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Questions tagged [microeconomics]

Microeconomics is a branch of economics that studies the market behavior of individual actors (usually firms and consumers) and the aggregation of their actions in different institutional frameworks (usually the market).

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6
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1answer
680 views

Roy's identities for Stone-Geary utility functions

I'm having trouble showing Roy's identity for the following Stone-Geary utility function: $$U(x)=\prod_{i=1}^n\left(x_i-\gamma_i\right)^{\beta_i}$$ where $\sum \beta_i=1$ and $\gamma_i$ is the ...
6
votes
1answer
282 views

How is labor disutility modeled in Arrow-Debreu model?

In DSGE models, utility function contains labor disutility components. But I cannot not see how labor disutility is incorporated in Arrow-Debreu-Mackenzie model.
6
votes
1answer
53 views

Meaning of $dF(z)$ in expected utility framework

Background: from a Microeconomics course, $F$ is a cdf. In other words, if $F$ has a density function $f$, then $$F(z)={\int_{-\infty}^z f(x) dx} $$ Write the Bernoulli utility function $u:...
6
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2answers
724 views

Deriving the translog production function

Ive been having difficulty deriving the translog production function defined as: $$\ln y=\alpha_0+\sum_{i=1}^n\alpha_i \ln x_i+\frac{1}{2}\sum_{i=1}^n\sum_{j=1}^n\ \beta_{ij}\ln x_i\ln x_j $$ I know ...
6
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2answers
1k views

In auction theory, why is my own valuation a random variable?

Auction theory typically (always?) begins by assuming that each bidder's valuation is a random variable. Now, it might seem reasonable (at least from a Bayesian perspective) for you to treat other ...
6
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2answers
2k views

Pareto optimality with externalities

I'm reading the book "Economics of natural ressources and the environment" written by D. Pearce and R. Turner. They explain that the competitive equilibrium is not a Pareto optimum in case of (...
6
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1answer
2k views

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 ...
6
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3answers
1k views

How can I draw an edgeworth box with 3 different goods?

If there are 3 types of goods(x,y,z) and 2 consumers (a,b) how can I draw the Edgeworth box? It must be 3 dimensional, right? Is there a software or online tool that I can use to draw a 3D Edgeworth ...
6
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3answers
1k views

What is the point of the indirect utility function?

Where does this have application? I understand how the demand function may be arrived at using the utility maximization problem but I don't understand where the indirect utility function is used and I ...
6
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1answer
1k views

If the Engel Curve of a Cobb-Douglas utility function is positive and linear, than does that mean it is neither a necessity nor a luxury good?

Since the concavity of the Engel Curve determines whether it is a necessity or luxury (i.e. how fast quantity demand changes in relation to changes in income), and since the second derivative of a ...
6
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2answers
2k views

Local Non-Satiation Proof

I have been having trouble with how to go forward with a proof for about three days now. I know the basic structure of the proof, but can't seem to construct it. Basically, I am trying to do a proof ...
6
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3answers
433 views

Establish demand curve with infrequent sales

I sell variations of an item on eBay. It is an unusual commodity which I purchase in bulk lengths and then cut to various sizes. They come in about 20 types, which I then sell as 10 different lengths, ...
6
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1answer
206 views

Shopping example in Kőszegi / Rabin (2006)

In "Section IV Shopping" of Kőszegi / Rabin (A model of reference-dependent preferences, QJE 2006), the example of consumer buying a pair of shoes is given. They claim that "her disutility from ...
6
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2answers
665 views

Does a General Equilibrium here require Pareto Optimality?

There are two consumers $A$ and $B$, and two producers $X$ and $Y$. he consumers are endowed with labour(L) and capital(K) $L_A,K_A$, and $L_B,K_B$ respectively. The preferences of the two consumers ...
6
votes
1answer
78 views

Why are Hicksian demand curves unobservable

I have read this paragraph in a book (Jehle, Reny: Advanced Microeconomic Theory): I don't quite understand why Hicksian demand curves aren't directly observable? What does observable stand for in ...
6
votes
1answer
382 views

Isoquant creator

I was wondering if anyone had an idea about the first author to have mathematically computed an isoquant or at least the first occurrence of a drawn isoquant ? My best guess would be F. Edgeworth in ...
6
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1answer
15k views

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 ...
6
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5answers
180 views

Why do firms losing money almost always reduce labor costs via layoffs instead of pay cuts?

