There are two countries, X and Z. Productivity in Country X is 1.8 times as high
ID: 1202529 • Letter: T
Question
There are two countries, X and Z. Productivity in Country X is 1.8 times as high as productivity in Country Z. Technology in Country X is 3.2 times as high as technology in country Z. How does efficiency in the two countries compare? b. Now assume only that the level of productivity in Country X relative to Country Z is 1.8, and the growth rate of technology is 0.75% per year. i. If technology in Country Z lags Country X by 10 years, what is the level of technology in Country X relative to Country Z, and what is the level of efficiency in Country X relative to Country Z? ii. If the ratio of efficiency E_X/E_Z = 1.5, and both productivity and the growth rate of technology have not changed from question part b.i. above, how many years must technology lag in Country Z?Explanation / Answer
a. Productivity = Efficiency*Technology
S0, Productivity in X/ Productivity in Y = EfficiencyOf X*Technology of X/ Efficiencyof Y*Technology of Y
1.8/1 = 3.2*EfficiencyOf X/Efficiencyof Y
EfficiencyOf X/Efficiencyof Y = 0.5625
b.
i. Tx = Tx-10*(1+g)^G
Since, Tz = Tx-10 and g =0.75% and G =10
= Tz*(1+0.0075)^10
= 1.077*Tz
So, the technology in X is 1.07 times the technology in Z
Productivity = Efficiency*Technology
1.8 = 1.07* Efficiency
Efficiency = 1.8/1.07 = 1.68
So the Efficiency in Country X is 1.68 times the Efficiency in country Z.
Technology lag G = ln(Ex/Ez)/2*ln(1+g)
= ln(1.68)/2*ln(1+0.0075)
= 0.518/2*0.0074
= 34.66
So , it will take 34.66 Years .
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