Questions tagged [general-equilibrium]
In economics, general equilibrium theory attempts to explain the behavior of supply, demand, and prices in a whole economy with several or many interacting markets, by seeking to prove that the interaction of demand and supply will result in an overall (or "general") equilibrium.
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Finding Walrasian equilibria when Walrasian demands are not unique
I'm trying to solve the following excercise:
Find the Walrasian equilibria for a pure exchange economy where agents' ($A$ and $B$) preferences and endowments are given by:
$u_A = x_A + y_A$
$u_B = 2 ...
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Why is there a Walrasian Equilibrium if excess demand goes to infinity as price goes to 0?
In one exercise, we have to argue that a Walrasian Equilibrium exists and the solution says that if we can see that excess demand goes to infinity as price goes to 0, and as price goes to infinity, ...
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How to find the contract curve when both agents have linear utilities?
I'm trying to solve the following excercise:
Find the contract curve for an exchange economy where agents' ($A$ and $B$) preferences and endowments are given by:
$u_A = x_A + y_A$
$u_B = s x_A + y_A$
$...
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How to find the contract curve when an agent has Leontief utility?
I'm trying to solve the following excercise:
Find the contract curve for an economy where agents' ($A$ and $B$) preferences and endowments are given by:
$u_A = x_{1A}^{\frac{1}{2}} x_{2A}^{\frac{1}{2}}...
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Competitive equilibrium vs Pareto optimal
What's the difference between competitive (or Walrasian) equilibrium and Pareto optimal equilibrium. Is a price equilibrium with transfer a competetive equilibrium?
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Second welfare theorem
Could you provide the intuition behind the second welfare theorem, and prove in a few rows the theorem itself?
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Non Continuous Walrasian Demand Function
I have a silly question.
I’m trying to solve some exercises that have to do with the walrasian demand function $x(p,w)$ and excess demand function $z$.
More especifically, I’m asked to show that there ...
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In GE, is price ever exogenous?
In general equilibrium models, is ever price exogenously given rather than endogenously determined in the equilibrium?
Now, which price am I talking about?
Consider an economy with production.
There ...
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How to find the competitive equilibrium?
Consider a $2$-good, $2$-person pure-exchange economy where $A$ is endowed with $(0,5)$ and $B$ is endowed with $(5,0)$. If the utility functions are $u_A = xy$ and $u_B = \min\{x,y\}$, what are all ...
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Finding the Contract Curve
I was doing a problem with the following data
we have two utility functions which are as follows:
$$U_1(x_1,y_1)=\beta \ln(x_1y_1) \;,\; U_2(x_2,y_2)=(\frac{x_2}{y_2})^\alpha$$
along with feasibility ...
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Efficient allocations with perfect complements
Consider a very simple economy with two agents (A, B) and two goods ($x$, $y$). Agent A has utility $u_a = \min \{x_a, 2y_a\}$; agent B symmetrically has utility $u_b = \min \{2x_b, y_b\}$. Suppose ...
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Second welfare theorem: can it be used to show there does not exist any competitive equilibrium? (exchange economies)
The one version of the Second Welfare Theorem states that: if there exists a competitive/Walrasian equilibrium and an endowment $X$ is Pareto efficient, then there is a price vector $\hat{P}$ for ...
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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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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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Which algorithm is used to solve for an equilibrium in Nordhaus's RICE?
Nordhaus-Yang's paper on the RICE model is available here; see pg 24 for its defining equations. https://www3.nd.edu/~nmark/Climate/Nordhaus_Yang_AER.pdf
In S4 on pg 7, they explain that the solution ...
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Walrasian equilibrium with quasi linear function
There is a two-person exchange economy
Each agent has the following utility $u_i(x_i,y_i)=v(x_i)+y_i$ for agent $i=\{A,B\}$
Assume that $v$ is strictly concave and increasing function that has a ...
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Pareto efficient allocations in Cobb-Douglas utilities
Consider 2 agents and 2 goods with Cobb-Douglas utilities
$$
\begin{aligned}
&u_1\left(x_1, x_2\right)=\alpha \log x_1+(1-\alpha) \log x_2, \\
&u_2\left(x_1, x_2\right)=\beta \log x_1+(1-\beta)...
