$3.$ Suppose that the aggregate production function is adequately modeled as a Cobb$-$Douglas

function $=\mathrm{.}3,$ the capital input grows at a $4\%$ rate, and the labor input grows at a $6\%$ rate.

$($These are, of course, exponential growth rates.$)$

a$.$ If real output grows at an $8\%$ rate, what is the growth rate in multifactor productivity?

b$.$ If multifactor productivity grows at a $1\%$ rate, how fast will real output grow?

c$.$ If multifactor productivity grows at a $1\%$ rate, at what rate is labor productivity $$ i$.$e$.,$

output per unit of labor used $$ growing?