Questions tagged [consumer-theory]
the study of consumer choice and its fundamental underpinnings in preferences and constraints.
296
questions
2
votes
1answer
48 views
When the global optimal is outside of the constraint set, what will be the demand?
$u:\mathbb R^n\to\mathbb R$ is a quasi-concave utility function so the indifference curves are convex.
$a,b\in\mathbb R^n$ are two points. Our budget set is the (one-dimensional) segment $[a,b]$ that ...
1
vote
1answer
223 views
Can implicit costs make every option not worth doing?
I'm new to microeconomics so sorry if this is simplistic, but if an action should only be taken when benefits > costs and opportunity costs are included in cost calculations, how would one deal ...
2
votes
3answers
100 views
Relation between demands of $x, y$ and $z$
Question: Consider a consumer with utility function $U(x,y,z)=y\min\{x,z\}$. The prices of all three goods are the same. The consumer has $100 to spend on these three goods.The demands will be such ...
1
vote
1answer
44 views
Generalizing demand for perfect substitutes utility function
I have the utility function:
$U(x_1,...,x_n)=a_0+\sum_{i=1}^{n}a_ix_i\;\;\;\;\;\;\;\;\;a_j\in\mathbb{R}_+ \;\;\forall j=\{0,...,n\}$ (maybe $a_0$ could be zero)
$\sum_{i=1}^{n}a_i\in (0,K)\;\;\;$ ...
3
votes
3answers
208 views
Are Cobb-Douglas preferences monotone according to the marginal utility condition?
I understand that Cobb-Douglas preferences represented by $U(x,y)=x^ay^b$ are strictly monotonic, because increasing at least one of the goods in the bundle increases utility.
However, another ...
2
votes
2answers
92 views
In an intertemporal (2-period) consumption model, why is the investment rate independent of discount factor?
In lecture, my professor defined the following 2-period consumption model:
$c_i = $ consumption in period $i$.
$y =$ endowed income in period 1.
$r = $ interest rate in perfect credit markets.
$h = $ ...
2
votes
1answer
44 views
Lotteries = probability distribution?
Are "lotteries" in the model for choice under uncertainty not just probability distributions?
3
votes
1answer
35 views
Binary-continuous choice model in empirical consumer choices
There are quite a lot empirical research based on discrete choice models, in which the consumer selects one of J alternative goods to maximize her indirect utility. The key assumption of these models ...
0
votes
1answer
21 views
Expenditure function. Prove that this set is bounded
I need to prove that the following set is bounded in order to derive the expenditure function:
$e(p,v)=min_x px$
ST
$\{x \in R^n_+$ such that $U(x)\geq v\}$.
Knowing that $U(x):R^n \longrightarrow R$ ...
2
votes
2answers
68 views
Prove that budget constraint is Lower Hemi Continuos (LHC)
I need to prove that the following constraint is LHC.
$B=\{x \in R^n : px\leqslant pw)$
But Im not capable of finding and sequence $\{x_n\}$ such that $x_n \in B(p_n,w_n) \forall n$ and that $x_n\...
2
votes
0answers
16 views
Does anybody knows where I should look for a proxy for consumption to estimate a two factor C-CAPM?
Has anybody seen, any textbook recommendation that refers to the proper proxy for consumption. I am trying to estimate a two factor consumption CAPM, namely we I add a second factor apart from ...
0
votes
1answer
27 views
Does the duality of utility maximization and cost minimization hold in practice?
I recently learned about the relationship between utilization maximization and cost minimization.
Are there studies on whether this duality holds in real life?
Any information on this topic for a ...
1
vote
1answer
34 views
Whether a good is a Giffen good should be based on circumstance?
The textbook example of a Giffen good is the potato during the Irish Potato Famine. It is characterised by a positive income effect that is larger than the negative substitution effect when the price ...
1
vote
1answer
92 views
Mathematics of the income and substitution effects
I have recently been learning about the concept of utility and the indifference curve. I am having some problems understanding the effects on consumption of two goods $X$ and $Y$ of a change in the ...
4
votes
1answer
214 views
Price-consumption curve
Suppose a consumer whose income is $b$ has a utility function given by $U(x,y) = 2xy+y^2$ with the price of $x$ being $p_x$ and the price of $y$ being $p_y$.
Draw the price-consumption curve assuming ...
0
votes
0answers
9 views
Why is the demand, supply and Engel curves plotted with the dependant variable in the X axis and the independent variable in the Y axis?
I am new to economics and have read the first 7 chapters in Intermediate microeconomics by Hal R Varian. Throughout the text, graphs are drawn with the dependent variable (Quantity) in X and ...
3
votes
1answer
107 views
Marshalian and Hickisian Demands and Slutsky Equation
everyone.
