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This result is indeed a version of Berge's maximum theorem. If there is a continuous function $u:M\times H\to\mathbb{R}$ such that $x\preceq_e z$ if and only if $u(e,x)\leq u(e,z)$, one can derive the result directly from Berge's maximum theorem. If $H$ is locally compact, as it is the case if $H=\mathbb{R}^n$, then such a function can always be found, this ...


7

From the Chicago Federal Reserve: Following a minimum wage hike, household income rises on average by about \$250 per quarter and spending by roughly \$700 per quarter for households with minimum wage workers. Most of the spending response is caused by a small number of households who purchase vehicles http://www.chicagofed.org/digital_assets/...


6

Shell 1971 argues (in a ten page paper, so read it!) that the dynamic inefficiency stems from the double infinity of traders and goods, and not the dynamics. This allows us to do the Hilbert hotel switch. Therefore, even when all souls are able to transact business in the same Walrasian market, the absence of Pareto-optimality persists in the ...


6

UPDATE After e-mail communication with one of the authors G.W.Kaplan, I recalibrated the value of the vacancy-posting cost parameter $k$ in order to obtain a cross of the two nullclines for $u=0.05$. This is achieved for $k=7.41$ (rounded). Moreover, with this value of $k$, I get a second (but not a third) steady state. A close up diagram : This still is ...


6

Explosiveness The paper contains an error, which causes the explosive dynamics in your simulation (although presumably the underlying computations in the paper were correct). The equilibrium condition derived from eigenvalue decomposition is contained in the third row of matrix $Q^{-1}$ on page 12 of the paper, with variables ordered as $(c,k,h,z)$ (I'll ...


6

While many general equilibrium models do not need to model money to approach the questions that they would like to answer, there are many models that do include money to address questions that need money to be a relevant feature of the model. These models do it in a variety of ways -- some might be more relevant than others. I will try and describe two of ...


6

Competitive Equilibrium A competitive equilibrium ("Walrasian Equilibrium")'s defining characteristic is that it's competitive. It's about an equilibrium in which market forces (say, consumers, firms)' supply and demand responds to prices, and prices respond to supply and demand, and no Pareto-improving trade possibility remains in the end. To be technical,...


6

...no-arbitrage models (such as Black-Scholes and HJM) are equivalent to equilibrium models (such as CAPM or C-CAPM). Short Answer Yes, for models where asset prices are assumed to be Ito semimartingales (where the martingale part is a Brownian integral), although a more general argument is needed than that suggested by the special cases typically ...


6

First, you need a vector space in order for convex combinations to be well-defined. However, not every metric on a vector space works. Indeed, under the discrete metric, the result will trivially fail unless space consists of the point $0$ alone. What works is a metric on the vector space such that the vector operations of addition and scalar multiplication ...


5

Higher order approximations such as those generated by Dynare may help a bit in terms of expanding the neighborhood in which the approximation works well, but the fundamental problem remains that the approximation is made about the steady state and deviating too far from the steady state introduces large errors. Judd, Maliar and Maliar have a paper in ...


5

Side note: This is one way of solving it - the alternative would be formulating a Bellman equation and iterating on that. If you assume that the real economy is on or sufficiently close to the steady state, you can also infer about responses to shocks. That is, you can look at the impulse response functions to a change in whatever interests you, and see how ...


5

Final NEWS March 20, 2015 : I have e-mailed prof. K. Salyer, one of the authors of the User Guide. In a repeated communication, he verified that both issues (see my answer below, as well as @ivansml answer), do exist: a) The correct equation for the law of motion of consumption is as @ivansml shows b) The number $0.007$ is wrongly called "variance" (p. ...


5

Competitive equilibrium is the price vector $(p_x, p_y, w =1, r)$ such that it solves the following system of equations: Demand for $X$ = Supply of $X$ Demand for $Y$ = Supply of $Y$ Demand for $L$ = Supply of $L$ Demand for $K$ = Supply of $K$ where these demands and supplies are either exogenously given or are derived by solving utility maximization ...


5

Inherently discrete variables (like "count data") have special properties, and it matters when it comes to econometric estimation. The usual criterion to treat a variable as continuous or discrete, is I believe not what we observe but what could be conceivably observable. Example: if one counts number of people, the variable is inherently discrete. In ...


