Chapter 9, Problem 15CQ

(a)

To determine

Filling of table with marginal cost, average variable cost, average total cost, and the profit schedule.

Explanation of Solution

Marginal cost can be calculated using the following formula:

$\text{Marginal Cost}=\frac{\text{Change in Total cost}}{\text{Change in Total output}}$        (1)

Substitute the respective values in Equation (1) to calculate the marginal product for unit 1.

$\begin{array}{c}\text{MC}=\frac{\text{Change in Total cost}}{\text{Change in Total output}}\\ =\frac{\text{1200}-1000}{\text{1}-0}\\ =\frac{200}{1}\\ =200\end{array}$

The marginal cost for producing first output is $200.

Average variable cost can be calculated using the following formula:

$\text{Average variable cost}=\frac{\text{Total cost}-\text{Fixed cost}}{\text{Quantity}}$        (2)

Substitute the respective values in Equation (2) to calculate the average variable cost for unit 1.

$\begin{array}{c}\text{AVC}=\frac{\text{TC}-\text{FC}}{\text{Q}}\\ =\frac{1200-1000}{1}\\ =\frac{200}{1}\\ =200\end{array}$

The average variable cost for producing first output is $200.

Average total cost can be calculated using the following formula:

$\text{Average total cost}=\frac{\text{Total cost}}{\text{Quantity}}$        (3)

Substitute the respective values in Equation (3) to calculate the average total cost for unit 1.

$\begin{array}{c}\text{ATC}=\frac{\text{TC}}{\text{Q}}\\ =\frac{1200}{1}\\ =1200\end{array}$

The average total cost for producing first output is $1200.

Profit earned by the firm can be calculated using the following formula:

$\text{Profit}=\text{Total revenue}-\text{Total cost}$        (4)

Substitute the respective values in Equation (4) to calculate the Profit earned by the firm for unit 1.

$\begin{array}{c}\text{Profit}=\text{TR}-\text{TC}\\ =(\text{P}\times \text{Q})-\text{TC}\\ =(500\times 1)-\text{1200}\\ =500-\text{1200}\\ =(-700)\end{array}$ 

Thus, the profit earned by the firms for the first output is a loss by $700.

Use these values, which can fill the table as follows:

Table 1

Output (Tons per month)	Total cost	Price per ton	Marginal cost	Average variable cost	Average total cost	Profit (Monthly)
0	$1,000	$500	-	-	-	$1,000
1	$1,200	$500	$200	$200	$1,200	-$700
2	$1,350	$500	$150	$175	$675	-$350
3	$1,550	$500	$200	$183	$515.67	-$50
4	$1,900	$500	$350	$225	$475	$100
5	$2,300	$500	$400	$260	$460	$200
6	$2,750	$500	$450	$291.67	$458.33	$250
7	$3,250	$500	$500	$321.43	$464.29	$250
8	$3,800	$500	$550	$350	$475	$200
9	$4,400	$500	$600	$377.78	$488.89	$500
10	$5,150	$500	$750	$415	$515	-$150

(b)

To determine

Production of tomatoes when the tuckers are profit maximizers.

Explanation of Solution

A profit maximizing monopoly will produce its product when its marginal cost equals to its marginal revenue. According to the table selling six or seven ton of tomatoes, they get same $250 as profit.

(c)

To determine

Firms output level and the maximum profit, if the market price of tomatoes increases to $550.

Explanation of Solution

When the firm’s price of tomatoes increases to $550 per ton, the output produced by the firm may be increased from 7 to 8 ton. Then, its profit can be calculated as follows:

$\begin{array}{c}\text{Profit}=\text{TR}-\text{TC}\\ =(\text{P}\times \text{Q})-\text{TC}\\ =(550\times 8)-3,800\\ =4,400-3,800\\ =600\end{array}$

The profit earned by the firm is $600.

(d)

To determine

Production and profit of truck tomato farm if the price fell to $450per ton.

Explanation of Solution

When the firm’s price of tomatoes fell to $450 per ton, the output produced by the firm may be 6 ton. Then, its profit can be calculated as follows:

$\begin{array}{c}\text{Profit}=\text{TR}-\text{TC}\\ =(\text{P}\times \text{Q})-\text{TC}\\ =(450\times 6)-2,750\\ =2.700-2,750\\ =(-50)\end{array}$

There is no profit earned by the firm because by this production, it earns $50 of loss and it does not cover its average variable cost at price $450.