Question

The table below reports per capita GDP and capital per person in the year 2014 for 10

countries. Your task is to fill in the missing columns of the table.

a)Given the values in column 1 and 2, fill in columns 3 and 4. That is, compute per capita GDP and capital per person relative to the U.S. values.

b)In column 5, use the production model (with a capital exponent of 1/3) to compute

predicted per capita GDP for each country relative to the United States, assuming there

are no TFP differences.

c)In column 6, compute the level of TFP for each country that is needed to match up the

model and the data.

d)Why do you think that A is close to one for some countries, but not for others?

In 2014 dollars Relative to the U.S. values (U.S. 1) Capital per Per capita Capital per Per capita predicted Implied TFP to match data A GDP 51,958 43,376 37,360 34,961 20,074 2,971 GDP person United States 141,841 128,667 162,207 120,472 53.821 4,686 person Canada France South Korea Argentin:a Kenya

Answer 1

a).

Here we have given the values of “capital per person” and “Per capita GDP” for six different countries. So, here the “capital per person relative to U.S.” for different countries is the ratio of it’s own “capital per person” to “US”. Similarly, the “per capita GDP relative to U.S.” for different countries is the ratio of it’s own “per capita GDP” to “US”. So, on the basis of the given information we can calculate all these values.

b).

Now, the capital exponent is “1/3”, => labor exponent is “2/3”. So, the production function is given by, “Y=A*K^1/3*L^2/3”, => “y = A*k^1/3” in per worker form. Now, TFP factor is same for all country, => if want to get the predicted relative per capita GDP, then “A” term will cancel out for all country with US. So, the “predicted y” will be “capital per worker for different country relative to US” with exponent “1/3”. So, on the basis for the information in column “3” we can find out “5”.

c).

Now, to match the given data the TFP is the ratio of “actual y” to “predicted y”. So, on the basis of “4” and “5” we can get the “A”.

d).

Now, as we know that TFP is the ratio of “actual y” to “predicted y”, => if “A” is close to “1”, => “actual y” is close to “predicted y” => technological improvement is more or less same than expected. Similarly, if “A” is less than “1”, => “actual y” is less than the “predicted y”, => technological improvement is less than expected.