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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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Positive monotonic transformation

I want to draw an indifference curve for this preference relation on $ℝ^2$ $$x ≿ y \leftrightarrow (x_1+x_2)^2 ≥ (y_1+y_2)^2$$ Can I just take the square root(and then drop the absolute value sign ...
Jonathan's user avatar
1 vote
0 answers
41 views

Indifference curves given preference relation

Let's say I have a preference relation on $ℝ^2$ given by $$x≥y \leftrightarrow x_1+x_2 ≥ y_1+y_2$$ So, from my understanding, the bundle x is preferred at least as much as the bundle y if and only if ...
Jonathan's user avatar
0 votes
1 answer
37 views

How do you calculate price elasticity of aggregate demand?

Price elasticity of demand is defined as $\frac{\delta q}{q}\frac{p}{\delta p}$. If aggregate demand $q = q_1 + \ldots + q_n$, then $\delta q = \delta q_1 + \ldots + \delta q_n$, and the price ...
Reddit At Work's user avatar
1 vote
2 answers
59 views

Does duality hold for u(x, y) = x^2 + y^2? (Corner solution)

Could you please help me evaluate this logic? I've been told that "if preferences are strongly monotonic, duality holds." In the case of utility u(x,y) = x^2 + y^2, we will get a corner ...
Martin's user avatar
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0 votes
1 answer
26 views

Value of information for risk neutral agent?

Maria is a risk neutral agent who can invest in one of the two projects: Project A where she must pay 200 upfront and gain 600 if it rains, 800 if it snows, 400 if it hails and $0 if it is sunny. The ...
Mayu's user avatar
  • 1
5 votes
3 answers
2k views

Economists Working At the Intersection of Pure Math and Economics

As a math student interested in economics I was recently reading some of the papers by Graciela Chichilnisky on social choice theory and some of her papers applying topology to other areas of ...
throwawayaccount's user avatar
1 vote
0 answers
26 views

Optimal pricing policy

The setup is as follows: A theatre has a monopoly over the rights to screen a new movie over two successive weeks $t = 1, 2$. Customers want to see the movie at most once. There are two types of ...
Fjeeds Arcade's user avatar
0 votes
0 answers
34 views

Equivalence of two definitions of revealed preference

Given a choice structure $(\mathscr{B},C(.))$ we can construct a preference align with this structure, write it as $\succcurlyeq^C$ defined as $$x\succcurlyeq^C y\Leftrightarrow \exists B \in \mathscr{...
Nonenicht's user avatar
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29 views

Equilibrium Non-Existence in Moral Hazard with Bilateral Risk Neutrality

Suppose we have one agent and one principal. The agent picks effort level $e\in \{0,1\}$ which is not contractible. The agent is risk neutral with ex-post utility $w-ce$ where $c>0$ and $w$ is the ...
Joseph Basford's user avatar
0 votes
1 answer
41 views

Why does the budget line cross the price offer curve instead of just touching it?

As far as I understand, the price offer curve shows all the utility-maximizing bundles generated by varying the price ratio but with the utility function remaining the same. However, in the image, the ...
Lex's user avatar
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2 votes
0 answers
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Berge's theorem of maximum's application to expenditure minimisation problem

Let $f:X\times A \rightarrow \mathbb{R}$ be a continuous function, and $\Gamma:A \rightrightarrows X$ be a non-empty, compact-valued and continuous correspondence, with $X$,$A$ be Euclidean Space. ...
Nonenicht's user avatar
  • 113
2 votes
0 answers
47 views

Proof of Second Welfare Theorem with infinitely many goods

I'm trying to understand the proof of the Second Welfare Theorem and I'm still struggling with the intuition behind the use of a linear functional as a mathematical instrument in order to prove that ...
Pepus's user avatar
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5 votes
1 answer
99 views

About Two Methods of Computing Bayesian Equilibria

Question I want to compute the Bayesian equilibria for the following Bayesian game: With probability $p$, player 1 would be of type 1.1. With probability $1-p$, player 1 would be of type 1.2. Player ...
Beerus's user avatar
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-3 votes
1 answer
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Economics as non zero sum game [closed]

If economics is not a zero sum game then why its difficult to earn money.I mean just increase the size of the cake and distribute it.
quanity's user avatar
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2 votes
0 answers
85 views

Prove that any lexicographic preference $(u_1,u_2)$ must be complete and transitive

Let $\succsim$ be a lexicographic preference represented with $(u_1,u_2)$. $x\succsim y$ if $u_1(x)>u_1(y)$ OR $u_1(x)=u_1(y)$ and $u_2(x)\geq u_2(y)$. Is it obvious that $\succsim$ must be both ...
dodo's user avatar
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0 answers
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Equivalent assumptions in Revealed Preference and Classical Preference Theories

I have read that there are dualities between Revealed Preference Theory and Classical Preference Theory. Suppose, I have $X$ as the set of all conceivable choices, and $\mathscr{B} \subseteq 2^X$ the ...
Ishan Kashyap Hazarika's user avatar
2 votes
1 answer
148 views

Zero-Sum Game with two Mixed Equilibrium Interpretation

In the attached Zero Sum Game, i have solved for two Mixed Nash Equilibrium, $(l,m)$ and $(m,r.)$ In $(l,m)$ the payoff is $8/5$ to $P_1$, and $-8/5$ to $P_2$. Here $P_1$ mixes between Top and ...
CormJack's user avatar
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2 votes
0 answers
58 views

Are there Sequential Equilibria that are not Trembling Hand Perfect Equilibria, that don't involve Weakly Dominated strategies?

