# 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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### Fundamental equations in economics

For the other sciences it´s easy to point to the most important equations that ground the discipline. If I want to explain Economics to a physicist say, what are considered to be the most important ...
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### Is it possible that the minimum point of a short run cost curve does not touch the long run cost curve?

In the answer to this question, the answerer said "the minimum point of a short run cost curve will be above the long run cost curve". Is it true? If so, how would it be so? I thought that if e.g. ...
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I am trying to understand how substitutability relates to mixed partial derivatives. I thought the change in marginal utility with respect to a change in the amount of $x$ would correspond to $$\frac{\... 12 votes 2 answers 41k 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 = \... 7 votes 2 answers 12k views ### Consumer surplus in case of perfectly inelastic demand How do we define consumer surplus in the case of perfectly inelastic demand? This question was inspired by the comments following this answer. For a graph of inelastic demand please also see the ... 11 votes 2 answers 1k 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, ... 11 votes 5 answers 2k views ### What are the arguments against the rational expectations hypothesis? I believe the rational expectations hypothesis says that agents in a model bear expectations that are the same as mathematical expectations. Under what circumstances does this hypothesis become ... 9 votes 2 answers 5k views ### Meaning of Additively Separable, Linear in X Often I see both in micro and macro two common terminology : Additively separable. Linear in price or linear in probability. I understand exactly as they sound by looking at the functional form ... 8 votes 2 answers 2k views ### Alternatives to Pigouvian tax Two common drawbacks of Pigouvian subsidy mentioned in the literature are related to monetisation and measurement of social cost (Baumol) and reciprocity of social cost (Coase). What alternatives to ... 7 votes 2 answers 2k views ### Why do top professional sport players get usually paid so much? I'd like to find an answer to this question as I can't see how something like this can be happening. I can see three reasons that they would earn that much but any of them if thought better is wrong. ... 7 votes 2 answers 1k 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 ... 6 votes 1 answer 6k views ### (Preference Relation/Set) Continuous \succsim imply closedness of upper and lower contour sets [ADDED/MODIFIED] : I have put my proof where the commodity space is simply \mathbb{R_+}(e.g. nonnegative reals) for simplicity below. Please share your 2 cent. I have put words to aid my own ... 6 votes 3 answers 710 views ### Does returns to scale always lead to economies of scale? I can tell the difference between returns to scale and economies of scale, but then I still don't know if returns to scale ALWAYS leads to economies of scale? Please could you help me? 6 votes 3 answers 3k 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 ... 4 votes 1 answer 153 views ### Who is the first one to equate "rational" with "complete and transitive preference"? MWG taught that, suppose that the menu is finite, "rational" is the same as "complete and transitive". But it seems that it does not cite any sources. Who said this first? vNM said ... 4 votes 1 answer 12k views ### How to derive utility function from indirect utility in this exercise [closed] Derive the consumer’s direct utility function if his indirect utility function has the form$$v(\boldsymbol{\mathbf{p}},y)=yp_1^\alpha p_2^\beta$$where \beta ,\alpha are negative. 4 votes 1 answer 316 views ### Rational preferences/individual decision-making theory I am taking advanced micro course this semester. In one of the problems we need to determine whether the preference relation is rational (i.e. complete and transitive). Since we have not really ... 3 votes 1 answer 1k views ### Showing that production technology exhibits decreasing returns to Scale The Question Suppose a firm has a production function given by$$y=F(L,K)=L^{1/4}K^{1/4}$$where L and K denote inputs used in the production of y units of output. (a) Determine whether marginal ... 3 votes 1 answer 823 views ### Intuition: Difference in price elasticities of demand due to different bases Source: pp 91-92, Principles of Microeconomics, 7 Ed, 2014, by N Gregory Mankiw If you try calculating the price elasticity of demand between two points on a demand curve, you will quickly ... 1 vote 0 answers 146 views ### Please check for payoffs which I calculated in the incomplete and imperfect game Taxpayers may either have a high income or low income, and they may be either opportunistic or honest. The tax collector cannot observe any of these characteristics, but after receiving a report from ... 33 votes 6 answers 12k views ### Why do celebrities get high wages? In the youtube video Why We Look down on Low Wage Earners the author argued: "economics states that wages are determined [...] by the number of people willing and being able to do a given job that ... 23 votes 4 answers 2k views ### What are Giffen Goods? What exactly are Giffen goods and are they of purely theoretical interest or has there been empirical evidence of their existence? 15 votes 12 answers 15k views ### If I gain, then someone else loses. Correct? On a very small scale, it's certainly true that if I gain, somebody else might lose. If I take away my brother's chocolate, then he will lose it, and will most probably not get anything comparable. ... 15 votes 3 answers 1k views ### Consumer optimum in an economy with a continuum of commodities Consider an economy with a continuum of commodities, with one commodity for each point in [0,1]. Suppose a consumer wants to maximise$$U = \int_0^1 c_i^\theta\,di\qquad 0<\theta<1$$subject ... 14 votes 2 answers 13k 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 ... 12 votes 6 answers 6k views ### Why are cost functions often assumed to be convex in microeconomics? Why are cost functions typically assumed to be convex in producer theory of (introductory) microeconomics? For me this goes against the intuition of economies of scale. There are fixed costs (FC) ... 11 votes 5 answers 19k views ### When do supply and demand curves shift? Let's assume that the price of apples has risen and that the quantity of apples sold during the last couple of weeks has decreased. From that, we can infer that the supply curve must've shifted to the ... 9 votes 3 answers 4k views ### Why absolute value in elasticities and marginal rate of substitution? This is a point I find very confusing and very hard to justify to students. Depending on the books, one finds many different conventions regarding the sign of elasticities and marginal rate of ... 8 votes 4 answers 716 views ### Can u(x) = \sqrt{x_1 x_2} + \sqrt{x_3 x_4} be solved by Kuhn–Tucker conditions? Consider \max_{x_1, x_2, x_3, x_4} u(x) = \sqrt{x_1 x_2} + \sqrt{x_3 x_4} s.t. \; p_1x_1 + p_2x_2 + p_3x_3 + p_4x_4 \le w I know we can solve the max problem through separately considering ... 8 votes 4 answers 6k 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 ... 8 votes 3 answers 3k views ### Quasilinear Utility: Pareto Optimality Implies Total Utility Maximization? I read that if we have quasilinear utility for all consumers, then any pareto optimal allocation maximizes the sum of utility levels of all consumers. That is: \textbf{What we know:}$$1)\quad u^i(...
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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,...
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### 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 ...
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### 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 ...
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### Pure exchange economy: Given an initial endowment are multiple equilibria possible?

Consider a pure exchange economy with two goods ($x_1,x_2$) and two consumers $A,B$. Both users have an initial endowment, $(\omega_1^A,\omega_2^A)$ and $(\omega_1^B,\omega_2^B)$ respectively. A price ...
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### Is it possible to have a preference relation that is complete but not transitive?

I've been doing my own reading on non-rational preference relations. I'm currently under the impression that transitivity follows as a direct result of completeness of preferences. However my (much ...
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I already read and ask NOT about pp 52-54, Principles of Microeconomics, 7 Ed, 2014, by N Gregory Mankiw. I understand such numerical examples that corroborate Comparative Advantage, but how can I ... 5k 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 ...
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### 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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### 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 ...
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### 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 ... 3k views

### 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 ... 