Suppose that the (total factor) productivity level A can be broken down into a technology level...

Suppose that the (total factor) productivity level A can be broken down into a technology level T and efficiency level E as follows: A = T ?E. In the USA, the average growth rate of A is 0.81% per year while the efficiency level does not change. Productivity in Canada is 77% that of the USA. Suppose that Canada is five years behind the USA in terms of technology. What is the efficiency level in Canada relative to the USA?

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Given that the total factor productivity level A is given as A =T * E . But given that in the U.S.A,the average growth rate of A is 0.81% per year while the efficiency level does not change.So this means that the entire growth rate in A is solely due to the growth rate in technology level T

Asuming the current value of technology level as 100 which also implies that the value of A is also 100 ; it is already given that the growth rate of A is 0.81% per year

So,calculating the value of technology level T of U.S.A five years ago

Technology level around 1year back from now is 100 / (1+0.81%) i.e., 100 / (1.0081) which is equal to 99.1965. ( I considered the denominator as (1+0.81%) because after the value which was existing in the previous year grew by 0.81% then it became 100)

Technology level around 2 years back from now is : (99.1965) / (1.0081) which is equal to 98.3995

Technology level around 3 years back from now is (98.3995) / (1.0081) which is equal to 97.6088

Technology level around 4 years back from now is (97.6088) / (1.0081) which is equal to 96.8245

Technology level around 5 years back from now is (96.8245) / (1.0081) which is equal to 96.0465

Given that the productivity level of Canada is 77% of U.S.A ,so it would be 77% of 100 i.e., 77.Let the efficiency level in Canada which is to be found out be ''x"

So, substituting the assumed values in the equation A = T *E we get:

77 = 96.0465 * (x)

=> x = 0.80169 which means the efficiency level E of canada is approximately 80.17% that of U.S.A

Hope this solution helps!! Please provide a "Thumbsup" rating for this solution !!

Rahul Sunny answered 1 year ago

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