# Questions tagged [consumer-theory]

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

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### Marginal value curve is the inverse of demand function

From Introduction to Economic Analysis by McAfee and Lewis. They write that: the marginal value curve is the inverse of the demand function, where the demand function gives the quantity purchased at ...
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### If both goods are considered economic goods in the economy, then how can their demand be negatively sloped when in a state of satiation or bliss?

if both goods are economic bad, then we can say that they have a negatively sloped demand curve. But how can we say the same for economic goods in a state of satiation or bliss?
1 vote
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### consumption, income and utility

Question Description: Consider an economy populated by a large number of Farmers (F) and Computer Scientists (CS). Each person divides his 24-hour day into labour and leisure. If a Farmer decides to ...
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### Finding Utility Function for Optimal Allocation in Consumer Choice Model

I'm working on a consumer choice model involving a consumer with one good and a numeraire. In this model, the price of the numeraire is assumed to be one. My objective is to identify the utility ...
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### Why do revenue neutral taxes result in a change in behaviour

Suppose we have the following utility function defined over two commodites, $c_{1}$ and $c_{2}$. The function is: $$U\left(c_{1},c_{2}\right)=\ln\left(c_{1}\right)+\ln\left(c_{2}\right)$$ subject to ...
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1 vote
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### Monotonicity of Concave Indifference Curves

I'm doing an intermediate micro course, and we've been given a problem asking to draw curves that correspond to the utility function with the expression of a circle centred at (3,4). I understand that ...
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### Simultaneously a substitute and a complement (validity of a claim)

I have read the following claim: Sometimes the relationship between products can be both substitute and complement; that is, two products may be complements for one purpose but substitutes for ...
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### How to aggregate goods with different units of measurement to reduce the economy with a Cobb Douglas utility function?

I want to model a economy where consumers have a Cobb Douglas utility function and where X1 = goods that pay a value added TAX (VAT), and X2 = goods that are exempt from this tax. I am working with ...
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### Confusion regarding the Slutsky equation

I'm reading Henderson and Quandt's Microeconomic Theory textbook and in the derivation process of the slutsky equation the final formula confused me a bit. The first term on the right of the equation ...
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### Prove: The law of demand holds if WA, Walras' law, homogeneity of degree 0, and homogeneity of degree 1 in wealth hold for Walrasian demand functions

Problem I am asked to prove the following result (MWG Exercise 2.F.5): The law of demand always holds if the walrasian demand function $x(\mathbf{p},w)$ satisfies the weak axiom of revealed ...
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### Proof for Marshallian Demand function

If you have a Marshallian demand function that is strictly convex, then it satisfies WARP. How to prove this?
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### Question on Isolating The Wealth Effect in Analysis of Changes in Price-Wealth Combinations - MWG Exercise 2.F.3 Parts (e) and (f)

I am doing exercises in Chapter 2 of MWG. I feel I got completely lost in exercise 2.F.3 parts (e) and (f). $\textbf{Exercise}$ Here is the question: I have solved parts (a) to (d). In particular, I ...
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### Does money illusion suggest Hicksian demand curves are more accurate?

I interpret "money illusion" to mean that consumers tend to falsely equate their nominal income or wealth to their objective utility level. If that is the correct interpretation, it seems to ...
257 views

### Question on The Weak Axiom of Revealed Preference and The Definition of Revealed Preference Relation

I am solving the following problem (from Exercise 2.F.3 (b) in MWG) and I got confused by the weak axiom of revealed preference and the definition of the revealed preference relation. Here is the ...
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### MWG Exercise 2.E.5

Exercise Suppose that $x(\mathbf{p},w)$ is a demand function which is homogeneous of degree one with respect to $w$ and satisfies Walras' law and homogeneity of degree zero. Suppose also that all the ...
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### substitution effect in slutsky equation

We know Slutsky equation decomposes the price effect into substitution effect and income effect, where the substitution effect is the partial derivative of Hicksian demand function against the change ...
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1 vote
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### Does utility representation theorem need locally-nonsatiated as a condition?

I'm reading MWG's Microeconomics, and I'm a bit confused about the utility representation theorem. It states that a rational and continuous preference relation can be represented by a continuous ...
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### Negative marginal utility and negative marginal product

In microeconomics, we usually 'allow' utility functions with negative partial derivatives, indicating a 'bad' commodity, such as $u(x,y)=x^2-y$. Naturally, a utility-maximising consumer with a usual ...
33 views

### What does GARP in revealed preferences mean and how to regocnize it graphically?

I have a froblem understanding GARP in revealed preferences. I know what WARP means, and that SARP adds transivity such that it allows for indirect preferences, but what about GARP? How can you ...
1 vote
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### Calculate consumers WTP for product attributes

I have a large panel on the city level of how many cars of each {model, fueltype} combination were newly registered in each year. This panel also includes a large variety of characteristics for each ...
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### Substitutable preferences vs. gross substitutes over indivisible items

I don't really have a background in economics. I'm trying to understand the relationship between these two terms, if they are related at all. The definitions that I understand are here: Substitutable ...
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1 vote
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### Vertical income expansion path: explanation?

On the horizontal axis we have good x, on the vertical axis good y. The income expansion path is vertical. Which of the following assumptions is wrong? no homotheticity no strong monoticity ...
1 vote
112 views

### Example of a utility function which yields inelastic demand function

I am looking for a example of a utility function which, when the utility maximisation problem is solved, results in an inelastic demand. The standard examples in textbooks always seem to have unitary ...
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1 vote
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### Utility function for a combination of a normal good and necessary good

I am trying to formulate a decision problem for an agent involving their heating-energy consumption $c$. Let $x$ denote all other consumption. What would be a reasonable utility function to employ ...
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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 ...
1 vote
358 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 ...
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1 vote
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### 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,
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### 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 ...
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### 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 ...
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1 vote
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### 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 ...
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### 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
510 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 ...
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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 ...