# Questions tagged [consumer-theory]

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

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### 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 ...
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### 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 ...
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### 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 ...
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### 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 ...
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### 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 ...
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### 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 ...
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### 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 ...
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### 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 ...
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### 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 ...
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### 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?
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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 ...
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### 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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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 $\... 1answer 279 views ### Why are allocation and distribution important consequences of the second welfare theorem? I'm reading Intermediate Microeconomics: A Modern Approach by Hal Varian. On page 606, he states: The Second Theorem of Welfare Economics states that as long as preferences are convex, then every ... 2answers 1k views ### Struggling with uncompensated/compensated demand I'm working on a problem set for my intermediate microeconomics course, but I'm having trouble deriving the compensated and uncompensated demand functions. This is the utility function:$U(x, y, z) = ...
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 ...