Figure 3.5 updated is above.

use the following Data set and answer entire question pls with explanation. pls pls

% dev Y % dev C % dev I 1947-01-01 2.537991 0.428096 -0.05731 1947-04-01 1.215986 1.264862 -9.39576 1947-07-01 -0.04411 0.768737 -13.7414 1947-10-01 0.45363 -0.01752 2.599503 1948-01-01 0.890216 -0.34172 11.03447 1948-04-01 1.456817 -0.02033 15.73808 1948-07-01 0.939409 -0.7035 15.49971 1948-10-01 -0.04513 -0.74761 9.377875 1949-01-01 -2.55121 -1.43057 -8.00298 1949-04-01 -4.03604 -0.76484 -23.4639 1949-07-01 -4.18503 -1.40985 -16.7094 1949-10-01 -6.22579 -0.82467 -22.9806 1950-01-01 -3.60489 -0.04512 -2.90285 1950-04-01 -1.84485 0.712637 6.064204 1950-07-01 0.679696 4.83787 13.15873 1950-10-01 1.313153 0.901288 24.03956 1951-01-01 1.400624 2.414209 12.2811 1951-04-01 1.87488 -1.33 13.66949 1951-07-01 2.691618 -1.05246 5.204818 1951-10-01 1.714504 -1.3542 -3.84893 1952-01-01 1.609768 -2.02509 -1.9788 1952-04-01 0.696797 -0.98434 -10.5066 1952-07-01 0.322489 -1.42174 -5.94569 1952-10-01 2.497581 1.12541 0.338001 1953-01-01 3.326656 1.369411 1.802375 1953-04-01 3.129532 1.044125 1.688378 1953-07-01 1.634888 -0.13065 -1.11985 1953-10-01 -0.78675 -1.73471 -9.33644 1954-01-01 -2.13531 -2.31274 -10.8115 1954-04-01 -2.86433 -1.9641 -11.8391 1954-07-01 -2.55413 -1.56493 -7.93658 1954-10-01 -1.4118 -0.42825 -4.47435 1955-01-01 0.63224 0.855401 4.219828 1955-04-01 1.492501 1.836186 9.322202 1955-07-01 2.110579 2.158646 10.08008 1955-10-01 2.007466 2.517007 11.65451 1956-01-01 0.943574 1.814605 8.100297 1956-04-01 1.103589 1.306905 6.71246 1956-07-01 0.372324 0.714195 5.26368 1956-10-01 1.378145 1.277883 3.812539 1957-01-01 1.393525 1.189949 1.764958 1957-04-01 0.552112 0.587989 1.175574 1957-07-01 0.90521 0.620169 2.947513 1957-10-01 -0.75968 -0.09831 -5.5756 1958-01-01 -4.0371 -2.24193 -13.1289 1958-04-01 -4.0542 -2.17581 -15.8048 1958-07-01 -2.46032 -1.29027 -9.1251 1958-10-01 -0.87096 -0.70678 -1.72919 1959-01-01 0.280413 0.333239 2.720339 1959-04-01 1.731607 1.078709 9.302284 1959-07-01 1.000098 1.323908 1.663538 1959-10-01 0.455151 0.637175 3.847724 1960-01-01 1.819421 0.770374 12.36109 1960-04-01 0.396321 1.191311 1.447825 1960-07-01 -0.03407 -0.05719 0.005822 1960-10-01 -2.27965 -0.79665 -12.9997 1961-01-01 -2.59298 -1.73119 -11.7992 1961-04-01 -1.93811 -1.17771 -6.47162 1961-07-01 -1.10353 -1.64873 -0.51945 1961-10-01 -0.26571 -0.64287 -0.49817 1962-01-01 0.361272 -0.61033 3.061846 1962-04-01 0.09163 -0.44082 0.52164 1962-07-01 0.111316 -0.72021 0.3916 1962-10-01 -0.78668 -0.43147 -4.43828 1963-01-01 -0.95662 -0.87934 -1.21455 1963-04-01 -1.12215 -1.11272 -1.57499 1963-07-01 -0.2486 -0.96539 -0.50365 1963-10-01 -0.90883 -1.35745 -1.27648 1964-01-01 -0.15486 -0.65913 0.410124 1964-04-01 -0.41118 -0.16818 -1.92736 1964-07-01 -0.20128 0.390796 -1.57758 1964-10-01 -1.23537 -0.60532 -2.55508 1965-01-01 -0.17973 0.317735 4.671057 1965-04-01 -0.24842 0.135161 3.115303 1965-07-01 0.64344 0.562027 4.792556 1965-10-01 1.636107 2.072621 3.790215 1966-01-01 2.78794 2.289527 9.909745 1966-04-01 1.909369 1.317644 6.944082 1966-07-01 1.566401 1.243637 4.825368 1966-10-01 1.236464 0.467457 4.119593 1967-01-01 1.010357 -0.12766 0.428019 1967-04-01 