高级微观经济学 黄有光 overview of inframargianl.docx

1、高级微观经济学 黄有光 overview of inframargianlOverview of the inframarginal analysisWhy economists shifted their attention from the economic organization problem to the resources allocation problem?1) David Ricardos concept of comparative advantage Exogenous comparative advantage Endogenous comparative advan

2、tage: Smiths concept of economies of the division of labour Comparative advantage may exist between ex ante identical v if they choose different levels of specialization in producing different goodsv if there exist increasing returns to specialization2) Marshalls neoclassical framework The dichotomy

3、 between pure consumers and firms The replacement of the concept of economies of specialization with the concept of economies of scale The marginal analysis of demand and supply.(Marshalls neoclassical framework cannot be used to analyse individuals decisions in choosing levels and patterns of speci

4、alization, so that the structure of division between pure consumers and firms is exogenously given)Two types of trade-offs: Neoclassical trade-off - the trade-off between the production and consumption of all different goods and services given the degree of scarcity of resources; (the problem of all

5、ocation of scarce resource)Classical trade-off - the trade off between transaction costs and the economies of specialization facilitated by the division of labour (the problem of economic organization)(a) Neoclassical framework (b) Flow chart in neoclassical economicsFigure 1: Neoclassical Analytica

6、l FrameworkNew Classical Economics (Yang-Ng framework)New classical general equilibrium model endogenizes individuals level of specialization and the level of division of labour for society as a whole within a framework with: 1) consumer-producers 2) economies of specialization3) transaction cosst4)

7、 corner solutions (a) Autarky (b) Partial division of labor (c) Complete division of laborFig.2: New Classical Analytical FrameworkA simple model of inframarginal analysis:An economy has M ex ante identical individual who are both consumer and producersTwo consumption goods X and Y Each consumer-pro

8、ducer has the following utility function.(1) Each consumer-producers production functions and endowment constraint are(2a) , , a 1(2b) .Each consumer-producers budget constraint is(3) pi is the price of good i. The left hand side of (3) is income from the market and the right hand side is expenditur

9、e. Corner solutions are allowed and we have the non-negativity constraints(4) x, xs, xd, y, ys, yd, lx, ly 0.Each consumer-producer maximizes utility in (1) with respect to x, xs, xd, y, ys, yd, lx, ly subject to the production conditions given by (2), the budget constraint (3), and the non-negativi

10、ty constraint (4). Since lx and ly are not independent of the values of the other decision variables, each of the 6 decision variables x, xs, xd, y, ys, yd can take on 0 and positive values. When a decision variable takes on a value of 0, a corner solution is chosen. Individual decision problemsTher

11、e are solutions include 63 corner solutions and one interior solution for each consumer and producer.Using the theorem of specialization narrows down the set of candidates for the optimum decisionsTheorem of Optimal Configurations: The optimum decision does not involve selling more than one goods, d

12、oes not involve selling and buying the same good, and does not involve buying and producing the same good.(Implications: interior solution can never be optimal, the marninal analysis for interior solution does not work for the new classical framework)This theorem, together with the budget constraint

13、 and the requirement that utility be positive, can be used to reduce the number of candidates for the optimum decision radically from 64 to only 3. The theorem is intuitive. Selling and buying the same good involves unnecessary transaction costs and therefore is inefficient. Selling two goods is als

14、o inefficient since it prevents the full exploitation of economies of specialization. The list of candidates for the optimum corner solutionTable 1: Profiles of Zero and Positive Valuesof the 6 Decision Variables +0+0+0+00+000+0000+00000+Three configurations(i) Autarky, or configuration A, is define

15、d by , The decision problem for configuration A is (5a) s.t. , , .Inserting all constraints into the utility function (5.5a) can be converted to the following non-constrained maximization problem.(5b) totally differentiate u with respect to lx(6) the corner solution for configuration A is (7) Two co

16、nfigurations of specialization:(ii) Configuration B: configuration with specialization is (x/y), specialization in producing good x, selling x and buying y. It is defined by x, xs, yd, lx 0, xd = ys = y = ly = 0. This definition, together with (1)-(4), can be used to specify the decision problem for

17、 this configuration.(8) s.t. , (production conditions) (budget constraint)Plugging the constraints into the utility function to eliminate, x, and yields the nonconstrained maximization problem(9) The corner solution for configuration (x/y) is (10) xs = 0.5, yd = pxxs/py = px/2py, ux = kpx/4py.(iii)

