Chapter 15, Problem 2P

Sub part (a):

To determine

The total cost, average total cost and the profit.

Explanation of Solution

The total cost can be calculated by adding all the fixed as well as the variable costs that the firm incurs during the process of production together, as follows:

$\text{Total Cost}=\text{Fixed costs}+\text{Variable costs}$ (1)

The average total cost is the average cost of producing a unit. It is calculated by dividing the total cost with the total output as follows:

$\text{Average Total Cost}=\frac{\text{Total cost}}{\text{Total output}}$ (2)

The profit is the excess revenue over the cost that the firm generates through the sale of the product. It can be calculated by subtracting the total cost from the total revenue.

Here, the fixed cost of capital of the firm is $1,000. The firm uses 100 units of labor and 450 units of raw materials. The cost of the raw materials and the labor is the variable cost of the firm. The cost of a unit of labor is $12 and that of raw material is $4 per unit. Thus, the total cost of producing 5,000 units of output can be calculated by adding the fixed costs as well as the variable costs together, using equation (1):

$\begin{array}{c}\text{Total Cost}=1,000+\left[\left(100\times 12\right)+\left(450\times 4\right)\right]\\ =1,000+\left[1,200+1,800\right]\\ =1,000+2,800\\ =4,000\end{array}$

Thus, the total cost of producing 5,000 units is $4,000. The average total cost can be calculated by dividing the total cost with the total output. The total cost is $4,000 and the total output is 5,000. Thus, the values can be substituted in equation (2) to calculate the average total cost as follows:

$\begin{array}{c}\text{Average Total Cost}=\frac{\text{4,000}}{\text{5,000}}\\ =0.80\end{array}$

Thus, the average total cost is $0.80.

Economics Concept Introduction

Concept introduction:

Total cost: Total cost is the summation of all the fixed as well as variable costs of the production.

Average total cost: Average total cost is the cost per unit, which can be calculated by dividing the total cost with the total output.

Sub part (b):

To determine

The total cost, average total cost and the profit.

Explanation of Solution

The quantity of labor used as well as the raw material used in the process of production is the same as before and thus, there is no change in the cost of production at all. Thus, the total cost of production remains the same; $4,000.

Since there is an increase in the total quantity of production, it will affect the average total cost of production. The total output increases to 6,000 and the total cost remains at $4,000. We can substitute these values in equation (2) to calculate the average total cost as follows:

$\begin{array}{c}\text{Average Total Cost}=\frac{\text{4,000}}{\text{6,000}}\\ =0.67\end{array}$

Thus, the average total cost is $0.67.

Economics Concept Introduction

Concept introduction:

Total cost: Total cost is the summation of all the fixed as well as variable costs of the production.

Average total cost: Average total cost is the cost per unit, which can be calculated by dividing the total cost with the total output.

Profit: It is the excess revenue over the cost.

Sub part (c):

To determine

The total cost, average total cost and the profit.

Explanation of Solution

The price per unit is given as $1. The total output in the first production process is 5,000. Thus, the total revenue can be calculated by multiplying the total output with per unit price as follows:

$\begin{array}{c}\text{Total Revenue}=\text{Total output}\times \text{Per unit price}\\ =5,000\times 1\\ =5,000\end{array}$

Thus, the total revenue from using the old method is $5,000. The total cost of production is $4,000 and thus, the total profit in the production can be calculated by subtracting the total cost from the total revenue as follows:

$\begin{array}{c}\text{Profit}=\text{Total Revenue}-\text{Total cost}\\ =5,000-4,000\\ =1,000\end{array}$

Thus, the profit is $1,000 from the old production process.

The total output increases to 6,000 in the modern production process and the price per unit remains the same. Thus, the total revenue from the modern production process can be calculated by multiplying the total output with the per unit price as follows:

$\begin{array}{c}\text{Total Revenue from new method}=6,000\times 1\\ =6,000\end{array}$

Thus, the total revenue from the new production process is $6,000. The total cost of production is $4,000 and thus, the total profit in the production can be calculated by subtracting the total cost from, total revenue as follows:

$\begin{array}{c}\text{Profit}=\text{Total Revenue}-\text{Total cost}\\ =6,000-4,000\\ =2,000\end{array}$

The difference in the revenue from the modern and the old production process is the profit of the firm from the improvement in the production process. Thus, the profit can be calculated by subtracting the old profit from the new profit as follows:

$\begin{array}{c}\text{Profit}={\text{Profit}}_{\text{New method}}-{\text{Profit}}_{\text{Old method}}\\ =2,000-1,000\\ =1,000\end{array}$

Thus, the profit from the improved production process is $1,000.

Economics Concept Introduction

Concept introduction:

Total cost: Total cost is the summation of all the fixed as well as variable costs of the production.

Average total cost: Average total cost is the cost per unit, which can be calculated by dividing the total cost with the total output.

Profit: It is the excess revenue over the cost.

Sub part (d):

To determine

The total cost, average total cost and the profit.

Explanation of Solution

There is only an additional profit of $1,000 for the firm while using the improved production process. When there is a one-time cost of implementation which is $1,100, there will be an increase in the total cost of production by $1,100 which will reduce the profit from $1,000. Thus, the firm will choose not to implement the progress when it considers only profit of 1 year.

When the firm considers future revenues, the one-time cost will only reduce the profit for the next year and for the rest of the life of the production, it will provide $1,000 more revenue than the old method. Thus, the firm will choose to implement the progress.

Economics Concept Introduction

Concept introduction:

Total cost: Total cost is the summation of all the fixed as well as variable costs of the production.

Average total cost: Average total cost is the cost per unit, which can be calculated by dividing the total cost with the total output.

Profit: It is the excess revenue over the cost.