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Adding an energy sector to Nordhaus's RICE model
This is a follow-up question:
Modelling effect of renewable energy investment on GDP (via integrated assessment models)
I'm interested in adding an energy sector to Nordhaus's RICE model. Has there ...
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Is a balanced BOP (without taking the official reserves account into consideration, desirable in the real world?
In general, BOPs(without taking the official reserves account into consideration( aren't balanced.
A BOP surplus is generally a good sign if the correct goods and being exported and a BOP deficit is ...
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A question on short run equilibrium in the simple Keynesian model
In the simple Keynesian model , it's generally assumed that there are no technological changes in the short run. However, as this is a macroeconomic model, changes in one or 2 industries, shouldn't ...
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Production economy general equilibrium
I encountered the following economic model.
Consider the following general equilibrium model with only two households, two consumer goods ($x$ and $y$) and two inputs (capital $k$ and labor $l$). ...
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Finding all symmetric mixed strategy equilibria in a finite game
There’s a pure strategy and one mixed strategy with probability distribution (0.5,0.5,0) and (0.5,0.5,0) for each player in this game.
But I was wondering if this example fails the fact that there are ...
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Question on the conditions for the existence of a Walrasian equilibrium
I have a production Economy with two consumers and one producer.
Consumers have a consumption set in $R^2_+$
Y is production possibility set and $$Y= \{y | max (2y_1+ y_2, y_1+2y_2)\le 0\}$$.
...
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Find the set of Pareto efficient allocations
There is an exchange economy with two people and two goods.
Utility functions are
$u_A(x_A, y_A)=\max\{x_A, y_A\}$
$u_B(x_B, y_B)=\max\{x_B, y_B\}$
Endowments are $w_A(1,\alpha)$ and $w_B(1,\alpha)$ ...
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For each Pareto efficient allocation, suggest how we might change the endowments so that the Pareto efficient allocation is a walrasian equilibrium
I have a two-person exchange economy
Each agent has the following utility $u_i(x_i,y_i)=v(x_i)+y_i$ for agent $i=\{A,B\}$
Assume that $v$ is strictly concave and increasing function that has a ...
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A question on the simple Keynesian model
In the simple keynesian model, the equilibrium is usually calculauted by dteremining where the aggreagate supply curve meets the aggregate demand curve curve, with the AS curve , usually taken to be a ...
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Are weak and strong pareto optimality equivalent in terms of efficiency and equity?
Can I claim that the concepts of weak and strong Pareto optimality are equivalent both in terms of efficiency and equity among agents and generate the same level of social welfare?
I know that when ...
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Can budget lines of two agents containing equilibrium allocations be different?
Consider a pure exchange economy that has two goods and two agents (people). Suppose the initial endowments of person $A$ and $B$ are $(e_x^{A}, e_y^{A})$ and $(e_x^{B}, e_y^{B})$ (resp.) such that $...
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Is there a way to proof why prices non-negative or strictly positive in some cases?
I am studying Microeconomics at a Graduate level with Mas-Colell and I found something in our course slides that I do not know how to prove:
If we allow free disposal in the production set, the ...
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Reason behind Pareto principle
Is Mathew effect or Pareto Principle are the laws of nature like Newton law of gravitation. What are the reason behind Pareto principle?
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Calculating Direct and Indirect Resource Use using Input Output Approach
I have been referring to Perman's book titled, "Natural Resource and Environmental Economics" for economy wide environmental modelling. In Chapter 8, Section 8.2 pg.257-259; it talks about ...
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Why did economic forecasters get inflations predictions so wrong?
I come from more of a statistics and applied math background, but I am interested in issues of social science. I have been trying to understand why economic forecasters or forecast models seems to ...
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Interesting example of general equilibrium effects contradicting RCT results
One of the concerns that one can have regarding the use of RCTs for evaluating policies is that while when done in small scales, the RCTs may show the result in one direction, scaling the policies may ...
