8

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

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,...


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

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 ...


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

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 ...


4

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 ...


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

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.


3

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 ...


3

Yes and no. Temporary Shock It is correct, that a temporary increase in TFP has unclear effects on leisure: The **income effect* will increase consumption and leisure The **substitution effect* will decrease leisure. On total, effects onto leisure are unclear. But, unless you have very specific preferences, consumption should increase. What are the ...


3

No you are not. Preferences determine the equilibrium, even if they are identical, because they determine the value of the endowments. Consider two agents, one ("A") having ice cream only, and one ("B") having lava only. Case 1: Both hate lava Assume lava burns tongues and is useless (typical Economist). Then, the initial endowments of B have zero value, ...


3

As you note in your question the (inner points of the) Pareto set are defined by $$ x_1^1 = \frac{\alpha_1 r^1 x_1^2}{\alpha_1 x_1^2 - \alpha_2 x_1^2 + \alpha_2 r^2} $$ In order to better examine this curve, let us treat it as a function. Let $$ f(x) = \frac{\alpha_1 r^1 x}{\alpha_1 x - \alpha_2 x + \alpha_2 r^2}. $$ As I stated in my comment $$ f(0) = 0 \...


3

It depends on the set of feasible allocations for the coalitions $S$. Suppose for all $S$ a best allocation exists (the sum of the individual utilities of the members of $S$ is maximal). Then as in usual cooperative games each coalition can be assigned this best utility sum as its value $v(S)$. Let us denote the utility vector each player gets from an ...


3

No, the marginal cost curves are not necessarily the same for each firm in the market. However the values of marginal costs are. To disprove the general claim that "The marginal cost curve of each firm in a competitive market is the same" we simply need to find one counter-example, such as the one given below: Suppose there are two firms in the market and ...


3

A stronger hint: Write $p_2=1-p_1$, so that $Z(p)=Z(p_1,1-p_1)$. Use the conditions $Z_1(0,1)>0,Z_1(1,0)<0$ etc. and the intermediate value theorem to argue that there exists a $p_1^*\in(0,1)$ such that $Z_1(p_1^*,1-p_1^*)=0$.


3

I couldn't think of a good hint. If you are having trouble with using the information given, (as the application of Walras + IVT is fairly straightforward), then there are not many tips that can help. I've opted to put out each step explicitly. Let me know if you don't understand a part, and I'll try to edit to make it clearer. In the future, it is better ...


3

1x2 model Consider a mode where production of a single good is given by a constant returns to scale CES production function: $$Y=A(\alpha L^\rho +(1-\alpha)K^\rho)^{\frac{1}{\rho}}$$ where the elasticity of substitution between the two factors is $$ \sigma = \frac{1}{1-\rho} $$ It can be shown that the marginal product of labour (equal to the real wage ...


3

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 ...


3

We have an allocation $(x^*,y^*)$ and a price system $p$ forming a price equilibrium with transfers.The assignment of wealth levels $(w_1,\ldots,w_I)$ has to satisfy $$\sum_i w_i=p\cdot\bar{\omega}+\sum_j p\cdot y_j^*.$$ One way to interpret the wealth levels is that the planner hands out coupons that can be traded at existing prices for commodities and ...


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