# Questions tagged [consumer-theory]

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

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### Showing UMP and EMP do not exhibit duality if the assumption of local non-satiation is absent

I have been trying to use the contradiction method to prove this, but it does not seem to be working. Suppose $x^*$ is optimal in both EMP and UMP. Then $u(x^*) \geq u(x')$ for all $x'$ in $B_pw$. And ...
114 views

### Marshallian demand for x^2+y^2

My question is regarding a simple marshallian demand calculation. Given a utility function $u(x,y)=x^2+y^2$ and a budget constraint $p_1x+p_2y=m$. What are the Marshallian demand functions for each x ...
19 views

### Change in Hicksian Demand of an Inferior Good when changing Utility

How can you rigorously show that Hicksian demand for an inferior good will decrease when utility increases? Thanks,
51 views

### Exponential Income Consumption Curve

From the Engel's Law we know that as income increases the share of income spent of foods decreases and the share of income spent on luxury goods increases. I wanted to represent this using Consumer ...
46 views

### Estimating the form of a utility function on two or more commodities

I am looking for experiments for estimating the form a utility function of a consumer on two or more commodities. In particular, I would like to know e.g. if the utility function of a consumer is of ...
64 views

### Reservation price and demand curve

Q1: There are $25$ consumers with each demanding 1 unit and each consumers' valuation of the product is $10$. How would the demand curve look like. Q2: Now suppose there's a monopolist with $MC=8$ and ...
21 views

### Consumer optimization problems with multiples cases

Does anyone know of any resources where the Lagrangian optimization of the consumer problem with one constraint has two cases for an answer? For example, when income is greater than x, the optimal ...
1 vote
121 views

### The sufficient condition for unique interior solution in utility maximization problem

Suppose the utility function is continuous, differentiable, strictly increasing and strictly quasiconcave. Whether the utility maximization problem has unique interior solution? If not, is there any ...
52 views

### Cobb Douglas Indirect Utility/Expenditure continuity proofs

How should I go about proving that the general Cobb Douglas indirect utility function and expenditure functions are continuous? There are many ways to prove continuity, but which would be the easiest? ...
33 views

### Intertemporal consumption with heterogeneous/multiple goods

I'm currently trying to build a CGE, and I'm stuck at the household's problem which is about intertemporal utility maximisation. The household consumes multiple heterogeneous goods $C_i$ (I'm limiting ...
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1 vote
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### Homotheic Function Definitions

There are a number of different definitions of Homothetic functions i have come across. I have used each of them to prove that a function $f(x, y) = x^a y^b$ with $a+b > 0$ is homothetic. But i ...
47 views

### Slutsy Equation and Income effect

Does the Slutsky equation always assume optimal levels of our variables, hence Marshellian demand = Hiscksian demand $x = h$ as indeed this is how the Slutsky is derived? I originally thought this ...
71 views

### Convex Combination of pairs of points

Is it appropriate/meaningful to write vector/points $(a,b) \le (c,d)$, where i would mean component wise each component is $\le$ Specifically is my example below with reference to concavity ...
30 views

### What pricing strategies does Amazon use and how do they affect consumers' purchasing decisions?

As a frequent Amazon customer, I have noticed that the prices of products I am interested in buying often fluctuate over time. These changes could either be an increase or decrease in price, and I ...
1 vote
66 views

### Testing for Concavity - Local Maximum & Global Maximum

My question is under which contexts Negative Definitness (ND) vs Negative Semi-Definitness (ND) is required for classifying a global maximiser. And also Global vs Local. I also want to understand what ...
53 views

### How does a lack of incentive to purchase new stuff affect economics?

How does a lack of incentive to purchase new stuff affect economics? I've perceived as if a lot of economics is rooted in the idea of continued innovation and consumption, but then I've realized that ...
83 views

### CES in Slutsky matrix (weird results)

We have a Slutsky matrix: \begin{bmatrix} \partial x_{1}^H/\partial P_1 & \partial x_{1}^H/\partial P_2 & \dots & \partial x_{1}^H/\partial P_n \\ \partial x_{2}^H/\partial P_1 &...
265 views

### The formula for expansion path

Is there a way how to precisely compute the expansion path? I know a consumer's utility function $U(\boldsymbol{x})$, I know the budget constraint $\sum P_i x_i \leq M$, I am able to compute the ...
71 views

### Prove strict monotonicity of utility function

I have the following utility function: $$u(x_1, x_2, x_3) = med(x_1, x_2, x_3)$$ Given that $UMG_{i}$ ≥ 0, the utility function represents a strictly monotonic preference. Does this assertion make ...
1 vote
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1 vote
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### FOC greater than 0

I couldn't get my head around this part. Basically, I have to prove that a consumer has to hold a positive amount of assets, i.e. $x > 0$. A hint suggested to find take the FOC, and then set $x = 0$...
241 views

### Composite good and preferences

Usually in economics, we could see some versions of multiplicative utility: $$U(\boldsymbol{x}) = x*y$$ The thing is that most of the time an additional statement is given that $y$ is some composite ...
49 views

### How to create a composite good?

Let's say I would like to create some composite score for multiple of goods... EDIT: More concise version based on @BrsG comments... I would come up with the following scenario. I have a consumer with ...
66 views

### Do Aggregated consumers make sense?

Aggregated consumers as a biased concept (in case of cross-price elasticity)? I try to approach aggregated consumption data as if it was a new consumer (similarly to approaching average data as if it ...
1 vote
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### Expected utility maximization question

If the utility function of an individual is $u(w) = 10 \sqrt{w}$ and the individual starts with $w = 100$ (where $w$ denotes the wealth available to him). If he buys a lottery that costs him $51$ and ... 1 vote
199 views

### Equivalent of shephard's lemma in consumer theory

I'm studying micro from the Mas-Colell, and I'm trying to understand the proof 2 of proposition 3.G.1. It is about proving that the derivative of the expenditure function w.r.t. the price of a ...
217 views

### Why do we need Complementary Slackness Condition for Karush-Kuhn-Tucker Conditions

Complementary slackness condition (CSC) state that $\lambda_j[g_j(x) − c_j] = 0 \hspace{5pt} \text{for} \hspace{5pt} j = 1, ..., m.$ Therefore, every constraint either needs to be an equality ...
Question Is there an example of consumer preferences over consumption bundles $(x,y)\in \Bbb R^2$ that would be concave when $x$ is abundant relative to $y$ and convex otherwise? Are there known ...