Suppose the Productivity Function Is Given By $\frac { Y } { L } = f \left( \frac { K } { L } , T \right)$

question 28

Essay

Suppose the productivity function is given by $\frac { Y } { L } = f \left( \frac { K } { L } , T \right)$ .
(A) Draw a graph that shaws the relatinghp between protuctivity and capital per haur of wark. What assumptinn are yau malang about the returns to capital? please explain.
pick an initial paint an your productivity function and label the paints $\frac { Y } { L _ { 0 } }$

(B) and $\frac { L } { L _ { 0 } }$

(C) Fill in the four blarks in the following table.

$\begin{array}{|l|l|l|l|}\hline & \begin{array}{l}\text { Productivity } \\\text { Growth }\end{array} & \begin{array}{l}\text { Growth Capital } \\\text { per hour Work }\end{array} & \begin{array}{l}\text { T echnology } \\\text { Growth }\end{array} \\\hline \text { Scenario } 1 & 2 \% & 3 \% & \\\hline \text { Scenario } 2 & 1 \% & & 1 \% \\\hline \text { Scenario } 3 & & -3 \% & 1 \% \\\hline \text { Scenario 4 } & 1 \% & & 2 \% \\\hline\end{array}$

(D) For prowth scenario 1, label the new levels of productivity and capital per hour af wark on your graph Exglain briefly.
(E) For prowth scenario 3, label the new levels of productivity and capital per hour af wark on your praph. Please draw a separate graph for this part. Explain briefly.
(F) For each of the four scenarios, identify whether labar and capital are prowing at the same rate, whether labor is prowing faster than capital or whether capital is growing fazter than labor.