Questions tagged [consumer-theory]

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

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3
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4answers
138 views

Teaching ethics and its Economic value

Is there any literature that considers the benefits of ethical behaviour or teachings in Economics in terms of its value added to human capital? If there is no difference in value added, then is ...
2
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1answer
400 views

How to interpret income elasticity of demand

My question: Income elasticity of demand for apple is $\gamma$. Cross elasticity of demand between apple quantity and orange price is $\psi$, What is the impact on apple's revenue if consumers'...
3
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1answer
381 views

Diminishing Nature of Utility Function From Convexity of Preference $\succsim$?

Is diminishing nature of utility function in consumer theory stemming from the assumption of convexity on the preference relation $\succsim$? My understanding is: $\succsim$ is convex. Then, $u(.)$...
2
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3answers
582 views

Linearity in Pricing and Duality, UMP EMP

I have read the statement below and don't quite understand what it means. This is probably because I don't have full understanding of duality with support function in math, but just to foster ...
2
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2answers
86 views

How to get this budget constraint?

I have an Euler equation $ (\frac{ c_ {t+1} }{c_t})^\sigma = \beta (1+r)$,where $c_t$ is the t period consumption,r is interest rate and $\beta$ is discount rate, and a budget constraint $\sum _{t=0}^\...
1
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1answer
76 views

Weierstrass Thm: Continuous Fn Attaining Extrema on Compact Domain $u:\mathbb{R^L}\rightarrow\mathbb{R}$

This is just semantics, but MWG doesn't use the Weierstrass Theorem in its Math Appendix when using the fact that a continuous function always has a max value on any compact set. Some books appeal ...
1
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1answer
1k views

Why is Price Vector Orthogonal to Vector connecting two bundles on Budget Hyperplane

Here is my revised version/understanding why price vector is orthogonal to any vector from a bundle on the budget hyperplane to another bundle on the hyperplane: (see below for original question) ...
1
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1answer
396 views

Continuous Preference Relation Imply Continuous Utility Fn Existence

I am reading MWG's explanation in Chapter 3 when showing continuous preference relation implies the existence of continuous utility function. First, the authors show $u(.)$ is continuous by using the ...
3
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1answer
3k views

(Preference Relation/Set) Continuous $\succsim$ imply closedness of upper and lower contour sets

[ADDED/MODIFIED] : I have put my proof where the commodity space is simply $\mathbb{R_+}$(e.g. nonnegative reals) for simplicity below. Please share your 2 cent. I have put words to aid my own ...
4
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2answers
869 views

Continuous rational and monotone preference relation implies $x\succsim0$?

I updated my proof to a general version as follows: please share your thoughts & 2cent. Thanks Show a monotone continuous complete preorder on $\mathbb{R^L_+}$ has $y\geq x\rightarrow y\succsim ...
6
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1answer
1k 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 ...
2
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2answers
101 views

Is it better for economic growth to invest in stocks or to purchase products?

I've recently been interested in economics and I admit that my understanding concerning it is limited. However my question is if investing in stocks is good for the economy. From my understanding, it ...
1
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1answer
4k views

Why is MRS equal to Price ratio?

I've seen a derivation of MRS, but it's not immediately obvious to me why letting MRS equal to the price ratio of two goods will give you the solution to an optimization problem. Can anyone link me to ...
6
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3answers
1k views

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 ...
5
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1answer
7k 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 ...
2
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1answer
64 views

Solve for the bundle component that makes one as 'well off' as earlier

Suppose we have a (presumably time independent?) utility function $U(x_1,x_2)$ for consumer Rita. 1. What is Rita's MRS of $x_2$ for $x_1$? $$MRS_{x_1, x_2} = \frac{MU_{x_1}}{MU_{x_2}} = \frac{\...
1
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1answer
185 views

Find Indifference curve/s and Marginal Rate/s of Substitution given only one point

Arka likes fries. She wants to consume as much as possible. She consumes either regular (1 oz) or large sizes (5 oz). Draw her indifference curve through $(x_R, x_L) = (10,0)$ and her ...
2
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0answers
63 views

Does this conditional increase in income affect a budget line in the same way as an unconditional increase in income would?

It's been awhile since I've taken introductory microeconomics. I remember increases in income move budget line outward. What if the increases have some condition? The problem: Jill has $I$ to ...
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0answers
377 views

Calculating a cross price substitution/income effect

I am given a utility function $U(x,y)$, income $I$ and prices $p_x,p_y$. Then the price of $y$ rises to $p_y' = 3 \cdot p_y$. How are we supposed to calculate the substitution effect and income effect ...
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 ...
1
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1answer
969 views

What is the difference between an Ordinary Demand equation and an Engel curve equation?

I mean, an Ordinary Demand Equation measures changes in quantity of X due to changes in price Px. Engel Curve measures changes in quantity of X due to changes in income M. But ODE has M in it's ...
5
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2answers
854 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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1answer
153 views

Conceptual explanation/prediction of utility function. Extraction of utility function from Big Data

It seems to me, that utility function usually is just a set of facts. Is there a framework or model for utility function that can explain or predict utility function. I. e. if user has value for item ...
2
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0answers
22 views

What type of data packages am I looking for?

I did a bit of googling and I see there are companies that sell market research data, and wanted to know if anyone knows more about it. I am specifically looking for consumer interest in the allergic ...
4
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1answer
196 views

Show that $x(p,w)=w\cdot x(p,1)$ with homothetic preferences

Someone gave me a proof of this, but I am not sure if it is correct. Let $B(p,w) = \{x: p\cdot x \leq w\}$ (the budget set). Then: \begin{align} x(p,w) &= \arg \max_{x\in B(p,w)} u(x)\\ &=\...
0
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1answer
1k views

Indifference curves passing thru few points [closed]

Tommy Twit’s mother measures the departure of any bundle from her favorite bundle for Tommy by the sum of the absolute values of the differences. Her favorite bundle for Tommy is (2, 7), that is, 2 ...
0
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2answers
718 views

Mix of two ads types [closed]

Question still unanswered Ads in the boring business magazine are read by 300 lawyers and 1,000 M.B.A.s. Ads in the consumer publication are read by 250 lawyers and 300 M.B.A.s. If Harry had \$4,200 ...
3
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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 ...
2
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2answers
123 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
45 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
85 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
297 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 ...
8
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1answer
539 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
261 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 ...
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0answers
463 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
75 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
462 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
364 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
331 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(\...
3
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0answers
308 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
935 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
466 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
478 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
350 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
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0answers
61 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
15k 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
102 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?