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Macroeconomics and microeconomics
Can we say macroeconomics is top down approach and microeconomics is bottom up approach .Is there any relation/connection between macroeconomics and microeconomics.
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what is the optimal allocation for this economy
A two-person two commodity economy has social endowment of x = 1 unit of food and y = 1 unit of wine. Agents preferences are increasing in own consumption but decreasing in wine consumption of the ...
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Learning Resource Question - Computable General Equilibrium Modelling
Several years after graduation, I would like to learn some practical computable general equilibrium (CGE) modelling such as a CGE that can handle distributional outcomes.
Does anyone know of open-...
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Existence of a Walrasian Equilibrium
I was wondering how to tackle part b of this question. I've already completed part a) using the usual method of equating the MRS (kink point for the second utility function) then looking at ...
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When is an allocation in the core of an economy but it's not a Walrasian equilibrium?
So I was given this problem where both agents have Cobb-Douglas utility functions and I'm asked to find an allocation that's in the core but not a Walrasian equilibrium. Isn't the core of an economy ...
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Competitive equilibrium for an economy with a consumer and a producer
A representative agent’s preference over consumption $(c)$ and labour supply $(l)$ is given by the utility function $$ u(c_D, l_S)= c_D^a .(24-l_S)^{1-a}$$
Production of the consumption good $c$ is ...
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Understanding a paragraph in Debreu's Theory of Value
I wish to understand the following paragraph (from section $2.7$ of Debreu's Theory of Value):
Imagine that a certain good circulates as money at location $s$, at date $t$,
and let $k$ be the index ...
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What does it mean when an economist talks about "equilibrium"
In economics, there are many equilibrium concepts, like equilibrium under perfect competition, Monopolist equilibrium, competitive equilibrium, general equilibrium, nash equilibrium, equilibrium price,...
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Changes in TFP and wage rates across firms
Assume that you have two firms, firm A and firm B. Firm A faces the
production function:
$$
Y_{A}=A_{A}F\left(K_{A},L_{A}\right)
$$
and firm B faces:
$$
Y_{B}=A_{B}F\left(K_{B},L_{B}\right)
$$
Factors ...
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Perfect Competition, Zero profit rule and General Equilibrium
I'm reading a book where the definition of an equilibrium for a competitive economy is given as in
Kenneth J. Arrow; Gerard Debreu (1954) Existence of an Equilibrium for a Competitive Economy ...
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How to solve a general equilibrium problem with lexicographic preferences?
I have been unable to find a good example of this type of GE problem in our textbooks, and our professor has indicated that something like this may appear on our exam. So, here is a hypothetical ...
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How do I find the socially optimum and equilibrium value?
I am struggling with the following question. Could someone please explain how to do it?
People are trying to go to the city centre. A bus takes 1 hour and will always take 1 hour,
unaffected by ...
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How would a perfectly competitive industry respond to a macroeconomic demand shock in the long run?
In microeconomics, we are taught that in a perfectly competitive industry, the long-run industry supply curve is horizontal. This is because new firms would enter or exit until the profit is driven to ...
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In a box diagram, why does efficiency locus lie on one side of the diagonal, if both sectors haves constant returns to scale function?
The following is what I understand, so far.
If we measure labour in the $x$-axis and capital in the $y$-axis, the slope of diagonal of the box is the capital-labour ratio $K/L$ in the economy. Let $A$ ...
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Is this really a valid description of AS&AD after lockdown?
I understand that in the short run AS decreased (supply chains) and AD increased (stimulus, post-lockdown behaviour). But what's up with the lines in the long-run?
Also is this even a valid way of ...
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Non-existence of general equilibrium with quasi-linear utility
I recently came across an interesting example of why general equilibrium need not exist with quasi-linear utility (in case anyone is interested, I'm posting this at the end). To make the example work, ...
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What should I learn from heterodox economy? [closed]
As a graduate and master student, everything I've learned and I'm learning is from mainstream economy which in some parts seems like propaganda. Most of theories comes from the hypotesis of perfect ...
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