Questions tagged [consumer-theory]

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

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Proof of the tangency condition in UMP

When an indifference curve is tangent to the budget line such that the preferences are convex and monotone, why is the point of tangency an optimal for an UMP? Given the budget line $p_1 x + p_2 y = I$...
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Convexity of preferences (dissimilar definitions)

Varian's Intermediate Microeconomics describes convexity as $$\text{Given } x, y \in X: x \sim y \implies \forall t \in [0,1], tx + (1-t)y \succeq x,y$$ The other definition I read everywhere is: $$\...
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Economic interpretation of assumption on utility function

Suppose $u\colon \mathbb{R}_{>0} \to \mathbb{R}$ is a utility function, twice continously differentiable, $u' > 0, u'' < 0$, and the classic Inada conditions hold, i.e., $\lim_{c \to \infty} ...
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1 vote
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How to mathematically denote that a consumer behaves according to their preference structure at every point in time?

As the title says, I would like to mathematically denote that a consumer behaves according to their preference structure at every time $t$, $t+1$, $t+2$ and so on in a finite consumption set $X$, by ...
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How useful are basic economics (elasticity / consumer & producer theory) in real life?

I am thinking how these concepts will be applied in the industries / at a job. For example I could see elasticity as useful in projecting the outcomes of supply ...
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Expected utility function and Full insurance

Bob is an expected utility maximizer with utility function $u(x) = −e^{−ax}$, where $a > 0$ is a parameter. Bob has wealth $w$. There are two states of the world, a good state and a bad state. The ...
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Indifference curve in income and substitution effects

i have this task: "Mary spends her totally daily budget (30 euro) for chocolate and cakes. The price of chocolate bar is 5 euro and price of slice of cake is 2 euro. Now the price of slice of ...
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1 vote
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budget line for ration quota

In this situation there is a particular commodity, like rice, is both available at a subsidized rate from a fair price shop (ration shop) and at a higher price from the open market. Suppose a consumer ...
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35 views

Data-driven vs. theory-driven demand system estimation

Context: When one wants to study consumer demand based on observational data (e.g. household survey data), imposing theoretical restrictions on the coefficients of the demand model seems to be a good ...
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Microeconomics question on elasticity

Two drivers--Walt and Jessie--each drive up to a gas station. Before looking at the price, each places an order. Walt says, 'I'd like 10 gallons of gas.' Jessie says, 'I'd like $10 worth of gas.' What ...
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Conditions to use the Lagrangian method

I have seen that the prices and $\text{MU}_{i}$ are assumed to be positive (or, the preferences monotonic). This is always mentioned when a utility maximization problem is being solved with the ...
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Leisure and consumption maximization trouble

Not really sure how to to b). For a) I have (wh + Y – τwh) which I'm sure is fairly simple. I've never dealt with a utility function this complicated before and really confused by the notation in ...
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Price Offer Curve for a U(q1,q2)=max{q1,q2} Utility Function

Can someone help me understand how to draw out the price offer curve, or price consumption curve (PCC), for a U(q1,q2)=max{q1,q2} function? There's no information about this in my textbook and it's ...
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3 votes
2 answers
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Help solving utility optimization problem from Connelly 1992 (Economics)

I am working through a paper by Connelly 1992 in RESTAT and I'm hoping to get some assistance in working through the optimization problem that she sets up. I apologize that it might be simple for many ...
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Marginal utility meaning and properties

Consider goods $X$ and $Y$ such that the marginal utility of a unit of good $X$ is always that of $n$ units of good $Y$. $X$ and $Y$ are perfect substitutes. Question 1: What does the above mean ...
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Is Varian's definition of continuity of preference equivalent to standard definitions?

Here are two definitions of continuity of preferences. Denote the (weak) preference relation by ≽. We assume completeness, reflexivity and transitivity. Assume non-satiation or strict monotonicity ...
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In consumer theory, shouldn't necessity good and neutral good be different ? What will be the IC and utility function for both?

Necessity good for example salt, which regardless of income has to be consumed at certain quantity. But neutral good for example is Suppliments for a healthy person which regardless of income he/she ...
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What are the necessary and sufficient assumptions for indifference curves to be convex to the origin?