0.006061 0.079109 -4.39199 1967-07-01 -0.08429 -0.5444 -2.58073 1967-10-01 -0.3255 -1.04467 -1.47488 1968-01-01 0.734474 0.225542 -0.47152 1968-04-01 1.472263 0.661592 2.335478 1968-07-01 1.356747 1.462553 -1.34737 1968-10-01 0.89711 0.878171 -1.1533 1969-01-01 1.628573 0.961854 3.693717 1969-04-01 1.136917 0.604342 2.243517 1969-07-01 1.021055 0.104631 3.395938 1969-10-01 -0.22126 -0.07308 -2.41005 1970-01-01 -1.11084 -0.4195 -6.31773 1970-04-01 -1.70423 -0.92311 -7.00266 1970-07-01 -1.51791 -0.99999 -6.32516 1970-10-01 -3.32928 -2.22031 -12.7505 1971-01-01 -1.38937 -1.26016 -2.72406 1971-04-01 -1.59352 -1.28643 -0.94545 1971-07-01 -1.52391 -1.42985 -0.77206 1971-10-01 -2.04023 -0.715 -4.53029 1972-01-01 -0.97345 -0.32374 0.839317 1972-04-01 0.517517 0.653623 5.381232 1972-07-01 0.710003 1.290548 5.857493 1972-10-01 1.631317 2.739022 5.610538 1973-01-01 3.350212 3.696822 10.49946 1973-04-01 3.721189 2.821248 13.94121 1973-07-01 2.496472 2.364371 9.587057 1973-10-01 2.758505 1.273113 12.48356 1974-01-01 1.220412 -0.4041 6.048519 1974-04-01 0.785722 -0.8198 5.111697 1974-07-01 -0.83811 -1.16177 -0.7564 1974-10-01 -1.91228 -3.41343 -0.73642 1975-01-01 -3.83778 -3.36429 -18.9573 1975-04-01 -3.84738 -2.52986 -22.7358 1975-07-01 -2.89471 -1.92542 -16.1448 1975-10-01 -2.32645 -1.67199 -14.3871 1976-01-01 -0.8949 -0.5149 -6.29274 1976-04-01 -0.97434 -0.4242 -3.62654 1976-07-01 -1.25157 -0.19934 -4.58066 1976-10-01 -1.36737 0.273356 -5.19754 1977-01-01 -1.03687 0.636452 -2.07185 1977-04-01 0.044965 0.386583 3.440624 1977-07-01 0.993317 0.553876 6.979432 1977-10-01 0.169448 1.294291 3.087979 1978-01-01 -0.32013 1.13092 3.730306 1978-04-01 2.687344 2.549378 8.821743 1978-07-01 2.93329 2.300714 10.59461 1978-10-01 3.546715 2.468908 11.89683 1979-01-01 3.043494 2.379236 11.19832 1979-04-01 2.502037 1.734224 10.36547 1979-07-01 2.630546 2.143785 8.032951 1979-10-01 2.300346 1.853338 5.704408 1980-01-01 2.058103 1.17915 4.553514 1980-04-01 -0.55657 -1.62396 -4.74952 1980-07-01 -1.19616 -1.0662 -11.9676 1980-10-01 0.136589 -0.27077 -3.44678 1981-01-01 1.561148 -0.50359 4.998951 1981-04-01 0.293397 -1.08963 0.326601 1981-07-01 0.943955 -1.25609 5.324222 1981-10-01 -0.71346 -2.60861 1.185467 1982-01-01 -2.87233 -2.5835 -9.38999 1982-04-01 -3.0495 -3.03738 -10.2111 1982-07-01 -4.11154 -3.17391 -12.0011 1982-10-01 -4.79878 -2.29236 -21.052 1983-01-01 -4.26845 -2.2096 -18.7807 1983-04-01 -2.84644 -1.13739 -11.5589 1983-07-01 -1.74338 -0.34134 -6.84787 1983-10-01 -0.59487 0.226452 1.004629 1984-01-01 0.393994 0.013691 8.761116 1984-04-01 1.132385 0.345509 10.49255 1984-07-01 1.098512 0.012425 11.19188 1984-10-01 0.908701 0.216179 8.491147 1985-01-01 0.858885 0.816453 4.380385 1985-04-01 0.719604 0.647412 4.814322 1985-07-01 1.221794 1.45389 2.952957 1985-10-01 0.956149 0.605551 5.477827 1986-01-01 0.888363 0.427155 4.441915 1986-04-01 0.353284 0.481729 1.759461 1986-07-01 0.335274 1.226349 -1.81015 1986-10-01 -0.08104 0.854868 -2.27875 1987-01-01 -0.27413 -0.00252 -0.31161 1987-04-01 -0.11806 0.422692 -0.88718 1987-07-01 -0.14729 0.656175 -1.43332 1987-10-01 0.685671 -0.00368 4.660545 1988-01-01 0.357447 0.909665 -0.69472 1988-04-01 0.847577 0.836161 