Questions tagged [consumer-theory]

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

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2
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0answers
411 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 ...
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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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1answer
174 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}{\...
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1answer
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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
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1answer
11k 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
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2answers
543 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 $\vec{p}$,...
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2answers
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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 ...
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3answers
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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 ...
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2answers
10k 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 ...
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1answer
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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 ...
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1answer
465 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
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1answer
790 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 $U=LC$. ...
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2answers
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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 ...
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1answer
66 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,\...
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2answers
4k 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
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2answers
586 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 $$\...
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4answers
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Can someone explain graphically why MRS is invariant under monotonic transformation?

Let $U(x,y)$ be a utility function. Suppose I have an indifference curve for which $U(x,y) = \bar{U}$. Then $dU = 0$ along the curve and I can rearrange to find the MRS. Suppose I have a monotonic ...
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1answer
169 views

Relationship between Revenue-Elasticity and Price-Elasticity

I have attempted to solve this problem and would be grateful if someone looked over my solution 5% increase in price results in 5% decrease in total revenue. I need to determine price elasticity of ...
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2answers
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Editing formula for finding Marshallian Demand with Cobb-Douglas utility function

Suppose a utility function $u=x_1^ax_2^b$ with $a+b=1$. The following formula finds the values for $x$: $x_1 = \frac{am}{p_1}\\ x_2 = \frac{bm}{p_2}$ But what if the utility function looks like $u=...
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1answer
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How does one graph indifference curves for a set of Lexicographic preferences?

Two Questions: Since Lexicographic preferences are not continuous, is it still appropriate to use $\Bbb{R}^n_+$ to define my coordinate axes when drawing Lexicographic preferences? If not, what ...
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Marshallian Demand for Cobb-Douglas

When trying maximize the utility having a cobb-douglas utility function $u=x_1^ax_2^b$, with $a+b = 1$, I found the following formulas (Wikipedia: Marshallian Demand): $x_1 = \frac{am}{p_1}\\ x_2 = \...
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1answer
928 views

For a given set of consumption bundles, how do we know there are bundles that the consumer is indifferent between?

In my professors lecture notes (it's more like a book), he states four properties of preferences relations: monotonicity transitivity continuity completeness He then goes on to discuss utility ...
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3answers
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What properties must a utility function have such that we can define level sets and thus indifference curves?

I asked on Math SE a bit about level sets here. Based on what I learned, it seems like we usually assume a level set $L(f)$ and its function $f$ defined on $\Bbb{R}^n$ have the following properties: ...
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1answer
780 views

Does a monotonic transformation of a homothetic utility function imply the preference relation on the set of consumption bundles is still homothetic?

Does a monotonic transformation of a homothetic utility function imply the preference relation on the set of consumption bundles is still homothetic? Obviously, if a utility function on a set of ...
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1answer
448 views

Price difference of substitute goods when the supply increases?

In a competitive market, there are 3 types of goods: X, Y and money (m). X and Y are substitute goods, and the utility functions are quasi-linear with respect to money, i.e: $$U(x,y,m) = u(x,y) + m$$ ...
2
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1answer
62 views

From single-consumer-multi-units to multiple-consumers-single-unit

When I took a course in consumer theory, the economy always had a single consumer, represented by a monotone positive utility function $u(x,y)$ and an income $I$. Given prices $p_x$ and $p_y$, it is ...
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1answer
22k views

Gross substitutes vs. net substitutes

Wikipedia explains the difference between products that are "gross substitutes" and products that are "net substitutes". However, the mathematical explanation doesn't give much intuition about these ...
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3answers
18k views

Quasilinear Utility Functions

We know if the utility function is quasilinear (QL) w.r.t good 1, then the demand for other goods is independent of income (no income effect for goods $(2,\dots, N)$). But is the reverse implication ...
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1answer
3k views

Solving for optimal consumption bundle

Consider a consumer who can consume either A or B, with the quantities being denoted by $a$ and $b$ respectively. If the utility function of the consumer is given by $$-[(10-a)^2+(10-b)^2]$$(suppose ...
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0answers
691 views

Consumer Theory - Relationship between compensating variation (CV) and the equivalent variation (EV)

John consumes two products – X and Y and his preferences are represented by an unknown utility function – u(x,y) (we may assume his indifference curves are well-behaved). His income is m, while the ...
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3answers
198 views

Current knowledge about the empirics of consumer theory

I would like to get up to speed on the current state of empirical work done to test the assumptions and predictions of consumer theory (think Chapters 1, 2, 3, and 6 of Mas-Colell et al.). Can anyone ...
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2answers
3k views

Is non-monotonic local non-satiation supported by consumer theory in economics?

In general (Walrasian) equilibrium, local non-satiation is one of the assumptions that guarantee existence of equilibrium. Question is, is non-monotonic local non-satiation preference supported by ...
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2answers
13k views

The relationship between the expenditure function and many others!

I dont understand the relationships between Hicksian demand, walrasian demand (marshallian), the expenditure function and the indirect utility function (including the value function V(b)). I have ...
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1answer
592 views

Is it possible to derive indifference curves given marshallian demand function?

In a two good world, will a marshallian demand function the likes of D(p,m) where p is the price of one good and m the income yield a utility function or ...
9
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2answers
1k views

When can one safely talk about decreasing marginal utility?

One thing I hear a lot is talk of decreasing marginal utility—the idea being that additional units of a good become progressively less attractive the more units of that good one has already. However, ...
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4answers
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What are Giffen Goods?

What exactly are Giffen goods and are they of purely theoretical interest or has there been empirical evidence of their existence?

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