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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What happens to supply when a company can produce two different products
Let's suppose there is a company that can produce two goods: A or B. The price of good B increases. This will result in an increase in the quantity supplied of good B, but does this result in a ...
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What is the relation between Blackwell's order and Stochastic Dominance order?
In Kamenica and Gentzkow (2017) as well as in Bergemann and Morris (2016) the notion of Blackwell comparioson of experiments is used to compare different information structures. I am trying to find ...
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Intertemporal consumption with heterogeneous/multiple goods
I'm currently trying to build a CGE, and I'm stuck at the household's problem which is about intertemporal utility maximisation. The household consumes multiple heterogeneous goods $C_i$ (I'm limiting ...
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Transitivity of Preferences paper
I am going through some of my old grad school notes, and in my microeconomics notes on transitive preferences, the teacher made a note of a behavioral economics result where when presented with two ...
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Consumer theory with subproblem
Say the agent's problem is
$$\max_{c,\{h\}, N}\{U(c, v(\boldsymbol{h} ; \boldsymbol{\theta}))+\lambda(w N-c)\}$$, subject to $\sum_{i=1}^{I} h_{i}+N \leq 1, \quad N \in \mathcal{N}$.
Assume $U(c, v(\...
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Proving Expected Utility Theorem
I am struggling to understand the proof of the second step in the Expected Utility Theorem, particularly the part that deals with preferences over weighted sums of lotteries. The statement I am trying ...
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If the government subsidizes electric vehicle (EV) purchases , then we can predict a higher price for non-EV vehicles?
Hello this question came across on my homework. Here's what I know so far. I know the answer is false, but given we need to produce two graphs I am confused on how to represent my knowledge in two ...
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About Characterization of Homothetic Function - Mathematics for Economists by Simon and Blume Chapter 20 Exercise 18(3)
I am studying homothetic function and got the following problem:
Problem
Determine whether the function $x^3y^6 + 3x^2y^4 + 6xy^2 + 9$ is homothetic or not.
Here is my attempt.
My Attempt
I did it ...
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Equilibrium allocation 'reachable' and 'existence'
This is a figure from Microeconomics(Hal Varian) and I'm not sure about its market equilibrium and pareto efficiency. I'm sure that X is a point with pareto efficiency, but I'm not sure if it can be ...
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When talking about the supply curve, does a price increase always result in an increase in quantity sold?
I thought I had an understanding of the law of supply (i.e that when price increases supply should also increase) but we were asked a question on a recent homework sheet that kind of puzzled me. the ...
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Ask labor supply under cobb-douglas preferences
Suppose an individual has an endowment of T units of time that she can devote to labor
supply (L) or leisure (R), so T = L + R. There is one consumption good in the economy,
denoted C, of which she ...
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How do you solve this problem [closed]
How do you solve this exchange economy problem?
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Give bundles $x,y\in \mathbb R^n$, there must exist a budget $B\supset\{x,y\}$ and a demand $D(B)\in[x,y]$?
For a problem in revealed preference. Give bundles $x,y\in \mathbb R^n$, must there exist a budget $B\supset\{x,y\}$ and a demand $D(B)\in[x,y]$?
Intuitively, this mean that we have two bundles, and ...
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Paradox of 'more quantity means greater satisfaction' in consumer behavior
I am trying to understand consumer behavior in microeconomics. Consider a market basket of food and clothing. Utility / Satisfaction of 200 gram food + 2 shirts is always supposed to be greater than ...
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what to learn to write a comprehensive strong paper?
to write an excellent comprehensive paper, what topics and techniques must an economist learn? One of my former professors wrote a paper I read, there are theories, calculations, and empirical tests. ...
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Edgeworth Box for exchange economy
Could you please tell me, if the Edgeworth Box I have drawn for the exchange economy is correct?
My professor's solution is really unclear.
Thank you!
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How can I write the unit cost function of this nesting production function
Assume that there is a production function as follow:
$$h=\left\{ \left[ \sum_{j=1}^N{s_{j}^{\mu}} \right] ^{\frac{1}{\mu}} \right\} ^{\beta}l^{1-\beta}$$
The price of $s_j$ is $p_j$ and the wage of $...
