Questions tagged [consumer-theory]

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

Filter by
Sorted by
Tagged with
5
votes
1answer
788 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 ...
7
votes
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
votes
2answers
355 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
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
votes
1answer
488 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
979 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
582 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
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
votes
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
votes
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
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
127 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
160 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
905 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
69 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 ...
3
votes
2answers
6k 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
776 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
9k 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
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 ...
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
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 $\...
1
vote
1answer
258 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
295 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
2answers
569 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
3k 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
52 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
435 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) = \...
6
votes
1answer
206 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
170 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
343 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
6k 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
3k 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
157 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
8k 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
501 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
58 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 ...
8
votes
3answers
4k views

Why does Slutsky compensation “overcompensate” the consumer?

Suppose I have a Marshallian demand function $x_M(p_x^0,p_y,m^0)$. As I understand it, Slutsky compensation is defined as $$T_S = \Delta p_x \cdot x_M(p_x^0,p_y,m^0)$$ Can someone explain why this ...
2
votes
2answers
8k views

Are Cobb Douglas goods complements or substitutes?

Given $$U(x,y)= x^\alpha y^{1-\alpha}$$ $\alpha \in (0,1)$, are Cobb Douglas goods (here $x$ and $y$) complements, substitutes, or neither? Why? An explanation with mixed partial derivatives would ...
1
vote
1answer
2k views

Confusion about the EMP approach to perfect complements. Solved UMP but struggling with EMP

I have successfully done the UMP for perfect complements. I got $$x^* = y^* = \frac{m}{p_x +p_y}$$ This makes intuitive sense because for whichever good I have the least of, I don't want to buy ...
2
votes
1answer
401 views

Why isn't the Law of Demand true for Marshallian demand?

My professor said, in practice, Marshallian demand follows the law of demand (ie that increase in price decreases demand). But he said in theory, the Marshallian case is ambiguous and it does not ...
2
votes
1answer
762 views

labor leisure trade off

Walras has available 24 hours per day. He has to alloacate this 24 hours between leisure $(L)$ and work. His utility function depends on leisure and the composite good $(C)$ and is given by $U=LC$. ...
3
votes
2answers
1k views

Does concavity of the utility function has any bite?

A utility function in general has only ordinal meaning, any monotone transformation preserves the order isomorphism of the underlying preference ordering. However, there are several econometrics ...
0
votes
1answer
62 views

Is the implicit function theorem needed to relate the EMP to UMP?

My professor says the expenditure function and the indirect utility function are inverses of each other. But how is this possible? Consider each. $$v:(p_x,p_y,m) \rightarrow \Bbb{R}$$ $$e:(p_x,p_y,\...
2
votes
2answers
3k views

Why do we need both the UMP and the EMP?

I understand that there are two common applications of Lagrangian multipliers in consumer theory: the utility maximization problem (UMP) ans the expenditure minimization problem (EMP). These seem ...
2
votes
2answers
495 views

Is Marginal Rate of Substitution a multivariable function?

Suppose I have $U(x,y)$ and a level set of indifference curves. Suppose the value of $U$ along a given curve is $\bar{U}$. We know $dU = 0$. We compute total derivative, rearrange, and now have $$\...