# Questions tagged [consumer-theory]

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

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### 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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### 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 ...
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 ...
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### 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 ...
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### 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 ...
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### 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 $$x_M =\frac{p_y^2}{4 p_x^2}$$ $$y_M = \frac{m}{p_y} - \frac{p_y}{4 p_x}$$ ...
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### 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 ...
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### 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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### 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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### 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 ...
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### 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 ...
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### 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 ...
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### 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 ...
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### 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?
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### 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....
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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: $$\frac{\partial x^M}{\... 1answer 2k views ### Corner solution-consumer theory [closed]$$U(q_1,q_2)=4{q_1}^{0.5}+q_2P_1=1$$and$$P_2=2$$Initially$$Income=40$$Then the question asks :how do I know what income I can get a corner solution? Anyone can help me with this? Thank you 1answer 8k views ### Calculate the substitution effect Utility function$$ U=4{q_1}^{0.5}+q_2 \\ Y=10  p_1=p_2=1 $$Then p_1 rises to 2. I would like to ask how to calculate the substitution effect on the demand for q1? What I have done is ... 2answers 501 views ### Does there always exist a consumption bundle at which the indirect utility function is the inverse of the expenditure function? Two questions: Given v(\vec{p},m) and e(\vec{p},\bar{U}), is there only a single point at which these are inverses of each other? Does an inverse always exist for a given price vector \vec{p},... 2answers 58 views ### Does anyone know of any resources that discuss the differences between Hicksian and Marshallian remanding in depth and in an organized way? I don't understand why the Marshallian and Hicksian demand have such different properties. Both are functions from$$\Bbb{R}^n_+ \times \Bbb{R}_+ \rightarrow \Bbb{R}_+^n$$both are solved using the ... 3answers 4k views ### Why does Slutsky compensation “overcompensate” the consumer? Suppose I have a Marshallian demand function x_M(p_x^0,p_y,m^0). As I understand it, Slutsky compensation is defined as$$T_S = \Delta p_x \cdot x_M(p_x^0,p_y,m^0)$$Can someone explain why this ... 2answers 8k views ### Are Cobb Douglas goods complements or substitutes? Given$$U(x,y)= x^\alpha y^{1-\alpha}$$\alpha \in (0,1), are Cobb Douglas goods (here x and y) complements, substitutes, or neither? Why? An explanation with mixed partial derivatives would ... 1answer 2k views ### Confusion about the EMP approach to perfect complements. Solved UMP but struggling with EMP I have successfully done the UMP for perfect complements. I got$$x^* = y^* = \frac{m}{p_x +p_y}$$This makes intuitive sense because for whichever good I have the least of, I don't want to buy ... 1answer 401 views ### Why isn't the Law of Demand true for Marshallian demand? My professor said, in practice, Marshallian demand follows the law of demand (ie that increase in price decreases demand). But he said in theory, the Marshallian case is ambiguous and it does not ... 1answer 762 views ### labor leisure trade off Walras has available 24 hours per day. He has to alloacate this 24 hours between leisure (L) and work. His utility function depends on leisure and the composite good (C) and is given by U=LC. ... 2answers 1k views ### Does concavity of the utility function has any bite? A utility function in general has only ordinal meaning, any monotone transformation preserves the order isomorphism of the underlying preference ordering. However, there are several econometrics ... 1answer 62 views ### Is the implicit function theorem needed to relate the EMP to UMP? My professor says the expenditure function and the indirect utility function are inverses of each other. But how is this possible? Consider each.$$v:(p_x,p_y,m) \rightarrow \Bbb{R}e:(p_x,p_y,\...
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 \...