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About Proof of Theorem 20.8 in Mathematics for Economists by Simon and Blume
I am studying homothetic functions using Mathematics for Economists by Simon and Blume. I am reading their proof of the following theorem:
Theorem$\quad$ Let $u: \mathbb{R}_+^\mathbf{n} \to \mathbb{R}...
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Compare cost and value of work in EU and Europe by taxes and social security
In Sweden, the social security tax paid by the employer is 31,42%. Part of that goes to the pension of the individual employee. I wanted to compare the cost for the company to employ and the value for ...
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About The Bayesian Conditional-Probability Systems in Myerson's Game Theory: Analysis of Conflict
I am self-studying game theory using Myerson's Game Theory: Analysis of Conflict. I got some trouble understanding his Bayesian conditional-probability system. The Bayesian conditional-probability ...
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Robinson Crusoe with tax
This question was asked in a micro exam last semester and I just dont know the answer, have been thinking about it for weeks.
Please help.
In a Robinson Cruse Economy Robinson produces Coconuts (C) ...
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Consumption with quantity discount
A consumer has the utility function:
u(x,y) = x*y
his initial budget constraint is: 12 = 2x+ 1y. He has a budget of $12 for the whole question, which has to be completely used.
so that he consumes 3 x ...
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Why do shareholders allow CEOs and other executives to have extraordinarily high salaries compared to regular managers and non-managerial employees?
The wage gap between CEOs and employees varies from country to country. A 2021 article from CNBC discussed how CEOs in the US on average earned 351 times more than the average US employee. The ...
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optimal delegation model extension
for my seminar paper I need to extend the model of optimal delegation, I have no idea how I can evaluate my ideas (because my professor keeps ignoring me) , can someone say if the idea of the ...
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Lexicographic preference relation not continuous
I’m having trouble understanding why lexicographic preference relations aren’t continuous. I need inspiration on how this proof would work.
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Solow Model in disrectly and continuously
what is the differences between solow model in disrectly time and continuously time?
Why in disrectly time function use the equation: k(t+1)=(1-δ)k(t) + sf(k(t)) and in continuously time function use: ...
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In Debreu's representation theorem of ordinal utility, is the assumption of "second countability" necessary?
Debreu's representation theorems
Debreu 1959 states that: second countability, continuity, and weak ordering sufficiently implies the existence of real (continuous) utility function. The second and ...
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Walrasian Demand and Indirect Utility Function [closed]
Given the utility $u = \min \{x2 + 2x1, x1 + 2x2\}$, obtain the Walrasian Demand and the Indirect Utility Function.
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CRS assumption in solow model
Can you explain why does Solow growth model assume "constant returns to scale"?
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On Cournot question
In a duopoly market, the market demand function is $y(p) = 120-p$ where $y=y_1+y_2$
Total function of firm 1 is $C_1(y_1)=20y_1$ while the reaction function of firm 2 is $y_2= 60-0.5y_1$. Assume that ...
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Does the near-zero value of Fannie and Freddie shares indicate the validity of the Discount Dividend Model?
The Discount Dividend Model posits that the value of equities is equal to the discounted value of future dividend payments of a firm; for a firm that doesn't pay a dividend, you presume that they are ...
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Core in a replicated economy
I'm trying to solve the following problem on general equilibrium:
Consider an economy with two individuals with utility functions $u^A(x^A,y^A) = \min \{ x^A, y^A \}$ and $u^B(x^B,y^B) = \min \{ x^B, ...
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How do the assumptions $p'+q_ip''<0$ and $p'-c''<0$ ensure the stability of the Nash equilibrium among private firms in basic mixed oligopoly model?
I have two quick question regarding basic oligopoly models:
What is meant by we impose the assumptions to $p'+q_ip''<0$ and $p'-c''<0$ to ensure the stability of the Nash equilibrium among ...
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How to calculate direct utility from indirect utility in this exercise?
