Calculate the growth rates of output, capital, and labor for each year in the da

Question

Calculate the growth rates of output, capital, and labor for each year in the data set. Then calculate the growth rate of TFP for each year assuming that China's output can be determined by the following production function:

What is the average growth rate of TFP?

(use percent change for the growth rate; round to 2 decimal places, you should not have a value for the growth rate in 1952)

Year Labor Output Capital 1952 209.9094 463996.1 495817.8 1953 215.165 508549.4 517064.3 1954 220.4425 519902 544015.1 1955 224.7875 544019.9 569533.8 1956 230.48 591439.3 601874.4 1957 237.3575 641285.6 638674 1958 254.5925 718558.8 704365.8 1959 266.265 737648 802392.1 1960 262.8211 704739.6 887659.4 1961 260.2388 493618.4 912265.8 1962 260.7647 537124.5 919103.7 1963 266.4395 604790.4 941306.6 1964 276.0496 691632.5 978848.7 1965 286.7422 756244.9 1034937 1966 297.4521 811773.8 1108159 1967 308.3288 766894.9 1153293 1968 319.0403 736139.1 1196818 1969 331.2617 825404.1 1249407 1970 344.0183 929618.1 1345060 1971 358.5814 976173.3 1449827 1972 370.7607 998655.3 1553749 1973 381.2419 1066033 1663912 1974 394.4494 1084832 1789866 1975 407.9577 1154747 1940378 1976 420.9138 1115404 2080415 1977 432.582 1174463 2223858 1978 445.5044 1306167 2399246 1979 460.5417 1398248 2577518 1980 479.1169 1455675 2783241 1981 500.9003 1541403 2977514 1982 519.1486 1676698 3194943 1983 533.1974 1794602 3434470 1984 546.7159 2000094 3711716 1985 560.2422 2189237 4049092 1986 572.0871 2322364 4411369 1987 582.4245 2504512 4796402 1988 598.1485 2625791 5236382 1989 619.0762 2654496 5563449 1990 637.0748 2668080 5851508 1991 651.2 2834056 6200814 1992 658.215 3103359 6703614 1993 664.8 3437912 7418662 1994 671.315 3725428 8222818 1995 677.6 4227655 9086238 1996 685.075 4385063 10025209 1997 693.85 4693969 11010464 1998 702.285 4713044 12159789 1999 710.155 4992596 13342564 2000 717.395 5309820 14586433 2001 725.55 5678756 16002954 2002 733.825 6290808 17620104 2003 740.86 6858146 19592794 2004 748.16 7585524 21840018 2005 755.125 8267831 24356182 2006 761.125 9249799 27190004 2007 766.95 10363165 30325914 2008 772.35 10893638 33799556 2009 777.375 11781561 38334244 2010 781.3768 12779162 43438692 2011 784.4269 13779918 48872912 2012 788.8708 14840971 54674592 2013 793.0223 15983726 60943980 2014 798.3678 17150538 67590072

Explanation / Answer

The growth rates of output, capital, and labor for each year in the data set are computed as follows:-

Based on the above steps, the figures computed for the growth rates of output, capital, and labor for each year in the data set provided in the question are provided in the table as follows:-

In order to calculate the TFP of China, the

As mentioned in this question, China's output is determined by the production function, Q= A K1/3 L2/3 , where, Q is the output, A is the TFP, K is capital and L is labor.

In order to compute growth rate of TFP for each year, firstly, TFP ie. A in the production function is computed for each year by dividing Q/(L2/3*K1/3) for each year. Thereafter, the growth rate of TFP for each year is computed for each year (except for year 1952) as the difference between the value of the TFP computed for the current year and the value of TFP computed for the previous year divided by the previous year's value of TFP expressed as a %.

The table below provides the computed figures for TFP and growth rate of TFP for each year.

The average growth rate of TFP is 1.95%. This value is computed by taking the average of the growth rates of TFP obtained for each year.

