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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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Is CES production representing the average of inputs?

I know that the Constant elasticity of substitution production function is given by: $$Q=\gamma\left[\delta L^{-\alpha}+\left(1-\delta\right)K^{-\alpha}\right]^{\frac{-1}{\alpha}}$$ where $\gamma$ is ...
Pallak Goyal's user avatar
-2 votes
0 answers
19 views

Select the correct answer [closed]

An increase in the price of petrol above equilibrium will ? A)Shift the petrol supply curve to the right B)Shift the petrol demand curve to the right C)cause a surplus of petrol D)cause a shortage of ...
user48100's user avatar
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17 views

Derivation of Euler Equation in presence of the Dixit-Stiglitz Aggregator

I reading the working paper of Sebastian Banz (2012). I have an issue with the derivation of the Euler equation. The author models the demand side of the economy as follows The representative consumer ...
Maximilian's user avatar
1 vote
0 answers
29 views

Diamond-Dybvig model - condition for bank run

I am following the textbook of Freixas and Rochet (p.249 and 253) and cannot understand where their condition for bank runs comes from: They say that bank runs occur iff $$C_1 > \pi_1C_1 +(1-\pi_1 )...
ABCBAA's user avatar
  • 91
1 vote
0 answers
25 views

Reconciling Continuity of Binary/Preference Relations with Continuity of Functions/Correspondences

There are various ways to express the concept of continuity of a binary relation, but one I've come across seems to imply the closed-graph property is sufficient. That is to say: For a nonempty set $X$...
hillard28's user avatar
2 votes
2 answers
231 views

All-pay auction question problem

In a sealed bid all pay auction, the highest bidder receives the good but every buyer pays the seller the amount of her bid regardless of whether she wins. Suppose there are two bidders whose ...
GraceLynn87's user avatar
2 votes
1 answer
56 views

Equivalence of two definitions of monotone preference

In MWG, the definition of weak preference is for all $x,y \in X$, $y>>x$ implies $y\succ x$ . But I have read some other articles that define weak preference as $y\geq x\implies y\succeq x$. ...
Nonenicht's user avatar
4 votes
1 answer
127 views

Quasi-linear microeconomics problem

Hey guys I need your help to solve the following problem. Here's my attempt. Given the function: $$u(x_1,x_2)=x_1+x_2^\beta, \ \ \beta \in (0,1).$$ Write down the UMP and solve for the Walrasian ...
giudale's user avatar
  • 41
2 votes
0 answers
26 views

Degrees of Risk aversion and Expected utility

There are two agents with utility functions $g_1$ and $g_2$, where the agent with function $g_2$ has higher (absolute) risk-aversion. The agents face a lottery $((q,x_1),((1-q),x_2))$, i.e. agents ...
Ramandeep's user avatar
4 votes
1 answer
93 views

Proof Mean with a Smaller Sample Size is a Mean Preserving Spread

I am attempting the following exercise from Annie Liang's excellent lecture notes: I have written an attempted proof (below), but I'm worried about the independence assumption I make. In particular, ...
matthewoulton's user avatar
1 vote
1 answer
79 views

What are the most common axioms to define a strict preference relation?

I am wondering which are the standard axioms with which indifference and (particularly) strict preference are usually defined. Normally, a weak preference relation for agent $i$ on a set $X$, denoted $...
EoDmnFOr3q's user avatar
1 vote
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50 views

Background courses for MSc in Finance

I'm a Mathematics bachelor student and next year I am going to pursue a 2-year MSc in Finance. In this question, as a total beginner in Finance and more generally in Economics, I'd like to get ...
Amanda Wealth's user avatar
2 votes
0 answers
36 views

Axiomatic characterisations of dictatorial social choice/welfare functions?

I am looking for axiomatic characterisations of dictatorial social choice/welfare functions; where a dictatorial social choice function is one that always picks the dictator’s favourite outcome, and a ...
EoDmnFOr3q's user avatar
1 vote
0 answers
27 views

What prices do firms impose on perfect substitutes?

Let's say we have a retail firm, which sells various products. Among these products, the firm also sells five or so products that are for almost all customers perfect substitutes, although the tastes ...
Athaeneus's user avatar
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6 votes
1 answer
64 views

Question About Proving $\alpha(\cdot)$ is Continuous in the Proof of Proposition 3.C.1 from MWG

See Proposition 3.C.1 from MWG Continue from this post, Microeconomic Theory by Mas-Colell et al. book said the following: What remains is to establish that all convergent subsequences of $\{\alpha(x^...
Champa's user avatar
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3 votes
1 answer
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Proof: Let $\epsilon>0$ and $x'\in\mathbb{R}^L_+$ be such that $\|x'-x\|\geq\epsilon$. Then $\alpha(x')$ belongs to some $[\alpha_0,\alpha_1]$

See Proposition 3.C.1 from MWG Continue from this post, the book (MWG) then started the proof that $\alpha(x)$ is a continuous function: We now argue that $\alpha(x)$ is a continuous function at all $...
Champa's user avatar
  • 167
2 votes
1 answer
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Public Good Provision and median voting principle

This is a question that came in one of the previous year's entrance test to a master's program in a reputed institution in my country. I am also attaching how I tackled the problem in each part of the ...
Kanooz's user avatar
  • 41
1 vote
1 answer
25 views

Trying to find a proof for Strong Axiom of Revealed Preference with general choice set

Note this is question is not about consumer demand with price and income data. This is a question about general choice theory. For reference, see: https://www.jstor.org/stable/2550390 See Debreu's ...
High GPA's user avatar
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5 votes
1 answer
73 views

Question About the Step Proving $\alpha(x)$ Represents Preferences in the Proof of Proposition 3.C.1 from MWG

Continue from this question, the book Microeconomic Theory by Mas-Colell et al. said We now take $\alpha(x)$ as our utility function; that is, we assign a utility value $u(x)=\alpha(x)$ to every $x$. ...
Champa's user avatar
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2 votes
0 answers
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Question About the Step Involving the Connectedness of $\mathbb{R}_+$ in the Proof of Proposition 3.C.1 from MWG

This is a small issue, but it confuses me. In the proof of Proposition 3.C.1 of Microeconomic Theory by Mas-Colell et al, the book said ... $\mathbb{R}_+\subset (A^+\bigcup A^-)$. The nonemptiness ...
Champa's user avatar
  • 167
1 vote
1 answer
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Why does an increase in the Dixit-Stiglitz price index lead to an increase in demand?