18、Configuration C: configuration with specialization is (y/x), in which the individual sells good y and buys good x, is defined by y, ys, sd, ly 0, yd = xs = x = lx = 0. The decision problem for this configuration is:(11) s.t. (production condition) (budget constraint)Following the procedure used in s

19、olving for the corner solution for configuration (x/y), the corner demand and supply functions and corner indirect utility function for configuration (y/x) is solved as follows:(12) ys = 0.5, xd = py/2px, uy = kpy/4px.Table 2: Three Corner Solutions Configuration Corner demandCorner supplySelf-provi

20、ded quantitiesLevel ofspecializationIndirect utilityfunction A 0 0x = y = 0.5 lx = ly = 0.5 uA = 2-2a(x/y) yd=px/2py xs= 0.5 x = 0.5 lx = 1, ly = 0 ux = kpx/4py (y/x) xd= py/2px ys= 0.5 y = 0.5 lx = 0, ly = 1uy = kpy/4pxStructures and Corner equilibriaThere are two organization structures: Structure

21、 A (Autarky) Structure D (Division of labour): A combination of configurations B and C. Let the number (measure) of individuals choosing (x/y) be Mx and the number choosing (y/x) be My.There is a corner equilibrium for each structure.The market clearing and utility equalization conditions are establ

22、ished by free choice between configurations and utility maximization behavior. In structure D, the corner equilibrium relative price of traded goods is: or the market demand for good x is Xd My xd = My py / 2 px ,the market supply of good x is Xs Mx xs = Mx / 2The market clearing condition for good

23、x is Xd = Mypy/2px = Xs = Mx/2, or px/py = My/Mx The corner equilibrium in structure D is px/py = 1, Mx = My = M/2.x = y = xs = ys = xd = yd = , uD = k/4Table 3: Two Corner EquilibriaStructureRelative priceNumber of SpecialistsQuantities of goodsPer capita real incomeAdy/dx = 1x = y = 0.5 a2-2aDpx /

24、py = 1Mx=My = M/2x = y = xs = ys = xd = yd = ,k/4General equilibrium and its comparative staticsProposition 1:The corner equilibrium that generates maximum per capita real income is the full equilibriumProposition 2: Equilibrium is the division of labour if and is autarky if Proposition 3: A suffici

25、ent improvement in transaction efficiency generates the concurrence of progress in labour productivity and the increases in the level of specialization, in the level of division of labour, the degree of market integration, the degree of interdependence, and the degree of commercialisation. ( a ) Str

26、ucture A, autarky ( b ) Structure D, division of labor Figure 2: Autarky and Division of LaborTwo types of comparative statics:1) inframarginal comparative statics of general equilibrium across the structuresexplain the relationship between economic growth and economic organization2) marginal compar

27、ative statics of corner equilibrium within each given structure.v New classical theory analyses both the adjustments within a given structure of economic organization and changes in economic orgainization.Welfare implications of EquilibriumThe first welfare theorem:In a new classical model with ex a

28、nte identical consumer-producers, each corner equilibrium is locally Pareto optimal for the given structure and the general equilibrium is globally Pareto optimal.Implication: corner equilibrium is allocationally efficient, the general equilibrium is both organizationally efficient and allocationall

29、y efficient.Consider structure D: Let Xi = xi, xis, yid be the decision of individual i choosing configuration (x/y) Yj =yj, yjs, xjd be the decision of individual j choosing configuration (y/x). the corner equilibrium values of Xi and Yi as Xi* and Yi*, respectively, and the corner equilibrium pric

30、e of good x in terms of good y as p. Suppose that the corner equilibrium in structure D is not locally Pareto optimal. Then there exists an allocation Xi, Yi in structure D such that (2a) ui ( Xi ) ui (Xi*) for all i, and ui ( Xi ) ui (Xi*) for some i(2b) uj ( Yj ) uj (Yj*) for all j.This implies that a benevolent central planner can increase at least one individuals utility without reducing all others utilities by shifting the decisions from Xi*, Yi* to Xi, Yi. That is, the corner equilibrium decisions Xi*, Yi* are not locally Pareto optimal.Since utility is a strictly increasing f