Suppose the aggregate production function is Y $=$ K$$ L

$1-$ where $0<1.$

a$.$ Find the intensive form of the production function, y $=$ f$($k$),$ where y $$ Y$/$L and k $$ K$/$L

b$.$ Find the marginal product of labor and the marginal product of capital $($MPK $$Y$/$K$).$

Use words to describe the MPL and MPK$.$

c$.$ Find the marginal product of capital per worker $($MPk $$y$/$k$)$ and describe the MPk$.$

d$.$ Show that MPK $=$ MPk$.$

e$.$ Suppose $=1/3.$ If population growth is $3\%$ and the capital stock grows $6\%,$ use t