Bài 7: Hàm chi phí và lợi nhuận

49 0 0
  • Loading ...
    Loading ...
    Loading ...

Tài liệu hạn chế xem trước, để xem đầy đủ mời bạn chọn Tải xuống

Tài liệu liên quan

Thông tin tài liệu

Ngày đăng: 08/04/2021, 21:12

reg3 (lcost lp_urea lp_npk loutput lp_urea2 lp_npk2 loutput2 lp_urea_npk lout_urea lout_npk) /*. * Generating cost share for npk[r] (1)THE DUALITY APPROACH: COST AND PROFIT FUNCTIONS (2)The primal vs duality approach Derivation of cost and profit function (3)Production Economics  optimal allocation of resources in the production of goods and services given  technology  resource constraints  output demand (and thus prices of outputs)  prices of inputs  Basic issues:  optimal input uses (4)The primal vs dual approach  Primal approach  optimal input and output levels are obtained by solving the optimization problem  Dual approach  Inputs demand and output supply functions can be derived from the dual functions   max x pf xwx min st   c x wx yf x   (5)Problems of the primal approach  endogeneity and simultaneity of the production function (need instrumental variables, and more advanced techniques to fix)  multicollinearity of inputs in the production function (may result in incorrect estimates, sometimes unable to obtain the estimates)  for some functional forms, it is hard to obtain input demands and output supply (the optimization is not always easy) (6)Specification of the cost function  Cost problem  Lagrangian function  FOCs  Solving FOCs to obtain  Cost function   min st c x wx yf x   c   L xwx  yf x      0 i i i L x w f x x         ,  conditional factor demand c xx w y  ,   ,  c cwx w yc w y (7)Specification of the profit function  Profit max problem  FOCs  Solve FOCs to get  Substitute into to obtain   max x   pf xwx   0 i i i pf xwx    ,  unconditional factor demand xx p w   pf x wx     ,  xx p wp w,    (8)Properties Issues in estimation (9)Properties of the cost function  1  2  3  4  5  6  7 Shephard lemma  Symmetry by Young theorem  ,  0 for , 0 c w yw y   ,  is non-decreasing in c w y w  ,  is non-decreasing in c w y y  ,  is linearly homogenous in c w y w  ,  is continuous and concave in c w y w  ,    , c i i c w y x w y w     , 0 0 c w          2 2 , , , , so c c j i i j j i j i x w y c w y c w y x w y w w w w w w       (10)Issues in estimating the cost function  Factor cost shares sum to 1  Homogeneity (11)Factor cost share  The factor cost shares sum to 1  For the translog cost function  The cost share equations are  ,    ,  , c i i i w x w y s w y c w yi  ,  1 i s w y   1 ln ln ln ln ln ln 2 i i ij i j i i i i j i c     w   w w   w y ln ln ln ln i i i ij j i j i i i w c c s w y w c w               (12)Homogeneity of the cost function  Proportional changes in input prices leave factor demand unchanged  For the translog cost function, linear homogeneity is satisfied if  ,   ,  0 c tw ytc w y t  1 i i    ij 0 i    i 0 i    1 ln ln ln ln ln ln 2 i i ij i j i i i i j i (13)Monotonicity  The cost function must be increasing in w  For the translog cost function ln ln 0 i i ij j i j i i i i c c c s w y i w w w               (14)Concavity  The cost function must be concave in w (15)Symmetry  Cross price effects of factor demand are equal         2 2 , , , , or c c j i i j j i j i x w y c w y c w y x w y w w w w w w       (16)In empirical studies  Cost shares: estimated simultaneously with the cost function (system of equations)  