I'm studying the graduate international trade lecture notes by Treb Allen and Costas Arkolakis posted on their personal homepage. The first chapter covers the Armington model. After deriving the ...
lidoor kulow's user avatar
1 vote
0 answers
33 views

bayesian nash equilibrium cournot game

Consider the Cournot game with two companies, whose function (Q) P is in the form of a relation: P (Q) = 60 − Q if Q ≤ 60 0 if Q ≥ 60 where q2 + q1 = Q is the sum of outputs in the market. The cost of ...
morteza bigdeli's user avatar
0 votes
1 answer
24 views

To find optimal number of customers in fully competitive market with both MC and AC increasing?

This graph indicates Marginal cost (MC) and Average cost (AC) curves to obtain customers. AC is increasing because MC is increasing. It is seen that the decreasing return to scale because MC has ...
Murat Yazıcı's user avatar
1 vote
1 answer
86 views

Public goods on cost of abatement

There is a manufacturer and a fishery. Let $E$ be the effluent of the manufacturer. The marginal cost of abatement borne by the manufacturer is $M C A=8-E$. The marginal external cost borne by the ...
PiVoyager's user avatar
0 votes
0 answers
30 views

Vertical integration and transfer price

A firm has an upstream engine division and a downstream car division. The total cost of engine production is $T C_U=Q^2 / 2$. The total cost of car assembly is $T C_D=Q^2 / 2$. The demand for the ...
PiVoyager's user avatar
0 votes
2 answers
19 views

Assuming a fall in price, does consumer surplus fall more with elastic or inelastic price elasticity of demand

I know that the total consumer surplus is higher for more inelastic P.E.D values, which makes intuitive sense: People would be willing to pay more than they actually do for inelastic goods e.g. a ...
Hallojvjknvve's user avatar
1 vote
1 answer
59 views

Present value calculation

Vincent is deciding whether to buy a painting. The current sale price of the painting is 100 dollars. The resale price of the painting after $T$ years is $100+T$ dollars, where $T$ is a positive ...
PiVoyager's user avatar
2 votes
2 answers
113 views

Proving quasi-concavity for a utility function

I have a utility function, and I want to prove that it is a quasi-concave function: $$ u(x_1,x_2)= 2x_1x_2+x_1+2x_2 $$ I do this by showing that the set of points where the utility is larger than or ...
Noah's user avatar
  • 65
2 votes
1 answer
63 views

Using lagrange on a quasi-concave utility function

A consumer has the following utility function $$u(x_1,x_2)=2x_1x_2+x_1+2x_2$$ I have maximized his utility function, and found its demand functions, for $x_1$ and $x_2$, using Lagrange. However, is it ...
Noah's user avatar
  • 65
2 votes
1 answer
174 views

Solving utility maximization, and finding demand function

A consumer has the following utility function $$u(x_1,x_2)=2x_1x_2+x_1+2x_2$$ I want to maximize his utility function. $$max: 2x_1x_2+x_1+2x_2. uc:p_1x_1+p_2x_2=y_A$$ Using Lagrange, I get $$L(x_1,...
Noah's user avatar
  • 65
2 votes
2 answers
23 views

Positive monotonic transformation and identical preferences

Two consumers, A and B have the following utility functions $$ u^{A}(x_1,x_2)=x_1(x_2)^\alpha$$ $$u^{B}(x_1,x_2)=\frac{1}{3}\ln(x_1)+\frac{2}{3}\ln(x_2) $$ I have to find $\alpha$ such that the ...
Jonathan's user avatar
1 vote
1 answer
63 views

Prove a preference preserved under limits if and only if its upper and lower contour is closed

I'm concerned with the reverse direction, that upper and lower contour is closed implies the preference is continuous, that is for any sequence $x_n$ and $y_n$, $x_n\succcurlyeq y_n$ for all $n$, ...
Nonenicht's user avatar
0 votes
0 answers
30 views

Comparing agent decision-making under risk-neutrality and risk-Aversion

I am working on the following question but have not been able to come up with a suitable way to proceed. The setup is as follows: There is a technology (for example, a vaccine) which reduces the ...
Ramandeep's user avatar
0 votes
1 answer
22 views

Changes in deadweight loss in a monopoly

When a per-unit subsidy is given to a monopoly, the marginal cost curve will shift downwards. It is unclear to me how this will affect deadweight loss, however. I can draw examples where the DWL ...
asdf's user avatar
  • 13
2 votes
0 answers
33 views

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
39 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
28 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
56 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
  • 53
0 votes
1 answer
25 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
25 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
33 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
0 votes
0 answers
24 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
37 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
  • 3
2 votes
0 answers
64 views

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
2 votes
0 answers
45 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
  • 93
5 votes
1 answer
94 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
  • 505
-3 votes
1 answer
53 views

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
  • 137
2 votes
0 answers
83 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
  • 293
0 votes
0 answers
12 views

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

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