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Questions tagged [consumer-theory]

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

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3answers
3k 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 ...
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2answers
6k 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
1k 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
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1answer
282 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
662 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
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2answers
752 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
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1answer
50 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
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2answers
2k 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
429 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 $$\...
3
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2answers
3k views

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
135 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 ...
2
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2answers
790 views

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=...
2
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1answer
2k views

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 ...
10
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2answers
22k views

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 = \...
2
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1answer
604 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 ...
3
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3answers
700 views

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: ...
6
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1answer
641 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 ...
2
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1answer
352 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
50 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 ...
6
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1answer
15k 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 ...
6
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3answers
15k 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 ...
4
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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 ...
2
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0answers
565 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 ...
14
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3answers
156 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 ...
3
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2answers
2k 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 ...
12
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2answers
9k 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 ...
10
votes
1answer
470 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 ...
8
votes
2answers
786 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, ...
22
votes
4answers
1k views

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?