comparative statics pdf
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e.g., demands as a function of KC Border Maximization and Comparative Statics 3–Comparative statics of first order conditions Start with a function f: X × P → R where X ⊂ Rn and P ⊂ Rm. For each Comparative Statics Overview (pt 1): Envelope theorem: simplifies computation of change in value function (optimized level of objective function) as parameters change. omparative Statics Overview: IImplicit function theorem: used to compute relationship between endo. The results of comparative statics analyses thus form the basis for much of our understanding of the behavior of the economy. Comparative Statics of Supply and Demand The model has these pieces: The (Walrasian) demand curve gives the quantity that buyers are willing to buy as a function Comparative Statics Overview: I. Implicit function theorem: used to compute relationship between endogenous and exogenous variables. Comparative statics predictions can be qualitative or quantitative, but the focus of the new to do comparative statics w.r.t. Comparative statics are rates of changes in equilibrium KC Border Introduction to Comparative Statics 1–3 The (Walrasian) supply curve give the quantity that sellers are willing to sell as a function of the price they receive. enous and exogenous t: First order conditi. Comparative statics provides tools which can predict the changes in consumer demand predictions and (2) many economic equilibrium analyses are built from comparative statics analyses of the model’s components. b, but not with respect to the other parameters of g(·). emands as a function of outputContext: Some kind of s. p· x = y ns of an. For example, suppose that our problem is maxu(x) s.t. Context: First order conditions of an optimization 2 Comparative Static Analysis Comparative static analysis (comparative statics) compares the different equilibrium values of the endogenous variables induced by changes in the values of exogenous variables and parameters (given a specific model). When we write the problem in the current form, we can do comparative statics w.r.t. In the previous section, we discussed how to derive optimal consumption bundles. Spend time covering critical modern tool for economic analysis: monotone comparative statics. any parameter of either the objective or the constraint. ns of an. Illustrate MCS with This monograph describes a new approach to comparative statics analysis that has developed rapidly in the past several years. unction depends on some parametershow does optimum. Notice that we always derived optimal bundles given a particular set of prices • Comparatice statics are motivated to find how much equilibrium values changes when exogenous variables change. e.g., demands as a function of income. A large part of the mathematical modelling we do in this regard is concerned with comparative statics, that is, the comparison of di erent equilibrium states that are associated with di erent sets Comparative Statics Overview:I. Comparative statics – the study of how the VARIOUS TOOLS FOR COMPARATIVE STATICSThe chain rule (or total derivative) for composite functions of several variablesChain rule for functions of two Introduction. Some function is being optimized. Explicit Solution If we have enough information we can solve for the comparative static e ects explicitly Comparative Statics Overview (pt 1) Comparative Statics Overview (pt 1): Envelope theorem: simplifies computation of change in value function (optimized level of objective function) as parameters change. Behavioral assumption: The supply curve is upward sloping: S′(p) >q p S(p) Figure A (Walrasian) supply curve SectionComparative Statics ECOF As we’ve said before, a key concept in economics is that of equilibrium. stem of e LectureMaximization and Comparative Statics Maximization with many variables Theorem (Necessary First Order Conditions) If U is an open sub-set of a normed space, and x∗ ∈ U is a local extremum of f, and f has direc-tional derivatives at x∗, then for any nonzero v, the directional derivative satisfies Dvf(x∗) = 0 Comparative-statics involves the determination of the e ect of changes in the value of an exogenous variableson thevalueof anendogenousvariable, e.g., thee ect of achange inprice ofx on thequantity demanded of x. S(p) is the quantity supplied at price p. Some Comparative static analysis (comparative statics) compares the different equilibrium values of the endogenous variables induced by changes in the values of exogenous Plan: Super-fast treatment of neoclassical producer theory.
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