Homogeneity, monotonicity, convavity and symmetry are either: (17)Uses of the cost function  Factor demand  Output supply  Morishima elasticity of substitution  ,   ,  c i i c w y x w y w     ,    1   , , c w y mc w y p y mc w p y           ,  ln , ln i j ij j i c w y c w y (18)Example: Ray (1982)  Title: A translog cost function analysis of U.S agriculture 1939-1977  Objectives  measure elasticity of substitution  measure price elasticity of factor demand  measure technical change (19)Example: Ray (1982)  Data  2 outputs  livestock  crop  5 inputs  hired labor  capital (real estate, motor vehicles and machinery)  fertilizers  purchased feed, seed and livestock  miscellaneous inputs (20)Example: Ray (1982)  Estimated equations:  cost function  cost share equations  revenue share equations  Functional form: translog cost function  Dependent variables:  farm production expense (index)  cost shares (21)Example: Ray (1982)  Technical change in the cost function   ln c w y, t  (22)Example: Ray (1982)  Treatment for properties of the cost function  homogeneity: imposed  monotonicity: ignored  concavity: ignored  symmetry: ignored  Findings  declining substitutability between capital and labor  price elasticity increase over time for all inputs (23)Properties Issues in estimation (24)Properties of the profit function  1  2  3  4  5  6 Hotelling lemma  7 Symmetry  p w,  0    p w,  non-decreasing in p   p w,  non-increasing in w   p w,  linear homogeneous in  p w,    p w,  continuous and convex in  p w,    ,    , k k p w y p w p      ,    , i i p w x p w w       ,   ,   ,   ,  so i k i i k i k p w p w y p w x p w p w w p w p         (25)Issues in estimating the profit function  Homogeneity  Monotonicity  Convexity: Hessian matrix positive semi-definite  Symmetry tp tw,  tp w,  t 0      ,  0 k p w p       , 0 i p w w      ,   ,  k i i k p w p w p w w p      (26)Issues in estimating the profit function  Although not required, profit function is usually estimated together with the revenue share equations and the input expenditure share equations       ln , , , ln y k k k k k k p w p w p y p s p w p p                  ln , , , ln x i i i i i i p w p w w x w s p w (27)Example: Alpay et al (2002)  Title: Productivity growth and environmental regulations in Mexican and U.S food manufacturing  Objective: compare productivity growth of Mexican (28)Example: Alpay et al (2002)  Methodology  profit function + revenue share equations + expenditure share equations  profit: short-run profit (capital fixed)  functional form: translog profit (29)Example: Alpay et al (2002)  Data: aggregate  output: restricted short-run profit  Inputs  labor  material  pollution abatement expenditure (30)Example: Alpay et al (2002)  Dual productivity growth from the profit function  The primal productivity growth could be derived from the dual productivity growth  technical changes that are unaffected by prices   ln p w, t   (31)(32)Primal and dual, what can they do?  estimate factor demand  estimate output supply  factor substitution  technical changes (33)Advantages of duality approach  sometimes it’s hard to solve the optimization problem for the primal production function  in production function, inputs are very likely to be co-linear (more than prices)  dual functions are more convenient to analyze (34)Disadvantages of duality  Prices are also co-linear  Properties/restrictions of the dual functions (homogeneity, monotonicity, concavity