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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Income and Substition Effect: Assumptions: Normality vs. Inferiority of Goods
A question concerning the income and substitution effect when the wage changes
Let us assume that the substitution effect leads to more less leisure as the relative price of leasure increases, and ...
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Walrasian Equilibrium with
I have such a question:
In an economy with $𝐼 \ge 2 $ consumers, each agent’s utility functions are given as:
$$
𝑈(x_1 ,x_2) =max\{2min\{2x_1,x_2\},min\{x_1,4x_2\} \}
$$
The endowments in the ...
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Why do firms in a perfectly competitive market get 0 economic profit in the long run and have no entry or exit costs
I get intuitively how if there are a lot of firms selling identical products the firm demand curve would be perfectly elastic, and I also get the definition of economic profit.
Say a firm is making $...
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Cost minimization and then log differentiation
I have trouble deriving the third equation from the second one. The model is in: https://www.nber.org/papers/w30240
The firm's cost minimization problem is as follows:
\begin{equation}
\min _{L_i, \...
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estimation of certainty equivalent without given utility function
The body of question is:
Assume the decision maker is risk averse, $u(40)=\frac{1}{2}(u(0)+u(100))$, $u(m)=\frac{1}{2}(u(0)+u(180))$, try to estimate the range of m.
It is easy to get the infimum of m:...
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Rationalizable strategies/ Nash equilibrium
For the question below, how can we solve it generally for every value of θ? As the θ is not discrete, I am not sure how to apply iterated elimination of dominated strategies in this question. And is ...
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How many subgames in a two-type two-signal signalling game?
In a two-type two-signal signalling game with asymmetric information, where we know that the receiver cannot "observe" the sender type but can react with one of two actions, how many ...
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CALCULATING REVENUES OF EACH PRODUCT IN RSTUDIO [closed]
Hello everyone,
I need to work with the data presented above. This question involves a little bit of knowledge of Rstudio, but I assume some of us work with this programming language throughout our ...
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Finding demand function in Walrasian equilibrium
Maybe the title doesn't reflect what I mean perfectly but basically, I wanna derive demand functions from those two utility functions:
where $x_{11}$ is the consumption of good 1 by agent 1 and $x_{...
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Clarity about positive and normative representative household
I'd like to understand if I understood theory about representative agent (positive and normative): firstly it is necessary to ensure the existence of a representative household an it depends on the ...
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How to check if a utility function represents locally non-satiated preferences?
I understand the distant definition of LNS but I don't get how to actually apply it to given utility functions like u=x1/x2 or u=x1-x2 or of any form? Is there structured math-y way to check if they ...
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Edgeworth Box (Non-Convex preference)
Consider a situation that agent A's indifference curves are concave, while B’s indifference curves are convex and both sets of indifference curves have exactly the same shape. A northeast movement ...
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Confused on finding same preferences
I'm confused on how to determine if utility functions represent the same preferences. The question is as follows:
Which of these utility functions represent the same preferences as $u(x,y) = \sqrt(xy)$...
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Expenditure function only dependent on prices
I'm struggling with a problem where I want to derive the Hicksian demand from a given expenditure function $e(p,u)$. I would do that by using Shephard's Lemma, so that the first partial derivative of $...
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Consumer theory question | MRS
Amy spends her income on two goods: x and y. She considers them to be perfect substitutes. Which of the following is correct? (where “I” is the income level.)
A) If MRSx, y < Px / Py, then the ...
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Interpretation of the Myerson (1981) Bidder Utility (Optimal Auctions, Mechanism Design)
In Myerson 1981, the bidders' utility function does not make sense. $p_{i}$ is a probability of winning the auction, $t_i$ is the bidder's type (or valuation of the item), and $x_i$ is the payment. $r$...
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How does the market respond when some suppliers of one product are forced to switch to supplying a similar product?
I'm interested in coming up with a basic model to describe the following simple situation.
Initially there is an equilibrium in the market for the consumption of product A and product B. Product A and ...
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Why isn't this state a price equilibrium with transfer?
This is probably a silly question, but I am misunderstanding something about the definition of a price equilibrium with transfers. Consider an Edgeworth Box (2 goods, 2 agents) consumer economy with ...
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How to determine which party should get property rigths if the conditions of coase theorem are not met?
Problem:
Crazytown is a densely populated city, with an airport next to it.
Without government intervention, the airplanes landing at, and
departing from, the airport would cause a lot of noise ...
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Necessity of hyperbolic absolute risk aversion for the concavity of consumption functions
I'm currently reading the paper with the same title as this question by Mr. Toda, I attached the link below.
https://www.sciencedirect.com/science/article/abs/pii/S0304406820301373
and I have several ...
user42301
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How to find cost function from leontief production
I saw the same type of questions are asked for that but I am new at this subject so I couldn't grasp it totally.
so basically for that production function:
$$
f(x_1,x_2) = min \{ 2x_1 +x_2 , x_1 +2x_2 ...
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Show that Hicksian Demand price elasticities satisfy a given equation (Use Shephard's Lemma)
I got a homework exercise that I am stuck with: Use Shephard's lemma to show that price elasticities of Hicksian Demand $\varepsilon_{jk}^{h}=\frac{\partial x_{j}^{h}}{\partial p_{k}} \frac{p_{k}}{x_{...
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Monopoly markets
A monopoly can produce any output level at a constant marginal (and average) cost of θ per unit. Assume the monopoly sells its goods in two markets separated by some distance.
The demand curve in the ...
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What does the second differential of the marginal rate of capital mean in the 'real world'? What's the explanation?
$\frac{\partial^2f}{\partial k^2}$
Marginal Rate of Capital means the extra production from adding a unit of capital.
Assume f(x) here means production. What does the second differential mean, if ...