I'm taking an advanced course (graduate level) in Game Theory. My class has covered several equilibrium concepts, up to Sequential Equilibrium. The professor said that there are already more ...
Nicolas Torres's user avatar
2 votes
1 answer
413 views

How do I measure well-being without Utility function?

This is a question from a test: "A consumer with \$1000 income spends \$200 on good X per month. His income increases to \$1100, and price of good X increases 50%, with no other price changes. In ...
calavera's user avatar
0 votes
2 answers
113 views

bertrand duopoly with discrete price

There is a 2 firm, engaging in price competition. Total costs are CA(q)=10q and CB(q)=21q and the inverse demand is P(q)=120-q What is the equilibrium profits? What is the maximum amount that firm A ...
Derin dur's user avatar
0 votes
1 answer
50 views

Lump sum transfers to implement any Pareto efficient equilibrium as the market outcome

If we have 2 consumers (a and b) and 2 goods (x and y) -- so we are in an exchange economy setup. From what I understand, due to 2FWT, we can choose any Pareto efficient outcome (x*), calculate the ...
badeconomist101's user avatar
0 votes
2 answers
157 views

How to solve a Leontief Production function?

I am solving for the Leontief production function in the form of y= min {L^1/2 , K^1/2} , in the short run (fixed K) and in the long run respectively. I am asked to solve the production in terms of w, ...
coco's user avatar
  • 3
3 votes
1 answer
99 views

Consumer surplus calculation

Suppose $P(Q) = 10-0.5Q$. If a firm is producing $q_1$ and $q_2$ units from its two different machines such that $Q = q_1 + q_2$, what is the consumer surplus at $(q_1, q_2)$? I think the consumer ...
consumer-surplus's user avatar
3 votes
1 answer
87 views

Question About Proof of Proposition 3.C.1 in MWG - Step 1

I have difficulties understanding the first step of the proof of Proposition 3.C.1 in MWG. Proposition 3.C.1$\quad$ Suppose that the rational preference relation $\succsim$ on $X$ is continuous. Then ...
Beerus's user avatar
  • 505
3 votes
1 answer
74 views

Understanding the definition of monotone

In Microeconomic Theory by Mas-Colell, Whinston, and Green, the definition of monotone preference relations is given as follows: Definition 3.B.2$\quad$ The preference relation $\succsim$ on $X$ is ...
Beerus's user avatar
  • 505
3 votes
1 answer
55 views

When are marginal rates of substitution consistent with a utility function?

Is it known when a marginal-rate-of-substitution function can be rationalized by some utility function? More precisely, and focusing on the case of two goods, what conditions are required on $M: (\...
John Sturm's user avatar
1 vote
1 answer
67 views

Total Effect, Substitution Effect, and Income Effect

We were given this information to compute the total, substitution, and income effects. $U=7.5x^{0.3} \cdot 5y^{0.2}$, $\text{Income} = 10,000$, $P_x = 5$, $P_y = 2.5$, $P_{x'}=4$. I am having a hard ...
Mikognito's user avatar
3 votes
1 answer
20 views

Paper suggestions on innovation-economics

I am in search of seminal theoretical papers in innovation economics, with a particular interest in recent works that model innovation processes. Ideally, I'm looking for papers that explore the "...
Lusian's user avatar
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2 votes
1 answer
58 views

Derive indirect utility function - Problem with CES

Consider the following CES utility function for the $h$ household \begin{equation} U^h(x^h_1,\ldots,x^h_N) = \left[ \sum_{j=1}^{N} (x^h_j - \zeta^h_j)^{\frac{\sigma-1}{\sigma}} \right]^{\frac{\sigma}{\...
Maximilian's user avatar
3 votes
1 answer
60 views

Net product marginal in Acemoglu's article "Modeling inefficient institutions"

I'm reading lecture notes by Acemoglu regarding institutions and I'm trying to study his famous model of non-democratic institutions, deeply described in his article "Modeling inefficient ...
Pepus's user avatar
  • 93
0 votes
0 answers
51 views

Modelling agglomeration effects

In this video, Glaeser sets up a demand curve for housing in a city, where there are agglomeration effects: bigger cities have higher wages, so demand (willingness-to-pay) is increasing in city size. ...
Macaulay's user avatar
1 vote
1 answer
65 views

Convex to origin - precise definition

This question asks about what "convex to origin" means. IMO even though there are half a dozen answers, they are all unsatisfactory. So in this question I ask for a precise definition of &...
Giskard's user avatar
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1 vote
1 answer
50 views

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 ...
lucas_vivier's user avatar
2 votes
0 answers
20 views

Marginal Costs of Supplying Space to Space Market and the 4Q Model - Property Investment

In analysis of the Property Investment Market Supply and Demand Curve, the Supply Curve is kinked, reflecting the high inelasticity of supply in the short run. The Supply Curve rises after the Kink, ...
Jonathan Lee's user avatar
1 vote
1 answer
18 views

Regression with one independent variable bounded for some observations

I am investigating the effect of a policy on land price. The land is transferred by English auctions. My regression looks like this: $$ \ln(y)=\beta_0+\beta_1 x_1+\beta_2 x_2+u, $$ where $x_1$ is the ...
Aaron's user avatar
  • 11
0 votes
1 answer
27 views

Strict monotonicity implies FOSD under EU?

