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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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### Independence axiom of lottery when $\alpha \ge 1$

When studying preference over lotteries we learned the independence axiom which goes like this: The preference relation $\succsim$ on the space of simple lotteries $\mathscr{L}$ satisfies the ...
469 views

### Moral Hazard or Adverse Selection?

I pay the doctor before he conducts the surgery. Can anyone explain to me whether this statement shows moral hazard or adverse selection?
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### Usage of natural gas in 1970 (where was the demand elasticity?)

The following historical graph of US Marketable Natural Gas volume has me puzzled: How was the gas used in 1970 (a peak production period), given that we would seem to be using a lot more gas now? ...
4k views

### What is a homothetic function?

Suppose we have the following equations for the MRS of a utility function. $$U(x, y)$$ Which of the following corresponds to a homothetic utility function? $$MRS (x, y) = \frac{x^2+y^2}{xy}$$...
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### Use of Slutsky equation

I know that the Slutsky equation is defined as: $\frac{\partial x_1^s}{\partial p_1} = \frac{\partial x_1^m}{\partial p_1} + x_1^o \frac{\partial x_1^m}{\partial m}$ My problem is right now is ...
522 views

### Are there two different meanings of the discount rate?

Today I suddenly became aware of how the term "discount rate" are frequently used in two different contexts: When people prefer to have something now rather than in the future. The reason is ...
286 views

### Explanation Rational Expectations

I am struggling understanding the concept of rational expectations. Can someone explain in simple words the concept of rational expectations? Does someone know a good (online) source explaining ...
274 views

### If the (direct) utility is concave in all goods, is the indirect utility necessarily concave in wealth?

Suppose that the direct utility $u(x_1,...,x_n)$ is concave in each of its arguments. Does this imply that the indirect utility $U(w,p)$ is concave with respect to $w$? If all goods are normal than ...
66 views

### Is there an economically sound way to decide between buying media or a streaming subscription?

How can a consumer (like myself) decide on whether they should pay for a music streaming service based on economic reasoning? Assumptions: The budget allows paying for a € 10/Month music ...
10k views

### What is the difference between a free market and a perfectly competitive market?

I am trying to find the distinction between a free market and a perfectly competitive market, and I can't find the right definition on what makes them different. Can someone give me a clearly ...
284 views

I just came from a coffee place with tipping and now I'm in one without tipping... prices are higher, but there is not tipping. It's not obvious why some places get rid of tipping and others don't. I ...
4k views

### What is the difference between Herfindahl Index and the Concentration Ratio

I was recently reading about the Herfindahl Index and from what I've learned so far, is that HHI is preferred over the Concentration Ratio. However, I didn't quite understand the reasoning that lead ...
996 views

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,...
148 views

### General mathematical model of incomplete contracts?

I have read various articles about incomplete contracts, like Hart's papers and Milgrom's papers. But I have not found a paper that defines mathematically, in the most general way possible, what an ...
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### Research at the county-level: Macro or Micro?

Is research at the county-level considered applied micro or applied micro? The standard undergrad definitions ("micro" = "individual", "macro" = "nation") are of no help with units of measurement ...
1k views

### Intertemporal Utility Maximization

Suppose an economic agent’s life is divided into two periods, the first period constitutes her youth and the second her old age. There is a single consumption good, C, available in both periods. The ...
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### Indifference curve - Does $dU = 0$ hold in higher dimensions? / Problem of integrability

In two dimensions, we have on an indifference curve that $dU=0$. Does this apply to indifference objects in higher dimensions? I was thinking that if $dU > 0$, then one is moving to a higher ...
275 views

### Is consumer surplus subjective?

The producer surplus is objective because the it is the total revenue minus the total variable cost. For example, if the producer sold 100 goods at 5 each, and the total variable cost was 300, then ...
226 views

### Estimating the second derivative of function from optimizers

Consider the following optimization $$x^*(s) = \max_{x\in X} \big(\,f(x)-sx\,\big)$$ where $f$ is assumed to be a strictly concave function and $X$ is an interval constraint, e.g $X = [0,b]$. We do ...
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### Clarification about Market Structure Oligopoly or Monopoly

As per the definition i found in the internet, Oligopoly, in which a market is run by a small number of firms that together control the majority of the market share. Monopoly, where there is only ...
164 views

### Tests of rational inattention

Can you provide a reference regarding a revealed preference test(s) of rational inattention models, as proposed by Sims, ergo, using a mutual information measure as the cost of putting attention. And ...
63 views

### Is there some kind of consensus on the determinant factors of education achievement?

There is quite a bit of literature on the economics of education. One of the most debated aspects of it arises when estimating the achievement of the student (usually in the form of standardized test ...
58 views

### How would you call a market for kidney donors and recipients?

I was wondering how you would call a market for kidney donors and recipients, where you have many 'buyers' and many 'sellers'. However, the 'seller' can only 'sell' his/her 'product' once. Since it's ...
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### What types of 'market mechanisms' are said to exist besides auctions?

