Questions tagged [consumer-theory]

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

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2
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2answers
129 views

How to find price elasticity in the following demand system?

We assume that the logarithmic function of $p_i$ equals the coefficients of the demand equation $w_i$. I have the following demand system: $$ w_{a}=-0.03-0.01 \ \ nk +0.02 \ lcons $$ $$ w_{b}=-0.26-0....
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1answer
47 views

What does this $(\gamma _{0.clothes} + \gamma _{1.clothes} * \ kids)$ term mean in my linear demand equation?

I have the following demand equation system (expenditure ratio model): $w_{clothes}= \beta _ {clothes} + \alpha_{clothes} * \ kids + (\gamma _{0.clothes} + \gamma _{1.clothes} * \ kids)* \ income + ...
2
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1answer
88 views

Are Preference Relations Robust to Aggregation

This is more a question of putting the theory into practice, or at least clarifying the theory in practice. The question has to do with the application of preference relation axioms and aggregation. ...
1
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1answer
310 views

performance as utility function / price?

I am trying to define a 'model' for the perceived performance of a product based on this definition: Presumably, customers take both price and quality into account as they form an overall ...
9
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1answer
614 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 ...
1
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1answer
265 views

On closedness: commodity space

In Intriligator (2002, p. 143) we find the following statement: \begin{align} C = \{(x_1,x_2,\ldots,x_n) : x_j \geq 0,~j=1,2,\ldots,n\} \subset [0,\infty)^n \end{align} Thus commodity space ...
1
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0answers
470 views

Utility function of a representative agent with quasilinear utility

Consider an economy with $n$ consumers with an identical utility function, which is quasilinear in $x$: $$ u_i(x,y) = x+u(y) $$ If we want to represent all consumers by a single representative ...
1
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1answer
84 views

Are these products substitutes or independent?

A consumer's preferences are represented by the following utility function: $$u(x,y,m) = x+y+m$$ where $m$ is money. Are the goods $x,y$ substitute goods or independent goods? Microeconomic ...
2
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1answer
499 views

Do the partial derivatives of the compensated demand have an interpretation?

When obtaining the Marshallian demand from a utility maximization problem we have a classification of normal goods, inferior goods, Giffen-goods, etc.. These are related to the first derivative of the ...
2
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1answer
2k views

Difference between 'ideal variety' and 'love of variety' - International trade

What really is the difference between the "ideal variety" (Lancaster) of a differentiated product approach and the "love of variety" (Dixit and Stiglitz) approach?
2
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1answer
368 views

Demand function of a family

Different family members have different utility functions, but All family members consume the same bundle. For example, consider a family $F$ that has to select a bundle of funiture ($x$) and ...
6
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2answers
359 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(\...
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0answers
315 views

Constrained optimization for $u(x_1,x_2,x_3,x_4)=\alpha \min \{a x_1, b x_2\} + \beta \min \{c x_3, d x_4 \}$ [duplicate]

Suppose preferences are represented by the following utility function \begin{equation} u(x_1,x_2,x_3,x_4)=\alpha \min \{a x_1, b x_2\} + \beta \min \{c x_3, d x_4 \} \end{equation} Write the ...
6
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1answer
1k 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
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0answers
475 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 ...
6
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1answer
483 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
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1answer
357 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 ...
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0answers
67 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
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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 ...
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
16k 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
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1answer
103 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
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1answer
847 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 ...
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2answers
3k 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
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2answers
417 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 ...
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3answers
2k 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
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1answer
516 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 $(-\...
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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
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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
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3answers
1k 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
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1answer
607 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
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4answers
397 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
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0answers
85 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
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2answers
2k 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
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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 ...
2
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2answers
129 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
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1answer
166 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
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5answers
954 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
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1answer
72 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 ...
4
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2answers
7k 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
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1answer
835 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
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2answers
10k 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
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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
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1answer
2k 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 ...
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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 ...
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2answers
2k 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 $\...
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1answer
279 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
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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) = ...
6
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3answers
298 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
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2answers
627 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 $$...