Year Labour Output Capital Growth rate of Output Growth rate of Capital   Growth rate of Labour   1952 209.9094 463996.1 495817.8 - - - 1953 215.165 508549.4 517064.3 9.60% 4.29% 2.50% 1954 220.4425 519902 544015.1 2.23% 5.21% 2.45% 1955 224.7875 544019.9 569533.8 4.64% 4.69% 1.97% 1956 230.48 591439.3 601874.4 8.72% 5.68% 2.53% 1957 237.3575 641285.6 638674 8.43% 6.11% 2.98% 1958 254.5925 718558.8 704365.8 12.05% 10.29% 7.26% 1959 266.265 737648 802392.1 2.66% 13.92% 4.58% 1960 262.8211 704739.6 887659.4 -4.46% 10.63% -1.29% 1961 260.2388 493618.4 912265.8 -29.96% 2.77% -0.98% 1962 260.7647 537124.5 919103.7 8.81% 0.75% 0.20% 1963 266.4395 604790.4 941306.6 12.60% 2.42% 2.18% 1964 276.0496 691632.5 978848.7 14.36% 3.99% 3.61% 1965 286.7422 756244.9 1034937 9.34% 5.73% 3.87% 1966 297.4521 811773.8 1108159 7.34% 7.08% 3.74% 1967 308.3288 766894.9 1153293 -5.53% 4.07% 3.66% 1968 319.0403 736139.1 1196818 -4.01% 3.77% 3.47% 1969 331.2617 825404.1 1249407 12.13% 4.39% 3.83% 1970 344.0183 929618.1 1345060 12.63% 7.66% 3.85% 1971 358.5814 976173.3 1449827 5.01% 7.79% 4.23% 1972 370.7607 998655.3 1553749 2.30% 7.17% 3.40% 1973 381.2419 1066033 1663912 6.75% 7.09% 2.83% 1974 394.4494 1084832 1789866 1.76% 7.57% 3.46% 1975 407.9577 1154747 1940378 6.44% 8.41% 3.42% 1976 420.9138 1115404 2080415 -3.41% 7.22% 3.18% 1977 432.582 1174463 2223858 5.29% 6.89% 2.77% 1978 445.5044 1306167 2399246 11.21% 7.89% 2.99% 1979 460.5417 1398248 2577518 7.05% 7.43% 3.38% 1980 479.1169 1455675 2783241 4.11% 7.98% 4.03% 1981 500.9003 1541403 2977514 5.89% 6.98% 4.55% 1982 519.1486 1676698 3194943 8.78% 7.30% 3.64% 1983 533.1974 1794602 3434470 7.03% 7.50% 2.71% 1984 546.7159 2000094 3711716 11.45% 8.07% 2.54% 1985 560.2422 2189237 4049092 9.46% 9.09% 2.47% 1986 572.0871 2322364 4411369 6.08% 8.95% 2.11% 1987 582.4245 2504512 4796402 7.84% 8.73% 1.81% 1988 598.1485 2625791 5236382 4.84% 9.17% 2.70% 1989 619.0762 2654496 5563449 1.09% 6.25% 3.50% 1990 637.0748 2668080 5851508 0.51% 5.18% 2.91% 1991 651.2 2834056 6200814 6.22% 5.97% 2.22% 1992 658.215 3103359 6703614 9.50% 8.11% 1.08% 1993 664.8 3437912 7418662 10.78% 10.67% 1.00% 1994 671.315 3725428 8222818 8.36% 10.84% 0.98% 1995 677.6 4227655 9086238 13.48% 10.50% 0.94% 1996 685.075 4385063 10025209 3.72% 10.33% 1.10% 1997 693.85 4693969 11010464 7.04% 9.83% 1.28% 1998 702.285 4713044 12159789 0.41% 10.44% 1.22% 1999 710.155 4992596 13342564 5.93% 9.73% 1.12% 2000 717.395 5309820 14586433 6.35% 9.32% 1.02% 2001 725.55 5678756 16002954 6.95% 9.71% 1.14% 2002 733.825 6290808 17620104 10.78% 10.11% 1.14% 2003 740.86 6858146 19592794 9.02% 11.20% 0.96% 2004 748.16 7585524 21840018 10.61% 11.47% 0.99% 2005 755.125 8267831 24356182 8.99% 11.52% 0.93% 2006 761.125 9249799 27190004 11.88% 11.63% 0.79% 2007 766.95 10363165 30325914 12.04% 11.53% 0.77% 2008 772.35 10893638 33799556 5.12% 11.45% 0.70% 2009 777.375 11781561 38334244 8.15% 13.42% 0.65% 2010 781.3768 12779162 43438692 8.47% 13.32% 0.51% 2011 784.4269 13779918 48872912 7.83% 12.51% 0.39% 2012 788.8708 14840971 54674592 7.70% 11.87% 0.57% 2013 793.0223 15983726 60943980 7.70% 11.47% 0.53% 2014 798.3678 17150538 67590072 7.30% 10.91% 0.67%

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