At least in the United States, firms seem to almost always reduce labor costs via layoffs rather than pay cuts. Pay cuts are so rare that they're literally headline news. From an economic standpoint, ...
6
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1answer
211 views

How to determine the price a monopolist will set when the demand curve the firm faces isn't known?

I'm reviewing the following question from my microeconomics course notes. I don't understand how to do part (b). A firm faces a perfectly elastic demand curve because the product it sells has a ...
6
votes
1answer
107 views

Can integrals be interpreted simultaneously as aggregates and averages? (Mas-Colell et al. 1995, Proposition 4.C.4)

I'm currently reading chapter 4 of Mas-Colell, Whinston, and Green (1995). I have a problem with the way integrals are treated. For instance, Proposition 4.C.4 (p.113) states that when wealth is ...
6
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2answers
3k views

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 ...
6
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1answer
480 views

Prove that a continuous $\succsim$ is quasilinear

This question is closely related to Mas-colell, Whinston, Green: Microeconomic Theory, Question 3.C.5b Let $\succsim$ be a strictly monotone, continuous, and rational preference relation on $(-\...
6
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1answer
347 views

Estimating Price Elasticity from sales

I'm looking at data for an online shop with clothing items listed at different prices. I'd like to use this information to do some kind of profit maximization (i.e. I'd like to have some understanding ...
6
votes
1answer
995 views

Weak Axiom of Revealed Preference

Maybe this is a well-known fact that I have somehow overlooked or forgotten etc., but I found myself curious recently if there are any conclusions about WARP holding over different dimensions for a ...
6
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1answer
59 views

Overlaping jurisdictions Model: Proof of Lemma 1; The Size of Nations

I've been reading the book 'The Size of Nations' by Alberto Alesina and Enrico Spolaore (can be found on the net if you know where to look) and I'm having trouble following their "proof" of the first ...
6
votes
1answer
322 views

Does vNM rationality depend on the good chosen?

The von Neumann-Morgenstern theorem states that, assuming a person's preferences under risk satisfy certain rationality axioms, then there exists a utility function u, the von Neumann utility function,...
6
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6answers
1k views

Why does supply equal demand?

My question is simple: in theory, why should we expect the total quantity that firms want to sell to be (at least approximately) equal to the total quantity that consumers want to buy? As I ...
6
votes
1answer
283 views

Does the envelope theorem hold at a corner solution?

Suppose we have the following production function: $$F(L,K)=\max_{L_K}H(L,L_K,K)=\max_{L_K}\left[(L-L_K+1)^\alpha(L_K+K)^{1-\alpha}\right]=(L-L_K^*+1)^\alpha(L_K^*+K)^{1-\alpha}$$ With the ...
6
votes
1answer
211 views

Where do the rich and poor live in a city? (Calculus)

I am reading 'Cities, Agglomeration and Spatial Equilibrium' by Ed Glaeser. People live in a monocentric city, where consumers of heterogeneous income $y$ work at the centre of the city. They buy $H(...
6
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2answers
321 views

Public Goods - Voluntary provision

I am currently reading the book "Microeconomics: Principles and Analysis" by Cowell (2006), page 452-453. e have a two-commodity world, in which there are ${n_h}$ agents (households): commodity 1 is a ...
6
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1answer
451 views

Where do computational economists work

Does anybody know what kind of work or where computational economists end up working? It seems most end up in research...
6
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1answer
897 views

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 ...
6
votes
1answer
242 views

Nash social welfare function with negative exponential utilities

I got one question about the Nash-SWF. Typically it is defined as the product of individual utilities, ie. $$ NSWF:=u_1(x_1) \cdot u_2(x_2) \cdot u_3(x_3) \cdot ... $$ For this to make sense, ...
6
votes
0answers
207 views

Has any progress been made on the Pacman Conjecture on Finite Time Horizons?

The Pacman conjecture states that the optimal strategy for monopolistic durable goods manufacturers is to set price high and slowly drop it (i.e. eating their way down the demand curve). Empirically ...
5
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3answers
1k views

Why are firms taken to be profit-maximizing? Shouldn't that make them risk-neutral?

