Input Perspective

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