A$.$ Please refer to the Excel spread sheet $1$ to answer the following question. Sheet $1$ displays certain data for $8$ national macroeconomies. It should be helpful if you find the values of some variable as in the yellow area.

Which country has the biggest real GDP and which country has the smallest real GDP$?$

Calculate the dollar value of real GDP per worker or the average productivity in the excel spread sheet. Which country's APN is the biggest?

Assume the Cobb$-$Douglas aggregate production function for each country, with the capital share of $a=\frac{1}{3}$

and the labor share of $1-a=\frac{2}{3}.$ Derive the mathematical equation that describes MPK in terms of $y($per worker output$)$ and $k($per worker capital or capital$-$labor ratio$).$

$($Hint:

Divide the CD production function $Y=A{K}^{\frac{1}{3}}{N}^{\frac{2}{3}}$ by labor $(N)$ and rearrange to get the equation in

terms of $y$ and $k$ so that $y=f(k)$; lower case means per worker.

Derive the MPK $=$ dY$/$dK by taking derivative w$.$r$.$t K and rearrange them to express the MPK in terms of $k$

Combine $1$ and $2$ to find the MPK in terms of only $k$ and $y$

Then, find the value MPK for each country in the excel spread sheet. Which country's MPK is the biggest?

$4.$ Based on #$3($from the value MPK and hint $2),$ calculate TFP for each country. Which country has the highest and which country has the lowest?