5

Perhaps you are confusing two things. If $Q_1$ and $Q_2$ denote the production of goods 1 and 2 in a single country and you are in the space defined by them given $L_1 + L_2 = L$ then it is indeed the inferior set (the production possiblity set defined by the feasible $(Q_1,Q_2)$ pairs) that is convex. Formally this means that for all feasible $L_1,L_2,L_1',...


5

Daron Acemoglu, in a paper called Theory, General Equilibrium and Political Economy in Development Economics, discusses the role of economic theory in empirical work in development economics, which investigates the causes of poverty and low incomes. He puts a special emphasis on general equilibrium considerations. He discusses why counterfactual analysis ...


5

Equilibria: in the macroeconomic sense of aggregate equilibrium where all markets clear, markets are most likely never in any equilibrium but rather in constant flux between different equilibria, because the market clearing macroeconomic equilibrium always depends on real and also in short run nominal factors which constantly change. Hence it does not make ...


5

I think the best candidate would be monopolistic competition as introduced by Dixit and Stiglitz (1977) Monopolistic Competition and Optimum Product Diversity, in which two models are introduced. One central theme was product variety and the endogenous determination of the number of product varieties. There are many models formulated within the ...


5

Partial answer: for simplicity let $P_c =1$. The budget constraint: $c= wn + \Pi$ Simplify (plug in $\Pi$): $c= F(n)- fc$ Goods clearing: $c = F(n)$ The household's budget constraint is inconsistent w/ goods market clearing. The firm pays a fixed cost that doesn't go to anyone. In a "true GE model" all payments have to go to someone in the economy. ...


4

I assume what you're asking based on your comments is: "How can I visualize indifference curves for 3 goods?" I can think of three options: 1) Use a tool like Matlab, or its open-source equivalent, Octave, to plot 3 dimensional indifference curves. Here is a tutorial on how to do that. 2) Make a series of 2-dimensional indifference curves for two of the ...


4

There is an unpublished 1982 working paper by Donald Brown and John Geanakoplos, called “Understanding Overlapping Generations Economies as a Lack of Market Clearing at Infinity” (a scan used to be available at Brown's homepage). The authors show that there is a one-to-one correspondence between the equilibria of an OLG economy and almost-equilibria in a ...


4

You write that the slope of one line is px/py and of another is -px/py. Take a piece of paper and draw the line y=2x and y=-2x are they orthogonal (answer: no)? In particular case the lines y=x and y=-x are orthogonal. If we regard it more formally, the vectors are orthogonal if the product is 0. Thus, <1,-p>*<1,p> = 1-p^2 This is 0 only if ...


4

Economists (most of them) build their models assuming most of the time stochastic dynamic equilibrium. So Economics does not contrast "dynamic" with "equilibrium" - it synthesizes them. It is stochastic in the sense that random shocks are acknowledged. It is dynamic in the sense that it may revolve around a deterministic or stochastic trend. And it is an ...


4

The main reason differential topology had some success in economics is that supplies powerful methods to show that something holds generically, mainly Sard's theorem and the transversality theorem. Some of these methods have been generalized to contexts without differentiability, see for example the paper "A Prevalent Transversality Theorem for Lipschitz ...


4

Convexity of the production set is indeed not needed for the proof of the first welfare theorem but for the proof of the second welfare theorem. It is not a necessary condition though. It is possible to interpret this as an existence issue. The first welfare theorem is about all competitive equilibria and holds trivially if there are none. The second ...


4

How about Walras's law? Walras's law is a principle in general equilibrium theory asserting that budget constraints imply that the values of excess demand (or, conversely, excess market supplies) must sum to zero.


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The way you have defined excess demand, it is only consumer excess demand. But Walras's law holds in any private ownership economy at all prices (at which demand and supply are well defined). Walras's law is basically equivalent to consumers spending their budget fully. Let there be $l$ commodities, so every commodity bundle is an element of $\mathbb{R}^l$. ...


4

Are convex preferences needed for the first welfare theorem? No, convexity of preferences is imposed for other reasons. A general sufficient condition is local non-satiation, which says the agent can be made better off by an arbitrary small perturbation of his consumption bundle. This can hold without the preference being convex. It would see so. For ...


4

Consider an economy with two commodities. Production is trivial, $Y=\{0\}$, there is a single consumer with endowment $(1,1)$ whose preferences are represented by the utility function given by $u(x_1,x_2)=\max\{x_1,x_2\}+1/2\cdot x_1 +1/2\cdot x_2$. These preferences are continuous, strictly monotone, but not convex. You can verify that there is no ...


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