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.
166
questions
4
votes
2answers
218 views
Arrow-Debreu Theorem of Existence: Non satiation
Let $n$ be the number of consumers and $m$ be the number of commodities.
The Arrow-Debreu theorem requires closed and convex consumption sets $X_i \subset \mathbb{R}^m$ for all buyers $i \in [n]$. ...
2
votes
0answers
20 views
Economics behind reverse auctions with occasional non-profiting suppliers
I was curious about the theory behind a reverse auction system where some suppliers act in a non-profit manner, namely, that their consideration of extra-auctions benefits of providing their service ...
3
votes
1answer
26 views
Monotonicity and continuity implies that all bundles are weakly preferred to 0
Suppose a consumer has a preference ordering $\succsim$ on $X$ that is complete. Show that if preferences are continuous and monotone, then $x\succsim0$ for any $x\in\mathbb{R}_{+}^{N}$, where $0$ is ...
3
votes
0answers
104 views
Comparing 2 equilibrium values (competitive vs centralized): can I compare only 1st derivative of objective function?
I have a rather complex model where analytical solutions do not seem achievable (I also tried symbolic solving in Matlab and Python and could not find any) so that I cannot get an explicit expression ...
1
vote
1answer
79 views
Offer curves in general equilibrium
I'm having trouble understanding how to find the offer curves in general equilibrium. Is there a general way that we can use to find it?
I can understand the Pareto set and contract curve but when it ...
1
vote
1answer
87 views
General Equilibrium with Perfect Substitutes
I came across the following problem:
The quantities of an economy’s only two goods are denoted by $X$ and $Y$; no production is possible. Ann’s and Ben’s preferences are described by the utility ...
4
votes
1answer
77 views
Walras Law in a production economy with fixed costs
Consider a price taking firm with fixed costs $fc \geq 0$:
\begin{align*}
\Pi
&=
\max_{n^D} \left\{ P_c F(n^D) - w\times n^D - fc \right\}
\end{align*}
A representative household owns this firm:...
2
votes
1answer
49 views
Meaning of «intertemporal substitution effect dominates the income effect»
Assume a household intertemporal optimisation problem, where they only either consume or labour, and one of the equilibrium conditions states that labour will be a positive function of productivity, ...
1
vote
1answer
47 views
LM curve from money demand
Let $M^d (Y,r)=a+bY-cr$ where $M^d = M/P$ is the money demand in the economy. $a,b,c>0$. Derive $LM$.
My try
$M/P=a + b Y - c r$
$b Y = -a + \frac{M}{P} + c r$
$Y = -\frac{a}{b} + \frac{M}{b P} + \...
1
vote
1answer
86 views
GDP in equilibrium
I have to find the GDP in equilibrium for a IS LM model. It is given that
$M^d (Y,r)=M_0+M_1Y-M_2r$ and $M^d=M/P$, $M_0,M_1,M_2>0$ and $M^d$ is money demand.
my solution so far
I have found that $...
0
votes
0answers
32 views
Second welfare theorem and non-continuous preferences
Are there any monotonic and strictly convex preferences that are not continuous but the second welfare theorem does not hold for them?
0
votes
1answer
105 views
Find pareto optimal allocations
Consumer 1: $U_1(x_1,y_1)=x_1y_1$
Consumer 2:$ u_2(x_2,y_2)=min\{x_2y_2 , 4\} $
Initial endowments e1=(1,4) and e2=(4,1)
I want to find Pareto optimal allocations and show its edgeworth box
My ...
0
votes
1answer
108 views
Question on General Equilibrium: how to write offer curves?
QUESTION:
Consider simple two-person, two-good economy in which agents’ utility functions are given by
$U_1(x_{11}, x_{21}) = min\{x_{11}, x_{21}\} $, and $U_2(x_{12}, x_{22}) = min\{4x_{12}, x_{22}\}...
2
votes
1answer
83 views
Market with changing number of goods and services
In the General Equilibrium framework of Arrow, Debreau and others, there are a fixed number of commodities, which I feel is a valid assumption in the short run but maybe not in the long run.
Over time,...
0
votes
0answers
69 views
General Equilibrium: Two Consumers with Perfect Substitutes and Perfect Complements Utility Functions
I am attempting to solve a general equilibrium in pure exchange economy problem where the first consumer has an endowment of $(3, 4)$ and a utility function of $U(x) = 3x + 5y$.
The second consumer ...
1
vote
1answer
51 views
preference convexity and existence of equilbria
Consider a production economy with $L$ goods, a single consumer and a single producer whose production set are given by $Y\subset R^L$. Question is to find the existence condition of equilibria of ...
