Question

-a where the delta symbols denote changes (so that Δ Y/Y describes the percentage change in Y). Y is output, K, L, and T are capital, labor, and resource inputs, respectively. R is the growth-accounting residual or the measure of TFP. a, b, and c are weights (1) 13 pointsl Your 14 year-old sibling is a very intelligent person but knows nothing about eco- nomics. Explain this equation to your sibling.

Answer 1

1).

Consider the given problem here the output “Y” depends on “K”, “L” and “T”. Now, if each of these factors will change that will also change the “Y”. So, the we can write the growth of “Y” in terms of growth of each factors.

=> dY/Y = a*dK/K + b*dL/L + c*dT/T + R. So, “a*dK/K” is the part of growth in “Y” coming from capital, “b*dL/L” is the part of growth in “Y” coming from labor, “c*dT/T” is the part of growth in “Y” coming from input resources. Now, the term “R” will represent the part of growth of “Y” which is unexplained by these three inputs.

2).

Now, these weights represents the income share of each factors, => “a” the coefficient of “K”, => it’s the income share of capital. Similarly, “b” be the income share of labor and “c” is the income share of input resources.

3).

YearYK L T dY/Y Calculation dK/K Calculation dL/L Calculation dT/T Calculation 1 40 20 40 100 2 80 60 50 110 3 120 90 0 110 100"-((80-40/40*100" 50 ((120-80)/80) 100" 200"=((60-20)/20)"100" 50-((90-60)/60) 100" 25"-(5040)/40)"100" 10 20((60-50)/50) 100"0 (110-1001/100).100" 0-((110-110)/110)"100"

Now, “a=0.2”, “b=0.6” and “c=0.2”, => the value of “R” from “year1 to 2” is given by.

=> R = dY/Y - a*dK/K - b*dL/L - c*dT/T = dY/Y – 0.2*dK/K – 0.6*dL/L – 0.2*dT/T.

=> R = 100% – 0.2*200% – 0.6*25% – 0.2*10% = 100% – 40% – 15% – 2%.

=> R = 100% – 40% – 15% – 2% = 43%.

Now, the value of “R” from “year2 to 3” is given by.

=> R = dY/Y - a*dK/K - b*dL/L - c*dT/T = dY/Y – 0.2*dK/K – 0.6*dL/L – 0.2*dT/T.

=> R = 50% – 0.2*50% – 0.6*20% – 0.2*0% = 50% – 10% – 12% – 0%.

=> R = 50% – 10% – 12% = 28%.

4).

Now, “a=0.3”, “b=0.6” and “c=0.1”, => the value of “R” from “year1 to 2” is given by.

=> R = dY/Y - a*dK/K - b*dL/L - c*dT/T = dY/Y – 0.3*dK/K – 0.6*dL/L – 0.1*dT/T.

=> R = 100% – 0.3*200% – 0.6*25% – 0.1*10% = 100% – 60% – 15% – 1%.

=> R = 100% – 60% – 15% – 1% = 24%.

Now, the value of “R” from “year2 to 3” is given by.

=> R = dY/Y - a*dK/K - b*dL/L - c*dT/T = dY/Y – 0.3*dK/K – 0.6*dL/L – 0.1*dT/T.

=> R = 50% – 0.3*50% – 0.6*20% – 0.1*0% = 50% – 15% – 12% – 0%, => R = 23%.