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How to read/estimate Demand System on data
I have difficulties understanding the concept of Almost Ideal Demand System or, most probably, I have a problem of how to perform microeconomic estimates from data, in general...
So my data look like ...
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ideal point and distance function
The question is from Ariel Rubinstein's book.
1-My first question is that is the ideal point x something like (x1,x2)?
2-Is the reason the utility function is expressed in negative form we are taking ...
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Indirect Preferences Through a Budget Set
The following theorem and proof are taken from the Lecture Notes of Ariel Rubinstein.
Assume that the demand function is derived from maximizing a preference relation $\succeq$ which satisfies ...
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Looking for a term I'm pretty sure exists
Let me describe the situation:
Company is selling a product; they buy it at x, sell it at some % over for profit. Taken on a monthly scale, you can see the profit of that particular object by ...
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Arrow's Dictator
Arrow's Impossibility Theorem is often presented as a negative result in graduate classes. I wonder if the 'dictator' is taken too literally. If the assumptions of the theorem hold, there exists an ...
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Why is isoelastic utility function so prevalent?
An isoelastic utility function is used in both simple and advanced models. I understand that it is fairly convenient to work with mathematically and that there are empirical estimations of its ...
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The dependent variable of one equation could be a regressor in another
I am estimating two different regression equations with two separate dependent variables. Each dependent variable has its own unique control variables, but they also share a similar regressor Ht.
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How to find the share price with respect to the type of share?
As someone coming from a mathematical background who has started reading into some basic finance, there are a few concepts that I am struggling to understand and would be grateful if I could check to ...
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Effects of retirement and unemployment on PPF
Which of the following will not shift a country's production possibility frontier (PPF) ? An increase in the age at which people retire or a fall in unemployment ?
To me, it is the increase in the age ...
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How are returns to scale of a non homogeneous production function defined?
Most of the production functions encountered in Intermediate Microeconomics are homogeneous (Cobb-Douglas, perfect substitutes, perfect complements).
So their returns to scale are easy to get, ...
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How to find the e(p,u) of u(x) = x1 + x2 + x3
If I do the LaGrangian for the Expenditure minimization problem, it comes as p1 = p2 = p3, how do I substitute it back in the constraint and find the Hicksian demand to find e(p,u)?
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Is the preference represented by the utility function below convex?
How do I prove that it is convex? How to prove it with the typical t in [0,1] definition? I am having a bad time typing equations here, sorry. please help me out
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how to derive marshallian demand functions from leontief preferences?
For only max or min problems, I understand we should proceed they are complements but for that
type of function, how do we really get demand functions? should we graph but can this be done without a ...
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IS-LM model question [closed]
If the firm reduces the wage-spending, so the point of the IS curve will move downward?
Is that correct?
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Every Nash equilibrium is Subgame perfect Nash equilibrium
Every Nash equilibrium is Subgame perfect Nash equilibrium.
This statement is wrong. I show this by an counter example.
Is this example enough and good to disprove this statements?
Please share your ...
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Income and substitution effect: why MRS=relative prices?
I'm trying to understand how to solve an exercise about income and substitution effects. I got the theory, I guess, but can't get the maths.
One of the steps would be to put in a system the equation ...
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How Demand of a product affects the currency
Question : Iron ore is Australia's largest export. Suppose that there was an unexpected increase in demand for Australia's iron ore exports globally. Explain what this would do to Australian Dollar ...
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How to prove that any preference relation on (countable) X has a utility representation with a range (0,1)?
Theorem: If $X$ is countable, then any preference on $X$ has a utility representation with a range $(0,1)$.
The stated proof in Rubinstein's lecture notes:
Proof: Let $\{x_n\}$ be an enumeration of ...
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Sequential version of all-pay auction
Sequential version of the all-pay auction. Two bidders alternate in bidding. A prize of \$5 is auctioned. At each move of the game, the bidding player decides whether to raise the current bid by \$1 ...
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How can an individual firm sell ANY quantity for the market price under perfect competition?
I keep hearing that under perfect competition, an individual firm can sell ANY quantity as long as they sell at the equilibrium price. But this doesn’t make sense to me. For the market supply and ...
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Why is the demand function homogenous of degree $0$ in all prices and income?
Why is the demand function homogenous of degree $0$ in all prices and income?
If I know that the expenditure function is homogenous of degree $1$ in prices and income, how do I show, using the lemma ...
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Can "thick preferences" be represented by a utility function?
From microeconomics,
$u$ is strictly quasi-concave if for all $x\ne y\in\mathbb{R}^2_+$ and $t \in (0,1)$, if $u(x)\ge u(y)$, then $u(tx + (1-t)y)>u(y)$.
You may also check the figure below.
Here ...
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Trying to understand externality
I am trying to understand about externality in simple words, the book is quite confusing. So I wanted to know how externality makes the demand curve or supply curve shift attached the below diagram ...
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What is weak monotonicity?
Which one's the correct definition of weak monotonicity?
$(x \geq y \implies x \succeq y) \land (x > y \implies x \succ y)$
$x \geq y \implies x \succeq y$
The first definition doesn't allow $(3,...
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Is the preference relation represented by $u(x)=min(x_1, x_2, x_3)$ convex? True or False [closed]
Taking two bundles $x$ and $y$,
$x = (x_1, x_2, x_3)$ and $y = (y_1, y_2, y_3)$,
I understand I have to consider three cases to prove convexity, when $x\sim y$, $x\succ y$, $y\succ x$.
I understand ...
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Heterogeneity of time invariant characteristic in event study model
I am trying to estimate the impact that the onset of a medical disease has on a number of outcomes, call them $O$. To do this, I am using an event study model with individual and time fixed effects...
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