Tham khảo tài liệu 'quantitative techniques for competition and antitrust analysis by peter davis and eliana garcés_1', kinh doanh - tiếp thị phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | . Technological Determinants of Market Structure 23 --Relative capital stock. 1899 100 A Relative numberofworkers 1899 K 0 -X Index of manufacturing production. 1899 100 in the United States between 1899 and 1924. Theirtime series evidence examines the relationship between aggregate inputs of labor and capital andnationaloutput during a period of fast growing . labor and even faster growing capital stock. Their data are plotted in figure Cobb and Douglas designed a 2unctiontha2couldcapture the relationship between output and inputs while allowinpCousubsttCutioeandwhicC hhuldbe Oeth oupiri-cally relevant and mathematically peoduction function is defined as follows Q aũLaLKaKu h Ing s 0 C Lrn L h lbt V where V Inu í ỉíìữo aadwherp ohepaecmeters ao dL aK can be easily estimated from the equation once it is log-linearized. As figure shows the a K- u H. . isoquants in this function exhibit a convex shape indicating that there is a certain degree of substitution among thchncats. Marginal products the increate inproOuctioeocghavadbyinceeasmg onehnitaO an input holding other inputs constaot arc dhfinehsg bhllowiin o Cobb-Doootac function ag tuo ict hsi 7. g MPl - h1h .L 2 K K Fbu ai dL b ul aK . dK K so that the marginal rate of technical substitution is 20 In their paper Cobb and Douglas 1928 the authors report the full data set they used. 24 1. The Determinants of Market Outcomes Kị L Figure . Example of isoquants for a Cobb-Douglas function. Year Figure . Cobb and Douglas s implied marginal products of labor and capital. Cobb and Douglas s econometric evidence suggested that the increase in labor and particularly capital over time wasincreasing output butnotproportionately. In particular as figure shows their estimates suggested that the marginal product of capital was declining fast. Natrrally nucha conolesionto I Ce weuld Oave profound implications for the liUelihoodotconlinued lasgc cceitaifluwsiotutra United .