I have the following question:
A consumer has the following indirect utility function:
$ V(p_1,p_2,b) = (p_2k-b)p_1^{-1} \left[ \frac{2p_2k - 2b}{p_2} \right]^{-2}, x_2 < k$
a) Find ...
0
votes
0answers
14 views
Aggregate CES Cobb-Douglas utility over different individuals
Suppose I have a CES Cobb-Douglas Utility function:
$$U_i=X^{\alpha_i} Y^{1-\alpha_i}$$
Can I add utilities of different individuals meaningfully? I.e, where people have different $\alpha_i$.
$$\...
0
votes
0answers
24 views
Soft Question: Econometric model recommendation - covid situation and supermarket sales
I am interested in modelling the impact of the current covid pandemic on supermarket sales (in a specific country in Europe) as part of my bachelor's thesis (next year), however, I am having a hard ...
0
votes
1answer
21 views
How has decreasing quality (or the need to pay more for the same quality) tracked with inflation?
I'm trying to identity a missing variable that could affect poor and middle class consumers more than more wealthy/resourceful individuals.
Assuming that there are decisions regarding cost reductions ...
0
votes
0answers
33 views
Relationship between strictly convex preference and convex preference
Let X be a convex subset of linear topological space and let binary relation >=
be a complete preordering.
prove: If preference relation is strictly convex and continuous, then it is convex.
Since ...
0
votes
0answers
15 views
Optimising behaviour for labour supply
Suppose someone has an uncompensated labour supply schedule h(w,m)=A+Bw+Cm where h is hours of work, w is real wage rate and m is real unearned income. What are the requirements for optimising ...
-2
votes
1answer
45 views
Cobb-Douglas function homotheticity
I've been given the Cobb-Douglas utility function:
$\ u(q_1, q_2)=a\ln q_1+b\ln q_2=q_1^aq_2^b \ $
If I want to prove homothetic preferences, I use the following condition:
$\ u(\lambda q_1, \...
0
votes
1answer
59 views
How do I derive the aggregate demand function given two utilities functions?
Assume that we have two people with the same utility function of $U_i = x^{1/2} + y^{1/2}$ where $i=1,2$ and $I_i$ is the income. Let $P_x$ denote price of good $x$ and $P_y$ denote price of good $y$.
...
3
votes
1answer
33 views
Empirical tests for symmetry of cross-price elasticities
It is a well known fact in consumer theory that for a Hicksian demand curve the cross-price elasticity of good $i$ with respect to the price of good $j$ equals the cross-price elasticity of good $j$ ...
0
votes
0answers
30 views
On Demand Functions and Engel Curves
A consumer has utility function $U(x,y)=(xā2)y$, where $xā„2$ and $yā„0$. The price of $x$ is $P_x$, the price of $y$ is $P_y$ and the consumer's income is $I>2P_x$. ($x$ and $y$ do not have to be ...
-1
votes
1answer
47 views
Minimizing consumption in a single market( Partial Equilibrium)
Let there be a good X where the optimal consumption is 0; i.e the social costs for any unit provided would always be greater than the utility surplus of the market.
We know that prohibiting it( ...
1
vote
1answer
70 views
Example of a utility maximization problem with a non-binding budget constraint
Given a utility function $U(x,y): \mathbb{R}^{2} \to \mathbb{R}$, the general utility maximization can be stated as follows:
$$
\max_{x, y} U(x,y) \text{ s.t. } p_{x}x + p_{y}y \leq m
$$
where the $...
1
vote
1answer
59 views
Why can utility functions be continuous, and what does this imply for marginal utility?
I am studying microeconomics at the introductory undergraduate level and two related but distinct questions are puzzling me.
First, my textbooks express utility functions as continuous functions by ...
1
vote
0answers
39 views
Shortcuts for elasticity of substitution
How can I find the elasticity of substitution (I know the definition) if I know the utility function $u(x,y)$? I know its increasing in $x$ and $y$, etcetera, and has everything else you want from a ...
0
votes
0answers
103 views
On shapes of indifference curves
I encountered this question in Microeconomics by Pindyck and Rubinfeld.
The question says that "Suppose Jones and Smith have each decided to
allocate $1000 per year to an entertainment budget
in the ...
0
votes
1answer
61 views
Budget Constraint in Utility Maximisation Problem with Lagrange Multipliers
Lets say we have a utility function $U: \mathbb{R}^{2} \to \mathbb{R}$ given by $U(x,y)$ and a binding budget constraint $p_{x} x + p_{y} y = m$, where $p_{x}, p_{y}$ are prices of goods $x,y$ and $m$ ...