0
votes
1answer
42 views
Competitive equilibrium with production
Consider an economy with four goods, two individuals and two firms. Firm 1 produces good $x$, firm 2 produces good $y$.
Consumers' utilities are $u_1(x,y,z,w)=\min\{x,2y\}$ and $u_2(x,y,z,w)=\min\{2x,...
2
votes
1answer
56 views
Bothersome Mean/Variance Analysis
I'm currently writing my thesis in which I compare a series of ESG General Equilibrium models. I fell over this proof in Pastor, Stambaugh, Taylor Sustainable Investing in Equilibrium (2019) page 42. ...
0
votes
0answers
8 views
log-linearize a forward looking variable (P/D) with recursive expression
I can solve the model in dynare but I need your help with the following problem: How does one derive a log-linearized expression for a forward-looking variable around the steady-state? For example, ...
0
votes
0answers
19 views
Determining a variable from empirical results obtained from regression analysis
For context, I am trying to estimate the excess supply and demand in the Commercial Real Estate market and the rental price adjustment mechanism following the change in vacancy.
I found a paper titled ...
0
votes
1answer
48 views
Regression approximation for the rate of change in occupancy rate of residential market with respect to price
I have historical data on occupancy rates for a given neighborhood, along with characteristics and other local economic variables.
I am looking to estimate the regression equation with occupancy rates ...
1
vote
0answers
33 views
Uniqueness of Arrow-Debreu Equilibria
I have been trying to figure out conditions on the preferences of traders in an exchange economy such that the equilibrium prices are unique but I cannot be sure since all sources seem to be ...
3
votes
0answers
42 views
Proof of excess community demand function in Sonnenschein (1973)
Consider the following passage in Sonnenschein (1973; full citation below):
Perhaps because I do not know much about the uniform Lipschitz condition, I do not follow his exposition after the first ...
7
votes
1answer
129 views
Are no arbitrage models and equilibrium models equivalent?
This YouTube video from WHU (starting from 3:50) claims that no-arbitrage models (such as Black-Scholes and HJM) are equivalent to equilibrium models (such as CAPM or C-CAPM).
He uses the Euler ...
1
vote
1answer
42 views
Why don't suppliers increase price after a positive demand shock?
Forgive me, I am new to economics. Suppose there's a demand shock in the pork market and D1 shifts to D2. Why not keep quantity supplied fixed at 220 and then raise prices to $3.70, instead of moving ...
1
vote
3answers
409 views
First welfare theorem and convexity
Are convex preferences needed for the first welfare theorem? It would see so. For example, we could have a situation in which B's indifference curve is non-convex, such that, at the equilibrium X, it ...
4
votes
1answer
104 views
Edgeworth box and identical tastes
If tastes are homothetic and identical, does this imply that the contract curve is the line connecting the lower left and upper right corners of the box?
My understanding: no, it does not. Consumers' ...
0
votes
0answers
31 views
Is an input-output model an equilibrium model?
I know the difference between CGE and input-output models.
But can an input-output model be called a equilibrium model?
1
vote
1answer
74 views
Deadweight Loss Due to Taxes Represented on a Graph of the Market?
Let's say a market is operating at equilibrium, with MSB=MSC, and a tax is imposed on the market. This would shift the supply curve to the left and cause a deadweight loss represented by the triangle ...
1
vote
0answers
12 views
Identify the Pareto welfare weights
I am asked to identify the Pareto welfare weights from the FOC of the following problem
$max_{{x_1}{x_2}} U_1(x_1)\ st\ u_2=U_2(x_2)\ and\ x_{1n}+x_{2n}=yn$
The Langrangian is: $L=U_1(x_1)+\lambda_1(...
4
votes
1answer
229 views
Properties of Financial Markets in Real Life
When studying financial economics, three concepts appear everywhere
Equilibria (investors maximise utility, markets clear and aggregated demand equals aggregated supply)
Completeness (there are ...
0
votes
0answers
11 views
What is the name for the techniques that are used to determine the determinacy of DSGE models with rational expectations?
What is the name for the techniques that are used to determine the determinacy of DSGE models with rational expectations?
For some context, see e.g. the work of THE SOLUTION OF LINEAR DIFFERENCE ...
0
votes
1answer
30 views
Financial Economics and International Economics
What is the difference of Financial Economics and International Economics? Why, How? What are the implications of these differences?
Will a model of international economics suddenly become a model of ...
1
vote
1answer
60 views
Simple General Equilibrium Model of Public Goods: Intuition?