I thought this required (quasi-)concavity of the utility, but can this (e.g. declining MRS) occur with fewer assumptions?
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4 answers
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Is the market price objective?

Is the market price objective, does it exist independently of human consciousness, how do we treat the market price in economics and the philosophy of economics? The market price is the current price ...
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13 votes
3 answers
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Economics term for those who benefit even though they didn't contribute

I believe there's an economics term that describes people who refuse to participate in a community project even though they receive the same benefit from the project. For example, the village needs a ...
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Convex Preference and utility function

How does convex preference imply quasi concave utility function (Intuitively and Mathematically)?
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3 votes
1 answer
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Is electoral abstention an example of non-complete preference?

In order for a preference to be rational, it has to be transitive and complete. Complete preference means that any two different bundles can be compared. I.e., a consumer can weakly prefer bundle X ...
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For any small perturbation dx, utility cannot change, or else, x* would not be optimal

I am having trouble understanding something that Varian says in "Microeconomic Analysis: Third Edition." For those of you who have the book handy, the question that I have regards something ...
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2 votes
1 answer
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Arguments of the Marshallian demand system of a Cobb-Douglas utility function

For a utility function of the form $U(x_1,x_2) = x_1^\alpha x_2^\beta$ and the standard budget constraint, the utility maximisation problem gives us a demand system characterised by: $x_1(\alpha, \...
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What utility function represents an agent with a time-discount factor?

Consider an agent who has a fixed budget, and should decide how to split it between consumption today and consumption tomorrow. For simplicity, suppose there is no interest, and no borrowing/lending, ...
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3 votes
1 answer
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Solve for the Walrasian demand, Utility of three variables, and Convexity of Preferences?

I am given $U(x,y,z) = x^\frac{2}{3}y^\frac{1}{3} + z$. I am asked to solve the following: (i) Prove the convexity of these preferences (convex, strictly convex or neither?) (ii) Solve for the ...
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MRS not invariant under monotonic transformation

Consider U(x, y) = ln(x)ln(y). Is it quasi-linear? My response was no, since applying an exponential would yield exp(ln(x)ln(y))= exp(ln(x+y)) = x+y. However, the original MRS was (y/x)(ln(y)/ln(x)). ...
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2 votes
2 answers
295 views

Violation of Monotonicity of preferences

Hi I am reading Jehle and Reny in my master's course and I have come across a problem in one of the exercises. My instructor herself was a bit confused when a student gave her a counter-example and ...
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1 vote
1 answer
81 views

Binary choices in consumer theory

Back when I was a teaching assistant, we were teaching utility theory and how it relates to price determination. So we were looking at continuous goods (e.g. "food") so as to get marginal ...
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Graphing indifference curves to visualize solutions?

I am having trouble with being able to graph indifference curves. This is a particularly important skill to have especially when trying to visualize corner solutions, and when the Lagrangian method ...
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1 vote
1 answer
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Marshallian demand for Cobb douglas function [closed]

would like to just check how one can obtain the Marshallian demand for Cobb Douglas function such as u(x1,x2) = x1^a x2^(1-a) ? Was attempting the question but got somewhat stuck trying to ...
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1 answer
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Existence of maximal element in a compact choice set

I have a compact subset of $\mathbb{R}$, $X$. An agent has a continuous, transitive and complete preference relation $\succsim$ over $X$. I am wondering whether there exists a $y\in X$ such that $y\...
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Optimal consumption for infinite number of periods and exogenous income

I have the following optimization problem: $\max_{\{c_t, s_{t+1}\}} \Pi_{t=0}^\infty c_t^{\beta^t}$ $\text{subject to } \space c_t + s_{t+1} = y_t + (1 + r) s_t \text{ and } s_0 = 0$ How do I find ...
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0 votes
1 answer
116 views

Calculate income and sustitution effect from utility funcion

Utility function $U(x_1 , x_2) = x_1 + 4 * x_2 $ $ p_1 = 3, p_2 = 8, m =120 $ $p_2$ changes from $8$ to $10 $ How can I calculate the income and substitution effect. I first thought about calculating ...
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5 votes
1 answer
90 views

Pigouvian tax with general utility function

Suppose person a's consumption of good $y$ imposes a negative externality on person b. Person a's utility maximisation problem is $$\max_{x_a,y_a} \ u_a(x_a,y_a),$$ subject to $$p_x x_a+p_y y_a=e_a.$$ ...
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3 votes
1 answer
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What is the difference between Impression Management and Signaling Theory?