0
votes
1answer
24 views
Optimizing Lagrangian Function Subject to 4 Input/Output Constraints:
The objective function:
$$\text{utility}=U\left(x_{c}, y_{c}\right)$$
subject to,
$x_{o}=f\left(y_{i}\right)$
$y_{o}=g\left(x_{i}, x_{o}\right)$
$x_{c}+x_{i}=x_{o}+x^{*}$
$y_{c}+y_{i}=y_{o}+y^{*}$
...
1
vote
1answer
56 views
How to find Marshallian demand of $u(x,y,z)=x+y^2+2z^2$?
Consider the utility function $u(x)=x+y^2+2z^2$. How to derive Marshallian demand for a consumer with these preferences?
0
votes
0answers
25 views
weakly preferred consumer bundles
I am currently studying consumer choice and saw that weak preference refers to when an individual prefers or is indifferent to two bundles (such as bundle A and bundle B).
I was wondering what is ...
-1
votes
1answer
34 views
Is Buy Nothing Day a classist protest of Black Friday?
I hope this isn't off topic, it seems specifically economic to me even though it probably intersects with other fields of study.
Black Friday is seen as an iconic hallmark of consumerism, and Buy ...
1
vote
1answer
218 views
Why is the marginal utility of money assumed to be constant in Marshallian Theory of Consumer Behaviour
While studying the Marshallian Theory of Consumer Behaviour, I came across the assumption that the marginal utility of money is assumed to be constant. Can someone please explain why is this so?
0
votes
0answers
66 views
Special case for wealth allocation with quasilinear utility functions
Building on this question, regarding the answer from Bkay:
Is it a general statement that when $m < \frac{p_y^2}{4 p_x}$, all income will be allocated to $x_M$? What about the case when the ...
0
votes
0answers
36 views
Change in Consumer Surplus with two goods
Suppose we have two goods, price changes in the two are independent; having seen this question I am considering why the change in total Consumer Surplus is the sum of the change in Consumer Surplus ...
0
votes
2answers
219 views
Corner solution of the maximization problem
Answer
Hello, I upload the actual question with my 8-pages answer. Please can you check it. Is there a corner dissolution for $c=\gamma$. Please share your ideas. Thanks.
7
votes
1answer
161 views
Are there any other rational preference relations without utility function representations, besides Lexicographic?
It seems like lexicographic isn't that "special". Like yes it is special in that supposing it has a utility function gives you a bijection from the rationals to the reals, but I mean unique in some ...
1
vote
2answers
307 views
Finding demand functions for an unusual utility function
I have a utility function: $U = x + \min\{x,y\}$
I want to draw the indifference curve and find the demand functions. Will it be the case of the usual perfect complements?
Also, what preferences ...
0
votes
0answers
21 views
Would households rather live in a world with or without the unemployment insurance?
Would households rather live in a world with or without the unemployment insurance? What is a good example of world in which unemployment insurance is seen as a benefit, and not a hindrance?
1
vote
1answer
62 views
Consumer Theory question [closed]
You plan to use the following specification for an empirical study:
$$e_i = \alpha_i + \sum_{j=1}^{n} \beta_{ij}p_i + \gamma_iy +\delta_i,
i=1,...,n$$
where $e_i$ is the consumer's expenditure on ...
4
votes
2answers
107 views
Is there any evidence for consumer utility-maximising behaviour, at individual or market level?
Even though utility maximisation is ubiquitous in economic textbooks to model consumer behaviour, its usefulness is rarely demonstrated by evidence.
Is there any evidence that some consumers do ...
0
votes
1answer
65 views
Log Utiliy Function Trick
I am watching Lecture 3 of Yale's Financial Theory Lecture (by John). At about minute 50 he explains something along this line (with reference to log utility functions).
MUx/Px=MUy/Py
And ...
1
vote
2answers
213 views
Derive demand function $x(p,w)$ from utility function $u(x) = \min\{x_1, x_2\} + x_3$
I know how to solve the two-good case with $u(x) = \min\{x1, x2\}$, but the addition of $x3$ confuses me.
Problem
Derive the demand function $x(p,w)$ from $u(x) = \min\{x1, x2\} + x3$
What I did ...
1
vote
0answers
17 views
Index Theorem for Regular Infinite-Agent Economies
A formulation of the Index theorem states that for a regular economy:
$\sum_{p | z(p) = 0, p_L = 1} index p = +1$
Does this hold for models with uncountably many agents?
1
vote
1answer
40 views
Prove that $h(p,u) = \nabla_p e(p,u)$ is implied by Roy's identity
I am struggling a bit with the math in my first graduate microeconomics course. I'm not sure if this belongs here. If it doesn't, please direct me to a more appropriate place.
Below is one question ...
0
votes
0answers
16 views
CPI Bias with consumers using computers extensively
I was studying Microeconomics from Microeconomics by Pindyck and Rubinfeld where it was written that CPI calculated on Laspeyres index has overstated the cost of living for consumers who use computers ...