1.282499 1988-07-01 0.645493 0.94459 1.51351 1988-10-01 1.211989 1.331184 2.75746 1989-01-01 1.497727 1.078558 5.868405 1989-04-01 1.563058 0.858036 4.709994 1989-07-01 1.634199 1.161678 3.647412 1989-10-01 1.19141 0.959688 2.757819 1990-01-01 1.66296 1.180414 3.599066 1990-04-01 1.429241 0.880955 3.461033 1990-07-01 0.915746 0.685501 1.296777 1990-10-01 -0.57111 -0.66664 -4.72696 1991-01-01 -1.60889 -1.63419 -8.46478 1991-04-01 -1.40479 -1.4057 -8.92182 1991-07-01 -1.48299 -1.51613 -7.53603 1991-10-01 -1.72801 -2.19198 -4.75555 1992-01-01 -1.14846 -0.98038 -7.45648 1992-04-01 -0.69705 -0.9677 -2.92526 1992-07-01 -0.36186 -0.58383 -3.23426 1992-10-01 0.007573 -0.10522 -1.45616 1993-01-01 -0.51542 -0.44759 -0.46872 1993-04-01 -0.64696 -0.28904 -1.34975 1993-07-01 -0.90568 0.051974 -3.58692 1993-10-01 -0.31316 0.139736 -0.1134 1994-01-01 -0.12696 0.472675 1.896485 1994-04-01 0.417635 0.425483 4.896768 1994-07-01 0.178757 0.344651 1.391604 1994-10-01 0.474262 0.563176 3.513376 1995-01-01 -0.03345 -0.06545 2.601908 1995-04-01 -0.61914 -0.08654 -1.49418 1995-07-01 -0.67414 -0.09939 -4.12798 1995-10-01 -0.9188 -0.33678 -3.74678 1996-01-01 -1.11278 -0.37219 -4.25491 1996-04-01 -0.41521 -0.27681 -1.68551 1996-07-01 -0.4943 -0.66661 0.625611 1996-10-01 -0.44418 -0.88775 -1.63552 1997-01-01 -0.79485 -0.87163 -1.75224 1997-04-01 -0.14567 -1.4744 2.097712 1997-07-01 0.09421 -0.85212 1.438839 1997-10-01 -0.05273 -0.7447 0.925299 1998-01-01 -0.05563 -0.83065 3.262513 1998-04-01 -0.12435 -0.18415 0.788356 1998-07-01 0.142412 0.01023 1.557827 1998-10-01 0.782603 0.344382 2.921179 1999-01-01 0.777961 0.272496 4.055126 1999-04-01 0.687897 0.707702 2.650254 1999-07-01 1.10518 0.755184 3.998942 1999-10-01 1.863214 1.15326 5.395886 2000-01-01 1.384711 1.6219 3.554909 2000-04-01 2.375521 1.540277 8.275756 2000-07-01 1.690087 1.506793 6.360396 2000-10-01 1.523466 1.414112 5.708559 2001-01-01 0.462253 0.836005 0.296073 2001-04-01 0.365785 0.118421 -0.27843 2001-07-01 -0.73762 -0.43144 -3.14879 2001-10-01 -1.15212 0.287722 -8.89768 2002-01-01 -1.01226 -0.35423 -6.66165 2002-04-01 -1.08097 -0.70138 -5.71906 2002-07-01 -1.35948 -0.84318 -6.5755 2002-10-01 -1.91207 -1.11759 -7.37271 2003-01-01 -2.08389 -1.44531 -7.36794 2003-04-01 -1.88317 -1.11805 -7.46325 2003-07-01 -0.92098 -0.5131 -4.67936 2003-10-01 -0.46321 -0.61568 -2.15967 2004-01-01 -0.57781 -0.46253 -2.73633 2004-04-01 -0.48037 -0.67849 0.442863 2004-07-01 -0.21014 -0.25245 1.301721 2004-10-01 0.154471 0.150724 2.761901 2005-01-01 0.626152 0.087342 5.026229 2005-04-01 0.501982 0.519247 3.290631 2005-07-01 0.701802 0.703655 4.333939 2005-10-01 0.716509 0.279282 7.402028 2006-01-01 1.537349 0.788308 8.89288 2006-04-01 1.299284 0.766781 8.415216 2006-07-01 1.004478 0.905437 8.349659 2006-10-01 1.436437 1.392303 6.856107 2007-01-01 1.360112 1.583594 6.76598 2007-04-01 1.664007 1.459921 8.58106 2007-07-01 1.967257 1.776011 8.383737 2007-10-01 2.311073 1.854453 8.034773 2008-01-01 1.667721 1.434011 6.299822 2008-04-01 2.026632 1.452525 5.409298 2008-07-01 1.303454 0.443203 4.289743 2008-10-01 -1.08935 -0.68234 -4.99411 2009-01-01 -2.44653 -1.15121 -16.565 2009-04-01 -2.80858 -1.85655 -21.957 2009-07-01 -2.65195 -1.40374 -21.8351 2009-10-01 -1.81241 -1.73962 -12.8552 2010-01-01 -1.55749 -1.39912 -10.6877 2010-04-01 -0.86094 -0.75981 -5.87027 2010-07-01 -0.38071 -0.31805 -2.01083 2010-10-01 -0.17539 0.006395 -3.02352 2011-01-01 -0.75309 0.083375 -5.7983 2011-04-01 -0.4375 -0.13821 -2.81992 2011-07-01 -0.85965 -0.17851 -3.6601 2011-10-01 -0.14979 -0.37216 2.476444 2012-01-01 0.239165 -0.04072 3.162672 2012-04-01 0.24791 -0.27527 3.988095 2012-07-01 -0.04045 -0.50612 2.941992 2012-10-01 -0.41066 -0.56437 0.518147 2013-01-01 -0.04139 -0.51279 2.63514 2013-04-01 -0.41173 -0.86208 2.206648 2013-07-01 -0.14537 -1.01408 4.478683 2013-10-01 0.030042 -0.76166 3.347587 2014-01-01 -0.86293 -0.94496 0.779019 2014-04-01 -0.13722 -0.60323 3.509676 2014-07-01 0.466594 -0.22112 4.188752 2014-10-01 0.358227 0.282331 3.01437 2015-01-01 0.610283 0.331561 5.226691 2015-04-01 0.633208 0.386053 4.377687 2015-07-01 0.403597 0.525404 3.090927 2015-10-01 0.001408 0.407691 0.857105 2016-01-01 0.045548 0.522799 -0.54203 2016-04-01 -0.18965 0.419856 -1.99066 2016-07-01 -0.12134 0.401877 -2.68069 2016-10-01 -0.14819 0.293879 -1.01232 2017-01-01 -0.19131 0.435834 -2.14555 2017-04-01 -0.13627 0.33258 -1.20082 2017-07-01 0.087595 0.340933 -0.47143 2017-10-01 0.543106 0.845451 -0.06992 2018-01-01 0.837379 0.914323 1.256919 2018-04-01 1.216885 1.251782 0.738115 2018-07-01 1.261733 1.405563 2.367035 2018-10-01 1.064327 1.341406 2.246081 2019-01-01 1.252945 1.013964 3.141437 2019-04-01 1.648097 1.413777 3.139433 2019-07-01 1.946257 1.731059 2.778931 2019-10-01 2.034289 1.68916 0.452545 2020-01-01 0.343798 -0.57582 -1.5768 2020-04-01 -9.40194 -11.2355 -18.9941 2020-07-01 -2.52018 -3.08216 -4.74772 2020-10-01 -1.81707 -2.78383 -0.01182 2021-01-01 -0.71189 -0.62849 -1.39687 2021-04-01 0.489836 1.64854 -3.23163 2021-07-01 0.62892 1.562869 -1.17303 2021-10-01 1.8616 1.60821 5.771418 2022-01-01 1.030255 1.480322 6.118411 2022-04-01 0.359931 1.156165 1.620524

Consider the updated version of Figure 3.15 in the Chapter 3 Power Point slides. As pointed out in the slide, over the entire 1948-2022 period, average labor productivity, output per worker, is procyclical since the correlation coefficient between the two percent deviation from trend series equals 0.61. However, upon closer inspection, we see that at the onset of the Great Recession (in early 2008) and during the Covid Recession (early 2020), average labor productivity was first countercyclical before turning procyclical. That is to say, in both episodes, ALP initially increased before it decreased (as expected). Given that both output and employment fell at the onset of both of these recessions, use a version of the production function given on the next page to show that average labor productivity can be countercyclical if there is no change in total factor productivity, z. On the graph, average labor productivity, Y/N, corresponds to the slope of a line that starts at (0,0) and goes to a point on the production function with coordinates (N,Y). Thus, you want to show that Y/N can increase even though both N and Y decrease as long as there is no change in z (or K ). Percentage Deviations from Trend in Aver. Labor Productivity and Real GDP