Homework $3$

Problem $1.($Each part is $10$ points$)$

A firm can employ capital $($k$)$ and labor $(1)$ to produce output using the following production function:

f$($k$,$ l$)=4$k $+1$

$(2)$

The price of capital is r $=$ $$8,$ and the price of labor is w $=$ $$4.$

$($a$)$ What input combination should be the firm use to produce q units of output?

$($b$)$ What is the firm's total cost of production as a function of the amount of output, q$?$

$($c$)$ What is its marginal and average cost of production?