The first column of the table below shows you the ratio real GDP per capita relative to the US level, across several countries. In the second column, you can see capital per capita (k) relative to the US level. Try to finish the table. Keep three decimal digits for your answer.

Country	GDP per capita (y)	Capital per capita (k)	Capital input k (1/3)	TFP (A)
US	1.000	1.000
Switzerland	1.147	1.416
UK	0.733	0.833
Japan	0.685	1.021
Italy	0.671	1.125
Spain	0.615	1.128
Brazil	0.336	0.458
South Africa	0.232	0.218

Note: Both GDP per capita and Capital per capita are the relative ratio to the levels of the US.

With the Cobb-Douglas production function we can calculate the value of national output or GDP (Y) with a combination of capital (K) and labor (L) inputs and total factor productivity (A).

Y = A * K * L^(1-);

At per capita level, we can rewrite Cobb-Douglas function as below. Here y = Y/L and k = K/L. Here we have GDP per capita (y) and capital per capita (k). Also we assume is the same.

y = A* k;

(1) Fill in the blanks (green color) of the values of capital input in the fourth column. Now you have the value of parameter = 1/3.

(2) Following the above question, now use GDP per capita (y) and capital per capita (k) to derive total factor of productivity (A) of each country. Fill in the blanks of pink color in the last column.

(3) Plot TFP (A) against GDP per capita (y). Is there any relationship between these two factors? More exactly, is it a positive or negative trend between them?

(4) Can you derive Cobb-Douglas function at per capita level using y and k from Cobb-Douglas function at aggregate level?

Y = A * K * L^(1-);