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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What is equilibrium economics
I was taking a course I complexity economics. My professor told me economics that are taught in say Romer, Blanchard are equilibrium economics.
My question is what does he exactly mean by equilibrium ...
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Taxation in a general equilibrium framework
Is there a good reference on taxation theory in a general equilibrium framework?
I am especially interested in the following questions.
Is the equilibrium independent of who pays the taxes?
Is the ...
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Negative externality in consumption to a Cobb Douglas utility function
I am performing a brief analysis with a Computable General Equilibrium Model approach. I want to apply a negative externality in consumption to a Cobb Douglas utility function, any idea to do it and ...
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Derivation total demand using Roy's identity
I have a "resource-balance" equation of the form (imports in sector $i$) = (number of $i$ demanded domestically) - (number of good $i$ supplied domestically). I can't figure out how the ...
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What is the intuition behind this full-employment condition?
I am given the following full-employment condition, where sectors of the economy are indexed by $i$.
$L+\sum_i\frac{\partial \pi_i(p_i,w)}{\partial w}=0$
Why, if all workers are employed, should how ...
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Economics of tradeable votes
In their book "Radical Markets", the authors (Posner and Weyl) suggest a market for votes, where citizens can freely buy and sell their votes. But there is a catch: in order to have $k$ ...
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How to find the amount of leisure time and the good consumed in a two-person and one-good economy?
Question:
Suppose an economy consists of two price-taking people, “a” and “b.” Person a has available 1
unit of “time” which he divides between rest $R(a)$ and labour $L(a)$. Person b has available 1 ...
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Competitive equilibrium in a two-person economy with substitutes and complements
Recently came across this question on a microeconomics test and there was something that did not sit quite right with me.
In an economy with two agents, A and B, and two goods, milk and honey, the ...
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Introducing productive sector into an exchange economy where only one agent is endowed with input
I'm trying to find a competitive equilibrium for an economy with consumers and some outside productive sector.
Consider an economy with two consumption goods $x_1, x_2$ and two individuals $A,B$ .
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Can we define the core as the intersection of Pareto efficient allocations and upper-contour sets?
Suppose that an economy has $n$ agents, each with endowment $\omega_i$.
Their preferences are represented by the quasiconcave and increasing function $u_i$.
Let the set of Pareto efficient allocations ...
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Find the competitive equilibrium of the following economy
The following question was given as a part of a task in microeconomic theory course. It is not from some textbook and since I still haven't figured a way to solve it I will leave it here. Thank you in ...
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Is the supply and demand elasticity equal at the equilibrium?
I am working through homeowrk problems and we were asked to calculate the supply and demand at the equilibruim using either the point or arc method. I chose to use the point method and will provide a ...
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How does Perfectly Competitive Output Level Compare to Cournot Output Level
So Let there be two firms with Output Level x1 and x2 .Inverse Demand Function $P=a-bX $ where $ X=x1+x2 $.Both firms have same MC denoted by $c$. Is the Perfectly Competitive O/t > Cournot O/t ...
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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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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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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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Leontief function nested in a cobb-douglas function for a computable general equilibrium
I am currently trying to build a CGE model, and I'm stuck with the specification of the agriculture sector. I'm trying to understand how to do nested production functions and also how to solve them. I ...
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Why is the Hicksian form of the CES demand used in CGE model forms rather than the Marshallian
I am curious to know why the Hicksian form of the CES is used in CGE models rather than the Marshallian form. I have a few hypotheses, but I am not sure which one is correct. If any?
Hypothesis 1: In ...
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Is there/can we define a notion of Giffen goods in pure exchange economies?
I was checking some questions I recently answered here on General Equilibrium, and a result from this one (Exchange economy with two agents, what's the competitive equilibrium?) drew my attention:
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Pareto efficient allocations for non-monotonic, quasi-linear utility function
Suppose we have an pure exchange economy with 2 consumers, and 2 goods $x_1$ and $x_2$. Fix some $\alpha_1$ and $\alpha_2$. The utility for consumer $i$ is defined by:
$$u_i(x_{1i},x_{2i}) = x_{1i} - |...
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How to find the equilibrium amount of $p_{2}$ in terms of $p_{1}$?
There are $100$ tons of crops remaining to supply for the two months. The crop holders consider whether to sell crops now or one month later. Holders face the demand curve of each period as below:
$...
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How to find the General Equilibria allowing for infinitesimal prices?
I know there can’t exist a usual Walrasian Equilibrium when both agents have the same lexicographic preferences:
If both agents had the preferences
$(x,y) \succeq (x’,y’) \iff:$ $x > x’ \text{ or } ...
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Robinson Crusoe Economy Question
Question:
Hypothetically, Robinson Crusoe is stuck on an island and can choose between working on gathering coconuts or leisure. The utility function is:
$U(C,L)=C^{2/5}L^{3/5}$
where C is the num of ...
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How to find the contract curve for a funky utility involving the min operator?
Suppose a pure exchange economy where agents’ ($A$ and $B$) preferences are given by the following utility functions:
$u_A = \min(3x+y,x+3y)$
$u_B = x^\frac{1}{2} y^\frac{1}{2}$
Find the contract ...
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How to find the Walrasian equilibrium for non monotonic utility functions?
I just say Amit's comment on this question: The second welfare theorem without monotonicity so I got curious and tried to find both the contract curve for that particular problem, and the Walrasian ...
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Have there been any other attempts to axiomatize/mathematize a model of an economy from the ground up like Debreu's Theory of Value
I'm looking for other attempts to axiomatize/mathematize the model of an economy from the ground up, into a sort of a long-winded general mathematical model, as it is done in Debreu's Theory of Value. ...
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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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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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