Chapter 11, Problem 11.1P

a)

To determine

To find: Area of land J should cut to maximize profit.

Explanation of Solution

Given:

Total cost:

  $\begin{array}{c}TC=0.1q^2+10q+50\\ MC=\frac{dTC}{dq}\\ MC=0.2q+10\end{array}$

Here,

  $\begin{array}{c}\mathrm{Pr}ice=\$20\\ TR=P\times q\\ TR=20q\end{array}$

Area of land J should cut to maximize its profit:

  $\begin{array}{c}MC=MR\\ 0.2q+10=20\\ 0.2q=20-10\\ q=\frac{10}{0.2}\\ q=50\end{array}$

b)

To determine

J’s minimum daily profit.

Explanation of Solution

Here,

  $\begin{array}{c}q=50\\ P=\$20\end{array}$

Therefore,

  $\begin{array}{c}TR=P\times q\\ TR=\$20\times 50\\ TR=\$1,000\end{array}$

And total cost is:

  $\begin{array}{c}TC=0.1q^2+10q+50\\ $ =0.1{(50)}^2+10(50)+50$=0.1(2500)+500+50\\ =250+500+50\\ =\$800\end{array}$

Therefore,

  $\begin{array}{c}\mathrm{Pr}ofit=TR-TC\\ =\$1,000-\$800\\ =\$200\end{array}$

c)

To determine

To draw: J’s supply curve.

Explanation of Solution

J is a price taker, so J’s supply curve will be equal to its marginal cost curve.

  $MC=0.2q+10$

Therefore,

  

Graph 1