The book Understanding Auctions states: The term auction covers a wide range of market mechanisms that are used to exchange products and services by determining who receives an item and how much is ...
214 views

### List of theoretical models of learning

What are the most advanced theoretical models about "learning" such as learning-by-doing or learning from others? Overall, learning in economics spans different areas. Here there is a largely ...
270 views

### When the convexity assumptions fail

We constantly assume convexity in economics. Convexity of production sets, convexity of preferences etc. Is there literature that addresses when convexities fail? For example, is there any ...
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### Economics: inductive or deductive? Verificationism or falsificationism?

Question 1: Are economic theories and models developed using induction or deduction? My view: If we gather historical evidence and figure "so, people tend to be like this and that so let's call this ...
758 views

### Does the Marshallian demand function always include prices and income?

I have the following utility function: $$U(x_i)=x_1x_2+x_3$$ with budget constraint: $$p_1x_1+p_2x_2+p_3x_3\leq I$$ I use the Kuhn-Tucker method to find the optimal choices of the Utility ...
712 views

### Is the contract curve orthogonal to the priceline?

Consider an exchange economy with two consumers A and B, two goods x, y. Consumers have identical preferences $U=xy$. Total available endowment are $E_x$ and $E_y$. This is the background of a ...
365 views

### Converting word definitions of Pareto-Optimal into math symbols

I'd like to have a mathematical version of the following two definitions just because I remember symbols better than words. But I lack the math prowess to convert them from words to symbols. Can ...
550 views

### Oligopolistic producers and retail price wars

Consider an industry with few producers selling differentiated products. The products must be sold through retailers of whom also there are a few and who therefore possess some degree of market power. ...
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### Higher order beliefs and coherency in game theory

I am reading about the higher order beliefs. Before getting into the formal definitions, I will define some common terminology which I will need for the formal definitions. If $X$ and $Y$ are two ...
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The utility function for goods can be modeled using something like the exponential utility: $$B(x)=\frac{1-\exp(-ax)}{a}$$ with $a>0$. So that marginal benefits are modeled as being within $[0,1]$...
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### Linear Expenditure System of Demands, Derivation Help

This problem I am working on comes out of--surprise--the Mas-Colell book for graduate micro (3.D.6). I think I have correctly used the FOC of the Lagrangian of the utility maximization problem to ...
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### The Sonnenschein-Mantel-Debreu results, what are the implications for macroeconomics?

I have always wondered why such a negative result such as Sonnenschein–Mantel–Debreu theorem (SMD) theorem is usually ignored or disregarded by practitioners, specially in macro. The result roughly ...
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### Understanding Classical Rationality at a Basic Level

I am a high school student in an intro Microeconomics class (note that we have not covered utility functions) and I'm utterly confused about the classical concept of rationality. I certainly ...
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### What term/theory describes more efficient utilization of a resource?

I may be asking the wrong question here, but I wonder if there is a term/theory that describes/studies the evolution of an economy that continually improves the utilization and allocation of certain ...
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### How to write the dual problem of this maximization problem?

On this note for Shapley-Shubik model, there's a maximization problem: $$\max_{x_{ij} \in \mathbb{R}^{M \times N}}\sum_{j \in N}\sum_{i \in M}v_{ij}x_{ij}$$ \text{s.t.} \ \sum_{j \in N}x_{ij} ...
471 views

### Instrumental variables for minimum wage

I was wondering if there is a classic instrument for minimum wage as there is for schooling or other variables. If so, how does it fares with respect to most established designs like spatial ...
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### If all firms in an economy are in monopolistic competition with constant elasticity of substitution, can they profit-maximize at $MC=MR=AC$?

Suppose all firms are monopolistically competitive with constant elasticity of substitution. Can they profit maximize at the quantity point $MC=AC$ (So $P \neq MC$ but $Q$ is set at where $MC=MR=AC$ ...
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### Teaching: from Microeconomics to Open-economy macro

I am a new faculty teaching MBA courses. Presently, I am teaching International Financial Management (IFM) and Macroeconomics. I have prepared the syllabus of macroeconomics based on first 9 chapters ...
I'm starting to read the literature of multidimensional screening models for monopolists selling $n$ goods to a continuum of buyers with $m=n$ dimensional types, and Rochet (1987) proves that a ...