We assume a two person economy, denoted by person A and B. Good y is an ordinary private good, and each person begins with an allocation of this good given by $ y^{A*} $ & $ y^{B*} $ respectively. ...
1
vote
0answers
43 views
Pareto Set with strictly convex preferences
Suppose the agents A and B have the following utility functions $x_A y_A+12x_A+3y_A $ and $x_By_B +8x_B+9y_B$ respectively with endowments (8,30) and (10,10).
The contract curve's equation turns out ...
0
votes
1answer
44 views
Why is macroeconomics about general equilibrium?
In a fairly popular paper published a couple of years ago ("On the future of macroeconomic models"), Blanchard (2018) makes the following statement, among other "widely believed propositions":
(i) ...
0
votes
1answer
44 views
Equations of “rational mechanics” and general equilibrium
Vilfredo Pareto, referring to the equations that determine equilibrium, wrote:
These equations do not seem new to me, they are old friends. They are
the equations of rational mechanics.
This ...
4
votes
0answers
114 views
Question about MWG 17.D.1
I tried to solve by myself the exercises of MWG(Mas Colell). However, I think the exercise has an error at 17.D.1.
The 17.D.1 asks us that "verify that there are multiple equilibria". However, The ...
0
votes
1answer
96 views
Is local non-satiation enough to talk about Walrasian Equilibrium being subset of Core
In Advanced Microeconomic Theory, the author mentions that the Cobb Douglas utility function is neither strongly increasing nor strictly quasiconcave over all of R+. But the condition of strongly ...
0
votes
2answers
55 views
Why are marginal rates of substitution are identical at equilibrium consumption levels?
According to wikipedia, "At equilibrium consumption levels (assuming no externalities), marginal rates of substitution are identical". Why is it so?
What does "equilibrium consumption levels" here ...
2
votes
1answer
39 views
Can you set $C / P^{\eta}$ to be the numeraire in a NK model?
Consider a static model with CES demand. Real aggregate demand is
$$
C = \left(\sum_j c_j^{(\eta-1)/\eta}\right)^{\eta/(\eta-1)}
$$
and labor supply is inelastic, so the budget constraint is
$
\sum_j ...
1
vote
1answer
56 views
What guarantees that endowed agents have non-zero prices in an Arrow-Debreu Economy
In my research I am trying to find minimal conditions to guarantee a quasi-equilibrium must always be a typical Arrow-Debreu equilibria in a rather specific production setting.
This may be rather ...
0
votes
1answer
31 views
Market Clearing with Dividend and Investment
In pure exchange GE models, a typical goods market clearing condition for good $n$ looks like:
$$\sum\limits_{i=1}^Ic_n^i=\sum\limits_{i=1}^Ie_n^i.$$
Consider a model with production where firms can ...
1
vote
0answers
9 views
Data for CGE experiments?
Does anyone know of any open-source U.S. data sets in a format appropriate to whole-economy CGE econometric modeling, i.e. data sets covering the entire economy, divided into at least 20 sectors, with ...
1
vote
0answers
46 views
Index of an Excess Demand Vector
Mas-Colell, Whinston and Green, in Microeconomic Theory (third edition), postulate the concept of an index for an excess demand vector, which is later used in the Index Theorem:
A regular equilibrium ...
0
votes
0answers
39 views
Equilibrium price determination in a 2 commodity framework
Following are the set of equations describing the demand and supply of two goods X and Y:
Demand functions:
$$X_d = a_1 - b_1P_x + c_1P_y$$
$$Y_d = a_2 - b_2P_y +c_2P_x$$
$a_1,~ a_2,~ b_1,~ b_2,~ ...
1
vote
1answer
106 views
How to calculate the spending multiplier from a given set of equations?
So i have this question:
I go along and get
Then i need to calculate the effect on the optimal output is G increases by 80:
And on the answer sheet it states that the spending multiplier is:
From ...
1
vote
1answer
146 views
Conditions for Radner Equilibrium
This is definition of Radner Equilibrium from Microeconomic Theory (Mas-Collel, Whinston and Green - Third Edition).
I'm confused about two conditions:
$\sum_k q_k \cdot z_{ki} \le 0$ (in yellow)
...
1
vote
2answers
38 views
Why do non-binding price ceilings have no effect?
My question seems trivial but I have a particular issue I don't understand. If there's a price ceiling above the price equilibrium, the customers can still use the ceiling as leverage when negotiating,...
-1
votes
1answer
102 views
Why incomes should decline in equilibrium state
According to Keynes, the prosperity of a population is measured by the aggregated income of each individual. Spending this income keeps the economy away from a depression. If there is too much ...
