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Input Perspective

TVP, AVP, MVP. TVP ? market value of the total product (output), price times quantityTVP=g(f(x))f(x) imperfect competitionTVP=pf(x) perfect competitionAVP ? average value of product.AVP=TVP/xMVP ? marginal value product (marginal revenue product)MVP=dTVP/dxGeneral case:Direct output effec

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Input Perspective

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    1. Input Perspective AGEC 534 Levan Elbakidze

    2. TVP, AVP, MVP TVP – market value of the total product (output), price times quantity TVP=g(f(x))f(x) imperfect competition TVP=pf(x) perfect competition AVP – average value of product. AVP=TVP/x MVP – marginal value product (marginal revenue product) MVP=dTVP/dx General case: Direct output effect (Value of marginal product, VMP)=pf’(x) Indirect price effect (change in total value product due to the change in product price) Perfect competition => VMP=MVP

    3. MVP,VMP,TVP

    4. MVP Derive Elastic demand : Ep <-1, -1<?p<0 MVP=VMP(1+ ?p) => 0<MVP<VMP Positive output effect dominates negative price effect What happens with TVP? Unitary elastic demand: Ep =-1, ?p=-1 MVP=VMP(1+ ?p) => MVP=0 Positive output effect is exactly offset by negative price effect TVP? Inelastic demand: 0>Ep >-1, -1>?p MVP=VMP(1+ ?p) => 0>MVP>VMP Positive output effect is dominated by negative price effect TVP?

    5. Example Inverse demand p=16-0.5y Production y=6x-0.5x2 TVP =96x-26x2+3x3-0.125x4 MVP=96-52x+9x2-0.5x3 VMP=96-34x+4.5x2-0.25x3 what is the optimal point of production? Look at mvp

    6. Graphically Inverse demand p=16-0.5y Production y=6x-0.5x2 TVP =96x-26x2+3x3-0.125x4 MVP=96-52x+9x2-0.5x3 VMP=96-34x+4.5x2-0.25x3

    7. Profit max Factor costs Fixed and variable factor costs Total costs C=rx+b Opportunity costs Profit=TVP-TVC FOC: MVP=MFC

    8. MFC and MVP graphically

    9. MFC and MVP graphically

    10. Factor demand Shows how optimal input use depends on prices of inputs (factors) and outputs X(r,p) Also known as input demand or derived demand Obtained from first order condition r=p*MPP

    11. Example

    12. Profit max with two inputs

    13. Perfect competition

    14. Budget line

    15. Expansion path

    16. Profit Max

    17. Profit Max

    19. Supply function

    20. Cost minimization

    21. Conditional demand functions

    22. Cost function

    23. Constrained output maximization

    24. example

    25. SOC Bordered Hessian

    26. Example

    27. Homogeneity of factor demands Factor demands are homogeneous of degree 0 under perfect competition True whether underlying production function homogeneous or not No money illusion: If all prices increase by the same percent, input demand does not change Lets check for Cobb-Douglas factors demand Check for CD not homogeneous of degree 0 Do not ignore homogeneity of factor demands in empirical studies: If this is violated then it means the producers are not maximizing profits and/or minimizing costs

    28. Comparative Statics Evaluates derivatives of functions. e.g. factor demands or isoquants How does demand for one input change as the use of the other changes? How does demand respond to prices? Use of Implicit function theorem

    29. Implicit function theorem Formally Given an implicit function F(x1,x2, D)=0 Has continuous derivative F1, F2, FD There is some point (x1’,x2’,D’), which satisfies F F1, F2 ,FD is non-zero => there exists a neighborhood of points around (x1’,x2’,D’), such that D is implicitly defined by x1 and x2. i.e. D=f(x1,x2) Practically F(x,y)=0 F has continuous partial derivatives w.r.t. x, y Fy is non zero at point of evaluation =>

    30. Example F(x,y)=x3-3x2y4+4y3-6x-1=0 Total differentiation Implicit function rule

    31. Comparative statics What is an effect of exogenous variable on the equilibrium levels of endogenous vars? Simple example p =pf(x)-wx-b px =pfx–w=0

    32. Comparative statics More from notes

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