and symmetry) (35)(36)The data – rice production activity (37)Preparing data  * GENERATING VARIABLE COST  gen cost = urea * p_urea + npk * p_npk  gen lcost = ln(cost)  * Generating log-var  gen lp_urea = ln(p_urea)  gen lp_npk = ln(p_npk)  gen loutput = ln(output)  * GENERATING INTERACTION TERMS  gen lp_urea2 = lp_urea * lp_urea  gen lp_npk2 = lp_npk * lp_npk  gen lp_urea_npk = lp_urea * lp_npk  gen loutput2 = loutput*loutput (38)The Cobb-Douglas production function _cons -2.443404 .386535 -6.32 0.000 -3.201219 -1.685588 loutput 9030405 .014217 63.52 0.000 8751676 .9309133 lp_npk 5981721 .2857531 2.09 0.036 0379434 1.158401 lp_urea 5704618 .2956906 1.93 0.054 -.0092499 1.150173 lcost Coef Std Err t P>|t| [95% Conf Interval] Total 5900.28906 4163 1.41731661 Root MSE = 84356 Adj R-squared = 0.4979 Residual 2960.26013 4160 711600993 R-squared = 0.4983 Model 2940.02893 980.009644 Prob > F = 0.0000 F( 3, 4160) = 1377.19 Source SS df MS Number of obs = 4164 reg lcost lp_urea lp_npk loutput (39)Linear homogeneity Prob > F = 0.2546 F( 1, 4160) = 1.30 ( 1) lp_urea + lp_npk = 1 test lp_urea + lp_npk = 1 (40)The translog cost function _cons -20.02878 5.772784 -3.47 0.001 -31.34653 -8.711038 lout_npk -.2041232 .2942038 -0.69 0.488 -.7809201 .3726737 lout_urea 0451066 .3052942 0.15 0.883 -.5534335 .6436467 lp_urea_npk -7.073271 10.24913 -0.69 0.490 -27.16705 13.02051 loutput2 0086156 .0091541 0.94 0.347 -.0093314 .0265625 lp_npk2 8205222 5.340899 0.15 0.878 -9.650498 11.29154 lp_urea2 3.172856 5.40346 0.59 0.557 -7.420817 13.76653 loutput 1.11335 .4502833 2.47 0.013 2305538 1.996146 lp_npk 15.02131 8.356314 1.80 0.072 -1.361537 31.40416 lp_urea 1.189279 8.8623 0.13 0.893 -16.18557 18.56413 lcost Coef Std Err t P>|t| [95% Conf Interval] Total 5900.28906 4163 1.41731661 Root MSE = 84238 Adj R-squared = 0.4993 Residual 2947.68538 4154 .70960168 R-squared = 0.5004 Model 2952.60369 328.067076 Prob > F = 0.0000 F( 9, 4154) = 462.33 Source SS df MS Number of obs = 4164 (41)Cobb-Douglas or Translog? Prob > F = 0.0071 F( 6, 4154) = 2.95 ( 6) lout_npk = 0 ( 5) lout_urea = 0 ( 4) lp_urea_npk = 0 ( 3) loutput2 = 0 ( 2) lp_npk2 = 0 ( 1) lp_urea2 = 0 (42)Testing linear homogeneity of the Translog cost function Prob > F = 0.0018 F( 3, 4154) = 5.03 ( 3) lout_urea + lout_npk = 0 ( 2) lp_urea2 + lp_npk2 + lp_urea_npk = 0 ( 1) lp_urea + lp_npk = 1 > */ (lout_urea + lout_npk = 0) > */ (lp_urea2 + lp_npk2 + lp_urea_npk = 0) /* test (lp_urea + lp_npk = 1) /* (43)Imposing linear homogeneity on the Translog cost function  constraint lp_urea + lp_npk = 1  constraint lp_urea2 + lp_npk2 + lp_urea_npk = 0  constraint lout_urea + lout_npk = 0  cnsreg lcost lp_urea lp_npk loutput lp_urea2 (44)Imposing linear homogeneity on the Translog cost function _cons -1.257867 .5809441 -2.17 0.030 -2.396828 -.1189055 lout_npk -.1345858 .2770172 -0.49 0.627 -.6776877 .4085162 lout_urea 1345858 .2770172 0.49 0.627 -.4085162 .6776877 lp_urea_npk -5.672884 10.25086 -0.55 0.580 -25.77006 14.42429 loutput2 0106869 .0083695 1.28 0.202 -.0057219 .0270957 lp_npk2 1.937082 5.07915 0.38 0.703 -8.020767 11.89493 lp_urea2 3.735802 5.236984 0.71 0.476 -6.531487 14.00309 loutput 7192963 .1365959 5.27 0.000 4514953 .9870973 lp_npk 6.290339 3.880915 1.62 0.105 -1.31833 13.89901 lp_urea -5.290339 3.880915 -1.36 0.173 -12.89901 2.31833 lcost Coef Std Err t P>|t| [95% Conf Interval] ( 3) lout_urea + lout_npk = ( 2) lp_urea2 + lp_npk2 + lp_urea_npk = ( 1) lp_urea + lp_npk = (45)Translog cost with cost share equation snpk 4164 .3089158 0.0133 57.27 0.0000 lcost 4164 .8416739 0.5001 10431.41 0.0000 Equation Obs Parms RMSE "R-sq" chi2 P Three-stage least-squares regression > */ (snpk lp_npk lp_urea loutput), constraint(4 7) reg3 (lcost lp_urea lp_npk loutput lp_urea2 lp_npk2 loutput2 lp_urea_npk lout_urea lout_npk) /* constraint [snpk]loutput = [lcost]lout_npk constraint [snpk]lp_urea = [lcost]lp_urea_npk constraint [snpk]lp_npk = [lcost]lp_npk2/2 constraint [snpk]_con = [lcost]lp_npk gen snpk = npk*p_npk/cost * Generating cost share for npk (46)Translog cost with cost share equation lp_urea_npk lout_urea lout_npk Exogenous variables: lp_urea lp_npk loutput lp_urea2 lp_npk2 loutput2 Endogenous variables: lcost snpk _cons 1.116778 .1409364 7.92 0.000 8405478 1.393008 loutput 0089511 .0051982 1.72 0.085 -.0012372 .0191393 lp_urea -.3792256 .065678 -5.77 0.000 -.5079522 -.2504991 lp_npk 0304985 .0428719 0.71 0.477 -.0535289 .1145258 snpk _cons -20.84974 5.387569 -3.87 0.000 -31.40918 -10.2903 lout_npk 0089511 .0051982 1.72 0.085 -.0012372 .0191393 lout_urea -.1963716 .1491281 -1.32 0.188 -.4886574 .0959141 lp_urea_npk -.3792256 .065678 -5.77 0.000 -.5079522 -.2504991 loutput2 0064543 .0085096 0.76 0.448 -.0102242 .0231328 lp_npk2 0609969 .0857438 0.71 0.477 -.1070579 .2290517 lp_urea2 -2.505675 .7265642 -3.45 0.001 -3.929715 -1.081635 loutput 1.238252 .4167321 2.97 0.003 421472 2.055032 lp_npk 1.116778 .1409364 7.92 0.000 8405478 1.393008 lp_urea 14.70696 3.820055 3.85 0.000 7.219785 22.19412 lcost (47)Testing homogeneity Prob > chi2 = 0.0009 chi2( 3) = 16.38 ( 3) [lcost]lout_urea + [lcost]lout_npk = 0 ( 2) [lcost]lp_urea2 + [lcost]lp_npk2 + [lcost]lp_urea_npk = 0 ( 1) [lcost]lp_urea + [lcost]lp_npk = 1 > */ (lout_urea + lout_npk = 0) > */ (lp_urea2 + lp_npk2 + lp_urea_npk = 0) /* test (lp_urea + lp_npk = 1) /* (48)Imposing homogeneity snpk 4164 .3089154 0.0133 69.54 0.0000 lcost 4164 .8430911 0.4984 10572.17 0.0000 Equation Obs Parms RMSE "R-sq" chi2 P Three-stage least-squares regression > */ (snpk lp_npk lp_urea loutput), constraint(4 10) reg3 (lcost lp_urea lp_npk loutput lp_urea2 lp_npk2 loutput2 lp_urea_npk lout_urea lout_npk) /* constraint 10 [lcost]lout_urea + [lcost]lout_npk = constraint [lcost]lp_urea2 + [lcost]lp_npk2 + [lcost]lp_urea_npk = constraint [lcost]lp_urea + [lcost]lp_npk = (49)Imposing homogeneity lp_urea_npk lout_urea lout_npk Exogenous variables: lp_urea lp_npk loutput lp_urea2 lp_npk2 loutput2 Endogenous variables: lcost snpk _cons 1.16657 .1309565 8.91 0.000 9099001 1.42324 loutput 0084214 .0051685 1.63 0.103 -.0017087 .0185515 lp_urea -.388852 .065142 -5.97 0.000 -.516528 -.2611761 lp_npk 0201149 .0410971 0.49 0.625 -.0604339 .1006637 snpk _cons -1.5325 .4902529 -3.13 0.002 -2.493378 -.5716221 lout_npk 0084214 .0051685 1.63 0.103 -.0017087 .0185515 lout_urea -.0084214 .0051685 -1.63 0.103 -.0185515 .0017087 lp_urea_npk -.388852 .065142 -5.97 0.000 -.516528 -.2611761 loutput2 0082655 .0077823 1.06 0.288 -.0069875 .0235185 lp_npk2 0402298 .0821942 0.49 0.625 -.1208678 .2013275 lp_urea2 3486222 .0628382 5.55 0.000 2254615 .4717829 loutput 7699614 .1236369 6.23 0.000 5276375 1.012285 lp_npk 1.16657 .1309565 8.91 0.000 9099001 1.42324 lp_urea -.1665701 .1309565 -1.27 0.203 -.4232402 .0900999 lcost
- Xem thêm -

Xem thêm: Bài 7: Hàm chi phí và lợi nhuận, Bài 7: Hàm chi phí và lợi nhuận