I think this result is very simple and very useful. However, I find no paper cover it. Is it on some textbook like MWG? Strict monotonicity means: $f(s)\succ g(s)$ for all $s$ implies $f\succ g$ and $...
dodo's user avatar
  • 293
4 votes
2 answers
180 views

Definition of economics

What is the accepted definition of economics? I've read basically two versions, one that defines it as the study of scarcity and the other as the study of how to coordinate human desires given ...
KEll's user avatar
  • 51
1 vote
0 answers
43 views

What is a utility function rationalizes these preferences?

For a consumer deciding between goods A and B, with a budget of w: If A and B are the same price (or if A is cheaper), the consumer will spend their entire budget on A. As the relative price of A ...
H Rogers's user avatar
  • 638
2 votes
3 answers
163 views

Individual Consumers Representation on the Demand Curve

I recently watched an educational video titled “Understanding the Demand Curve: Shifts and Consumer Surplus”. In the video, individual consumers were associated with specific points on the demand ...
Fam's user avatar
  • 143
0 votes
1 answer
25 views

Competitive input markets and allocative efficiency

Suppose two firms are operating in a competitive input and output markets. If the two firms' production functions are $(k_1l_1)^{1/3}$ and $(1+k_1)^{-1} (l_2)^{1/2}$ where $k_1, l_1, l_2$ denote the ...
guest's user avatar
  • 25
1 vote
1 answer
56 views

Judge prosecutor example of Kameinica and Gentzkow

Based on Kamenica and Gentzkow example about the prosecutor and the judge. The utilities of the sender and the receiver are $v(\alpha,\omega)=\alpha$ and $u(\alpha,\omega)=-(\alpha-\omega)^2$. The ...
Oliver Queen's user avatar
0 votes
3 answers
77 views

Tastes in Cobb-Douglas vs CES: Different degree of homogeneity

The question has been reworded based on Giskard's comment If we have a Cobb-Douglas function: $$U_1 = x_1^{\alpha_1} x_2^{\alpha_2}$$ The degree of homogenity depends on tastes $\alpha_1$ and $\...
Athaeneus's user avatar
  • 834
0 votes
0 answers
19 views

Opportunity Costs and Trade conditions

A and B can both bake cakes or grow carrots such that they are each self sufficient, or they can each specialize in one activity and trade between themselves. Cakes and carrots are both desirable for ...
Hypnos123's user avatar
0 votes
1 answer
46 views

Von Neumann-Morgenstern utility and taxes

"Consider a risk-averse individual with Von Neumann-Morgenstern utility and who invests in a risky asset. If the return on the risky asset is taxed, so the consumer has an incentive to invest ...
Felipe's user avatar
  • 1
0 votes
0 answers
28 views

Averaging estimates of cross-price elasticity

We have data for 3 goods (equilibrium prices and quantities) and we want to know the cross-price elasticities among them. I think, this could be estimated as the following system of regressions: $$ \...
Athaeneus's user avatar
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4 votes
2 answers
255 views

Question About Stable Matrices - MWG Mathematical Appendix M.D Matrices: Negative (Semi)Definiteness and Other Properties

I am self-studying the mathematical appendix of Microeconomic Theory (MWG). They defined a stable matrix as follows: Definition$\quad$ A matrix is stable if all of its characteristic values have ...
Beerus's user avatar
  • 505
0 votes
0 answers
22 views

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 ...
Santiago Valdivieso's user avatar
0 votes
0 answers
25 views

How to derive the indirect utility function of $u(x_1,x_2) = x_2+ 2\sqrt{x_1}$?

I derived the utility $u(x_1,x_2) = x_2 + 2\sqrt{x_1}$ from the indirect utility $V(x_1,x_2) = \frac{y}{p_2} + \frac{p_2}{p_1}$ but cannot go the other direction without finding very complicated ...
Ricky Li's user avatar
0 votes
1 answer
58 views

Is cross-price elasticity a Cobb-Douglas production function?

This may seem like a silly question... Well... I guess, because it really is... But I have just realized that the intuition behind both principles may not be mutually exclusive. Consider we would like ...
Athaeneus's user avatar
  • 834
2 votes
1 answer
106 views

What is the frisch elasticity and its meaning?

I understand that Frisch elasticity is the "elasticity of hours worked to the wage rate". I wonder why then we use this specific naming only for this? Is this to make it clear what this ...
student1's user avatar

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