A consumer has an indirect utility function given by
$$v(p_1, p_2, R)=\frac{R}{p_{1}+p_2}$$
Where $p_1$ and $p_2$ denote the prices of the two goods consumed by the individual and $R$ the income.
How ...
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Proving duality of UMP and EMP arguing with continuity of utility
In Mas-Colell et al.'s Microeconomic Theory Proposition 3.E.1(ii) (p. 58) states that if $\succsim$ is a rational (i.e. complete and transitive), continuous, and locally nonsatiated preference ...
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Properties of Consumer Preferences - Monotonicity
Was reviewing topics and I came across this question. I am confused because there is no reference to strict or weak monotonicity in this case. I first thought that monotonicity is violated b/c an ...
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General equilibrium with market power
I'm trying to solve the following problem:
Consider an exchange economy with two consumers, $A$ and $B$, whose utility functions are:
\begin{align*}
u_{A} & = x_1^A x_2^A \\
u_{B} & = x_1^B (...
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Minimal assumption for a “certainty equivalence” exists
Let $R$ be the set of real number. Let $N$ be an infinite set. Let utility $u:R^N\to R$. The utility function is strictly monotonic.
My question is, does the certainty equivalence $CE$ exist? Do we ...
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About Theorem 1.1 in Game Theory: Analysis of Conflict by Roger Myerson
I am self-studying game theory using Myerson's Game Theory: Analysis of Conflict. I got some trouble understanding his proof of Theorem 1.1, the Expected-Utility Maximization Theorem. The Theorem goes ...
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Reasons for why slutsky matrix may be non symmetric
In demand system estimation, theoretically we require this matrix to be symmetric. This unfortunately is not the case most of the time.
What are some reasons for why symmetry of the slutsky matrix may ...
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Consumer problem
In the basic problem of consumer's choice the budget set $B(p,w)$, with $p$ the vector of prices belonging to $\mathbb{R}^N_{++}$ and $w >0$ wealth, define a convex set. Following from that I don't ...
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How can I show what a discount factor is a function of in a bargaining model?
I was reading Espinosa and Rhee (1989) and I was wondering how can the impact of exogenous changes on the discount factor can be shown mathematically. For example, if $A$ represents some exogenous ...
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Specific term for disincentivized "doing something first"
Of course we can use "moral hazard" but we can use "moral hazard" for many things. Tragedy of the commons is a moral hazard (maximize your utility before the rest of the public ...
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Quasiconvex and quasiconcave utility function
I saw that the model of the quasi-convex utility function is similar to the concave utility function and also the quasi-concave utility function is similar to the convex utility function. How can ...
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Convexity preferences
What is the difference between convexity and strict convexity preferences? What is the difference between quasi-concavity and quasi-convexity? And is MRS still true in concave preferences?
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Samuelson Consumption loan paper and Overlapping Generations
The famous Samuelson paper on consumption loan and interest rates is a bit odd in my opinion. I wanted to understand it a bit better. The paper outline 3 generations.
Youth that produce 1 unit.
The ...
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Utility Maximization of a quasi-linear utility function
I am dealing with a quasi-linear utility function. For example
$U=(x_1x_2)^{0.5}+cx_3$ with constrain $w\ge x_1+2x_2+px_3$.By taking c, w and p as constant, I function that by using Lagrange ...
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How do I calculate total utility under discounted utility framework
Suppose we are given an instantaneous utility function and discounted rate with budget constraint. Using the exponentially discounted utility function, we can find the optimal consumption stream of a ...
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Continuity of preference
"A preference is continuous if for any $a,b\in X$ with $a\succsim b$ there are some neighborhoods $N_{\varepsilon}(a)$, $N_{\delta}(b)$ around $a$ and $b$ such that for every $x \in N_{\...
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Moral Hazard in Teams. Deriving Nash Equilibrium with bonus paying sheme
I have a few mathematical problems with the paper Moral hazard in teams, by Bengt Hölmstrom 1982. Theorem 4
Denote the conditional distribution of $x$, given the action vector $a$, by $F(x, a)$ and ...