Intro texts normally explain that insurance firms (casinos, etc.) "work" by diversifying risk from many clients. Unsaid, then, seems to be that risk is bad for both firm and client. But why should a ...
5
votes
3answers
779 views

Why is elasticity not defined simply as the slope of the graph?

It makes more intuitive sense to me: as I increase the quantity, this is how much the price changes. Why is a much more complex formula used that takes into consideration the current quantity and ...
5
votes
2answers
720 views

In microeconomics : is this the contradiction in the atomicity of firms ?

Let $p$ be the market demand. It is a function of the market production $Q$. Let $q_i$ be the production of firm $i$. Reading Steve Keen (in Debunking Economics, chapter II) quoting George Stigler, I ...
5
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3answers
327 views

The 'Economic Man' (Reference Request)

We are writing a paper about the 'economic man.' By this, we mean that the choices he makes epitomize a rational economic thinker. However, we also acknowledge the fact that there are other, non-...
5
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2answers
835 views

Why do so many models assume homothetic preferences?

...when Engels Law, backed by a good amount empirical evidence, demonstrates that overall consumer preferences are not homothetic. See for example, Jorgenson (1997)
5
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3answers
474 views

Is the Convex Combination of Two Pareto Optimal Allocations Also Pareto Optimal?

I am studying for my qualifiers, and I ran into this question from a previous year's exam. $\textbf{Question:}$ Consider a two-consumer two-good pure exchange economy. Both preferences are locally ...
5
votes
1answer
556 views

What does Hayek mean at the end of the first paragraph of The Use of Knowledge?

I reproduce here the first paragraph of Hayek's well-known essay The Use of Knowledge in Society: What is the problem we wish to solve when we try to construct a rational economic order? On certain ...
5
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2answers
96 views

Is ongoing economic growth possible without additional non-renewable inputs?

Can ongoing economic growth occur without use of additional non-renewable inputs? That is, any additional inputs would only be from renewable resources: all non-renewable resources would be reused, ...
5
votes
6answers
14k views

Why does quantity supplied increase with price in economics?

The Law of Supply is my worst enemy in economics because I could never truly understand it, and as a result, the stuff I learned after that was built on a weak foundation. The Law of Demand is totally ...
5
votes
2answers
211 views

Is a strong foundation in advanced microeconomic theory essential to study environmental economics at the graduate level?

Advanced theory of individual economic behaviour in production, consumption, and general equilibrium. Are these topics useful to study environmental economics a the graduate level, or is there not a ...
5
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2answers
297 views

Is it true that $\frac{dL}{dq}=1/\frac{\partial q}{\partial L}$?

Marginal costs MC is defined as $MC=\frac{dC}{dq}$. Taking into account that $C=wL+rK$, $$MC=\frac{dC}{dq}=w\frac{dL}{dq}+r\frac{dK}{dq}$$ Recall that marginal product of labor $MP_{L}=\frac{\...
5
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2answers
486 views

Why are we taking the logarithm for risk-averse decision-makers?

I'm a mathematics student learning a bit of Game theory. Many examples are given within a very economic setting and up to know I could follow most of it because they were very basic and I learnt some ...
5
votes
3answers
235 views

Collusion model with imperfect public monitoring

It is well known that consumers' intertemporal incentives may play a key role on the potential of firms to sustain collusion. To my knowledge, most previous efforts studying the topic have assumed ...
5
votes
2answers
410 views

Does consumer theory assume that utility functions are consistent overtime?

I'm interested in how we model a consumer with a changing utility function over time. Example: an individual's demand for candy/sweets at 10 years of age will be different when he is 20,30 or 40 ...
5
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3answers
20k views

Completeness of Preferences

Economists assume that consumers have a set of preferences that they use to guide them in choosing between goods. These preferences have to satisfy three properties: completeness, transitivity and "...
5
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1answer
983 views

What is the difference between preferences lacking “completeness” and being indifferent?

If two preferences are complete, at least one must have a relationship to the other. If neither has a relationship, doesn't that mean that the consumer doesn't care which one he/she purchases?