I'm interested in theories on how organisations shape their stakeholders' (especially consumers' and investors') perceptions and decisions. I read about Impression Management and Signaling Theory. ...
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2 votes
2 answers
234 views

Proving local non-satiation in arbitrary metric space

I have a pure exchange economy where every consumption set $X_i$ is non-empty and convex and every preference relation $\succeq_{i}$ is strictly convex. I am asked to show that preferences are locally ...
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How come a representative consumer with quasilinear utility need not economize?

Suppose a representative consumer has the following quasilinear utility function: U_i(x_1,x_2)=ax_1+ax_2-(1/2)*[(x_1)^2+(x_2)^2] + k where a>0 is a utility parameter, x_1 and x_2 are the goods, and ...
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-1 votes
1 answer
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Why do companies and stores never seem to take into consideration the fact that few people want ugly colours of the same product?

In 1997, I traveled far and wide to hunt down an original Tamagotchi. Whereas everyone else had one of the numerous clones, often with many more features, I had to have the real Tamagotchi. When I ...
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4 votes
1 answer
374 views

Are the goods in additively separable utility functions normal goods?

Inspired by this answer. To make it a bit more precise, by normal good I mean demand is (not necessarily strictly) increasing in income, and by additively separable utility function I mean that a ...
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If I had a new economical theory, how could I share it with academical environments? I call it “algorythmic economy”

If I had a new economical theory, how could I share it with academical environments? I call it algorythmic economy. I have made this same question on Quora. https://www.quora.com/unanswered/If-I-had-a-...
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0 answers
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How to derive consumer expenditures in EMEA 14.2.5

I am working on a problem 14.2.5 from EMEA by Sydsaeter, Hammond and Strom. Consider the consumer demand problem: $$ \max_{x,y} U(x,y) = \alpha \ln(x-a) + \beta \ln(y-b) \text{ s.t. } px+qy=m \tag{*} ...
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4 votes
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Is an income tax always more favourable for consumers compared to ad valorem/quantity tax?

I'm studying the optimal choice of consumers with regards to taxation. I read that for consumers, income tax is generally (for Cobb-Douglas preferences) preferred compared to ad valorem tax: If the ...
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2 votes
1 answer
92 views

Approaches in demand analysis

What is the difference between Engel Curve and the system approach of demand analysis?
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1 vote
1 answer
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Demand function for partially subsumable products

I am struggling with this question that should be simple for economists (I am not an economist at all): There is a market with a limited number of (heterogenous) consumers with two firms, each ...
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0 answers
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How to calculate substitution and income effect when only 1 bundle is given?

I was given information of a consumer that initially consumed 4 units of both good x and good y with the initial price of $5 for both goods (px = py = 5). The initial budget constraint is 40 = 5x +5y ...
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2 votes
1 answer
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How to prove that a utility function U(x,y)=min(x,2y) is quasiconcave?

I have a question that asks: "Let there be two goods 1 and 2.Let $x$ and $y$ denote their respective quantities.$(x,y)$ represents a bundle. Suppose a consumer’s preferences over bundles in $R^2_+...
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7 votes
1 answer
259 views

Interior Solution for profit maximisation problem

A function $c: \mathbb{R}^K_+ \xrightarrow{} \mathbb{R}_+$ is is said to be a cost function if The value of function $c$ at $y = \textbf{0}$ is $0$: $c(\textbf{0}) = 0$ $c$ is continuous on the ...
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4 votes
0 answers
139 views

Looking for an universal utility function

I'm trying to build a computer simulation of an economy which separate simulation for each household and I'm trying to figure out what utility function should I use to model the households behavior. I ...
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1 vote
2 answers
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What does price embody ? Do we constantly undervalue some type of products?

I'm not sure to fully get the meaning of prices. If I understand well, there are two drivers of it : The theory of demand and supply and thus prices are driven partly by the utility that agents get ...
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