effects of mergers from consumers' perspective

When Anthem Insurance acquired Cigna Insurance in July 2015, this reduced consumer choice and possibly transferred negotiating power from the consumer to the insurance provider. But the merger also ...
4
votes
2answers
1k views

Why do lump sum transfers affect prices?

Let's suppose that I want to maximize total welfare (Social Planner Problem) using lump sum transfers to individuals. It's known then that the price ratio changes relative to when there are no lump ...
11
votes
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 ...
2
votes
2answers
122 views

Reverse of broken window fallacy for file sharing/piracy

Adult Swim roughly brings forward the following argument in the video 'film piracy feeds babies': While jobs may be lost in the movie or music industry, they might be created in another. Money that ...
5
votes
1answer
139 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 ...
9
votes
6answers
851 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 ...
4
votes
1answer
68 views

How long are consumers willing to wait in order to find a bargain?

I have (what I believe to be) a microeconomics question that I'd like to explore: How long are consumers willing to wait to find a bargain on an item they'd like to purchase? I believe the ...
2
votes
2answers
5k views

How to derive utility possibility frontier?

I'm trying to derive the utility possibility frontier of a economy whose consumption contract curve is $$y_A = \frac {y} {x} x_A$$ and $$y_B = \frac {y} {x} x_B$$where $x_A + x_B = x$ and $y_A + y_B= ...
3
votes
1answer
507 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 ...
5
votes
2answers
6k 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 $$x_M =\frac{p_y^2}{4 p_x^2}$$ $$y_M = \frac{m}{p_y} - \frac{p_y}{4 p_x}$$ ...
8
votes
1answer
5k views

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 ...
4
votes
1answer
1k views

How does one calculate compensating variation for multiple price change?

For a single variable price change, $$CV = - \int_{p_x^o}^{p_x^f} x_H(\rho,p_y,v^o)d\rho$$ $x_H$ is the Hicksian demand function for good $x$. What happens if both prices change? How does one ...
5
votes
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 ...
2
votes
2answers
1k views

If strict convexity of indifference curves isn't assumed, does MRS have to be negative?

Strict convexity is defined as Let $X$ be a convex set in a real vector space and let $f: X\rightarrow \Bbb{R}$ be a function. $f$ is called strictly convex if $\forall x_1 \neq x_2 \in X,$ and $\...
1
vote
1answer
217 views

Why are allocation and distribution important consequences of the second welfare theorem?

I'm reading Intermediate Microeconomics: A Modern Approach by Hal Varian. On page 606, he states: The Second Theorem of Welfare Economics states that as long as preferences are convex, then every ...
3
votes
2answers
1k views

Struggling with uncompensated/compensated demand

I'm working on a problem set for my intermediate microeconomics course, but I'm having trouble deriving the compensated and uncompensated demand functions. This is the utility function: $U(x, y, z) = ...
5
votes
3answers
266 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 ...
3
votes
1answer
444 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 $$...
6
votes
1answer
2k views

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 ...
2
votes
0answers
49 views

Are there any situations where the elasticity version of the Slutsky equation can only be used compared with the regular Slutsky equation?

Regular Slutsky Equation: $$\frac{\partial x_M}{\partial p_x} = \frac{\partial x_H}{\partial p_x} - \frac{\partial x_M}{\partial m} x _M$$ Elasticity Slutsky Equation: \begin{align*}\varepsilon_{x,...
4
votes
2answers
338 views

Why does the definition of MRS follow from the implicit function theorem?

TRAIN OF THOUGHT 1: From what I understand, $MRS$ is calculated as $$dU = U_x dx + U_y dy =0$$ which by rearrangement yields $$\frac{dy}{dx}= -\frac{U_x}{U_y}$$ So suppose I have $$U(x,y) = \...
4
votes
1answer
162 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 ...
5
votes
1answer
142 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 ...
2
votes
0answers
275 views

Probability of states of nature

I've been given the following question and would really appreciate any help on part a. I've looked over all of my resources for this course and we have always been given the probability of the ...
6
votes
2answers
4k views

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?
2
votes
2answers
2k views

Sign of substitution and income effect of a price change

I just want to confirm with my understanding. It is correct to say that no matter price increase or price decrease, the substitution effect is always negative for both inferior goods and normal goods....
4
votes
1answer
129 views

Why does $\varepsilon_{x,p_x}^H =-s_y \sigma $?

Suppose I have two goods $x$ and $y$ and their associated prices $p_x$ and $p_y$. Income $m$. $x^H$ is Hicksian demand and $x^M$ is Marshallian demand. Slutsky Equation: $$\frac{\partial x^M}{\...
3
votes
1answer
2k views

Corner solution-consumer theory [closed]

$$U(q_1,q_2)=4{q_1}^{0.5}+q_2$$ $$P_1=1$$ and $$P_2=2$$ Initially $$Income=40$$ Then the question asks :how do I know what income I can get a corner solution? Anyone can help me with this? Thank you
3
votes
1answer
5k views

Calculate the substitution effect

Utility function $$ U=4{q_1}^{0.5}+q_2 \\ Y=10 $$ $$ p_1=p_2=1 $$ Then $p_1$ rises to 2. I would like to ask how to calculate the substitution effect on the demand for q1? What I have done is ...
3
votes
2answers
452 views

Does there always exist a consumption bundle at which the indirect utility function is the inverse of the expenditure function?

Two questions: Given $v(\vec{p},m)$ and $e(\vec{p},\bar{U})$, is there only a single point at which these are inverses of each other? Does an inverse always exist for a given price vector $\vec{p}$,...
2
votes
2answers
53 views

Does anyone know of any resources that discuss the differences between Hicksian and Marshallian remanding in depth and in an organized way?

I don't understand why the Marshallian and Hicksian demand have such different properties. Both are functions from $$\Bbb{R}^n_+ \times \Bbb{R}_+ \rightarrow \Bbb{R}_+^n$$both are solved using the ...