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?

Expert Solution

Solution

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

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Rahul Sunny answered 2 years ago

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