4. The empirical t of the production model (Chapter 4, Problem 5). The table below reports per capita GDP and capital per person in the year 2017 for 10 countries. You are asked to ll in the missing values. a) Given the values in columns 1 and 2, ll in columns 3 and 4. That is, compute per capita GDP and capital per person relative to the US. values. b) In column 5, use the production model (with the capital exponent equal to U3) to compute 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) Comment on the results you found. For example, what we learn from the calculation about these particular countries. Why might TF P be lower in Kenya than in Indonesia than in France? e) Explain what the model you used to calculate relative TFP assumed about production across countries. In 2011 dollars Relative to the U.S. values (U.S. = 1) (1) (2) (3) (4) (5) (6) Country Capital Per capita Capital Per capita Predicted Implied TFP per person GDP per person GDP y* to match data United States 175,075 54,807 1.000 1.000 1.000 1.000 Canada 153,390 42,540 France 136,004 38,841 Hong Kong 154,766 40,603 South Korea 142,891 36,521 Indonesia 26,620 10,598 Argentina 31,589 16,469 Mexico 41,866 17,070 Kenya 4,179 3,069 Ethiopia 2,938 1,596 If you are interested in other countries, let me know and I'll show you where to find the data. 5. The importance of capital versus TFP (Chapter 4, Problem 7). Create a new table containing only the last three columns of the table in problem 4. This time, instead of reporting the numbers relative to the U.S value, report the inverse of these numbers. For example, you should have found that per capita GDP in Kenya relative the that for the U.S. was 0.056. Express this number as a ratio of U.S. per capita GDP to Kenya's per capital GDP as 1/0.056 ~ 17.9. Fill in all three columns for each country. a) Explain in general how to interpret these numbers and in particular how the three columns are related. b) In the chapter, you read that about one quarter of the differences in per capita GDP across countries is due to differences in capital per person and about three quarters is due to differences in TFP. Carry out this calculation for Kenya. The U.S. is about 17.9 times richer than Kenya. What fraction of this is due to differences in capital per person and what fraction is due to differences in TFP? c) Repeat part (b) for Ethiopia