Chapter 58, Problem 2FRQ

a)

To determine

The firm’s marginal cost at each quantity.

Explanation of Solution

Q (tomatoes)	Variable cost	Total cost	Marginal cost
0	$0	$14
1	16	30	16
2	22	36	6
3	30	44	8
4	42	56	12
5	58	72	16
6	78	92	20
7	102	116	24

Marginal cost is calculated as:

MC = TC_n-1-TC_n where TC_n-1 is the new total cost and TC_n is the old total cost

Then MC for first unit:

  $\begin{array}{l}= T{C}_{n-1}-T{C}_n{}_{}\hfill \\ =30-14\hfill \\ =16\hfill \end{array}$

MC for the second unit:

  $\begin{array}{l}= T{C}_{n-1}-T{C}_n{}_{}\hfill \\ =36-30\hfill \\ =6\hfill \end{array}$

MC for the third unit:

  $\begin{array}{l}= T{C}_{n-1}-T{C}_n{}_{}\hfill \\ =44-36\hfill \\ =8\hfill \end{array}$

MC for the fourth unit:

  $\begin{array}{l}= T{C}_{n-1}-T{C}_n{}_{}\hfill \\ =56-44\hfill \\ =12\hfill \end{array}$

MC for the fifth unit:

  $\begin{array}{l}= T{C}_{n-1}-T{C}_n{}_{}\hfill \\ =72-56\hfill \\ =16\hfill \end{array}$

MC for the sixth unit:

  $\begin{array}{l}= T{C}_{n-1}-T{C}_n{}_{}\hfill \\ =92-72\hfill \\ =20\hfill \end{array}$

MC for the seventh unit:

  $\begin{array}{l}= T{C}_{n-1}-T{C}_n{}_{}\hfill \\ =116-92\hfill \\ =24\hfill \end{array}$

Economics Concept Introduction

Introduction: The difference in overall production costs caused by creating or producing one more unit is known as the marginal cost.

The profit is calculated by subtracting the total cost from the total revenue of the product.

b)

To determine

The firm’s profit-maximizing level of output

Explanation of Solution

Q (tomatoes)	Variable cost	Total cost	Marginal cost	Total revenue	Profit
0	$0	$14
1	16	30	16	14	(16)
2	22	36	6	28	(8)
3	30	44	8	42	(2)
4	42	56	12	56	0
5	58	72	16	70	(2)
6	78	92	20	84	(8)
7	102	116	24	98	(18)

Total revenue is determined as

= Price×Quantity

1^st unit

  $\begin{array}{l}=14\times 1\\ =14\end{array}$

2^nd unit

  $\begin{array}{l}=14\times 2\\ =28\end{array}$

3^rd unit

  $\begin{array}{l}=14\times 3\\ =42\end{array}$

4^th unit

  $\begin{array}{l}=14\times 4\\ =56\end{array}$

5^th unit

  $\begin{array}{l}=14\times 5\\ =70\end{array}$

6^th unit

  $\begin{array}{l}=14\times 6\\ =84\end{array}$

7^th unit

  $\begin{array}{l}=14\times 7\\ =98\end{array}$

Then, profit is the difference of TC and TR where TR is the total revenue and TC is the total cost

  $\begin{array}{l}{1}^{st} unit\hfill \\ =14-30\hfill \\ =-16\hfill \\ \begin{array}{l}\\ 2^{nd} unit\end{array}\hfill \\ =28-36\hfill \\ =-8\hfill \\ \begin{array}{l}\\ 3^{rd} unit\end{array}\hfill \\ = 42-44\hfill \\ =-2\hfill \\ \begin{array}{l}\\ 4^{th} unit\end{array}\hfill \\ =56-56\hfill \\ =0\hfill \\ \begin{array}{l}\\ 5^{th} unit\end{array}\hfill \\ =70-72\hfill \\ =-2\hfill \end{array}$

  $\begin{array}{l}{6}^{th} unit\hfill \\ =84-92\hfill \\ \begin{array}{l}=-8\\ \end{array}\hfill \\ 7^{th} unit\hfill \\ =98-116\hfill \\ =-18\hfill \end{array}$

The firm’s profit-maximizing level of output would be at unit 4 because at this level of quantity the firm is experiencing the highest level of profit which is zero but from other units, the firm is experiencing loss.

Economics Concept Introduction

Introduction: The difference in overall production costs caused by creating or producing one more unit is known as the marginal cost.

The profit is calculated by subtracting the total cost from the total revenue of the product.

c)

To determine

Firm’s profit at the profit-maximizing level of output

Explanation of Solution

The firm’s maximum profit is at quantity 4 which means the firm’s profit at this quantity would be the difference between total revenue and total cost.

  $\begin{array}{l}=TR-TC\hfill \\ =\left(4X\$14\right)-\$56\hfill \\ =\$56-\$56\hfill \\ =0\hfill \end{array}$

Economics Concept Introduction

Introduction: The difference in overall production costs caused by creating or producing one more unit is known as the marginal cost.

The profit is calculated by subtracting the total cost from the total revenue of the product.