Suppose the Country of Prescott Has the Production Function Y $$\begin{array} { c c c c } \text { Year } & Y & K & N \\\hline 2002 & 2000 & 1700 & 70 \\2003 & 2100 & 1785 & 75\end{array}$$

Essay

Suppose the country of Prescott has the production function Y = AK^0.25N^0.75. The following table shows Prescott's macroeconomic data for 2002 and 2003: $$\begin{array} { c c c c } \text { Year } & Y & K & N \\\hline 2002 & 2000 & 1700 & 70 \\2003 & 2100 & 1785 & 75\end{array}$$ a. By how much did productivity grow between 2002 and 2003?
b. If productivity remains constant from 2003 to 2004 and the labour force increases from 75 to 80, how large will the capital stock need to be to produce output of 2200 in 2004?