Chapter 2, Problem 1P

Subpart (a):

To determine

The best production technique.

Explanation of Solution

The production technique is the allotment and arrangement of the economic resources as well as the other goods and services, into the production of the consumer goods and services which optimizes the cost and allocates the resources in an efficient manner. In this case, each of the production technique produces 5 units of output and thus each are equally productive. When the cost structure is analyzed, the technique 2 is the least cost combination ($13 compared to the $15 each under the technique 1 and technique 3). The technique 2 produces the output (5 units) similar to other two techniques and at a least cost of production ($13).

When the price of the soap bar declines to $2.75, it affects the revenue of the firm but it does not affect the cost of the firm. The revenue of the firm at a new price level can be calculated as follows:

$\begin{array}{c}\text{Revenue of the firm}=\text{Number of units produced}\times \text{Per unit price}\\ =5\times 2.75\\ =13.75\end{array}$

Thus, when the price decreases from $3 to $2.75, the revenue of the firm reduces to $13.75 from $15 but not the cost. Thus, the firm will continue to use the least cost combination of production, which is the technique 2 which provides the minimum profit to the firm with a low cost.

When there is an increase in price to $4 from $3, the revenue of the firm increases, but it does not affect the cost of the production. Thus, the firm will continue its production at the least cost combination and make use of the higher prices to increase the profit margin of the firm. Since, the technique 2 remains as the least cost combination production technique, the firm will continue its production using technique 2.

Similarly, when the price increases further to $5, the least cost production will help the business owners to maximize their profit margin which will lead to use the technique 2 for the production.

Economics Concept Introduction

Concept introduction:

Production technique: The production technique can be considered as the arrangement of the factors of production and the resources involved into the production of the consumer goods in such a way that it minimizes the cost of production and maximizes the profit maintaining a better work flow.

Subpart (b):

To determine

The number of bar soaps produced at $2 price.

Explanation of Solution

The total cost of production in the least cost combination of production is $13 which is under the technique 2. When the price falls from $3 to $2, the total revenue of the firm can be calculated as follows:

$\begin{array}{c}\text{Revenue of the firm}=\text{Number of units produced}\times \text{Per unit price}\\ =5\times 2\\ =10\end{array}$

Thus, the total revenue of the firm is lower than the total cost incurred by the firm in production. When the total revenue is lower than the cost of production, then, the firm will face the loss and thus, it is not profitable to carry on the production using any of the techniques at the price level of $2 per soap bar.

Economics Concept Introduction

Concept introduction:

Profitability of production: The profitability of production takes place when the total revenue is greater than the total cost of the production. The difference between the total revenue and the total cost in this situation is known as profit. When the total cost is higher than the total revenue, then the difference between the total cost and the total revenue is known as loss.

Subpart (c):

To determine

The Least profitable combination of production at price of $1 for each input.

Explanation of Solution

When the cost of production changes with per unit change in the price of the inputs, it will lead to the profitability of each production technology to change. When the price of each unit of factor declines to $1, we can calculate the total cost of production under each production technique as follows:

Resources	Price per unit of Resource
		Technique 1		Technique 2		Technique 3
		Units	Cost	Units	Cost	Units	Cost
Labor	$1	4	$4	2	$2	1	$1
Land	1	1	1	3	3	4	4
Capital	1	1	1	1	1	2	2
Entrepreneurial ability	1	1	1	1	1	1	1
Total cost of $15 worth bar soap			$7		$7		$8

From the table above, it can be easily identified that the technique which incurs high cost of production will be the least profitable combination. Here, technique 3 incurs a high price of production when each factor has a price of $1 in the economy.

Economics Concept Introduction

Concept Introduction:

Profitability of production: The profitability of production takes place when the total revenue is greater than the total cost of the production. The difference between the total revenue and the total cost in this situation is known as profit. When the total cost is higher than the total revenue, then the difference between the total cost and the total revenue is known as loss.

Subpart (d):

To determine

The Least profitable combination of production at price of $1 for each input.

Explanation of Solution

When the new production method which gives 3 units of output is introduced at the normal level prices of the factors of production which uses one unit of each factors of production, the cost and revenue of using the new production technique can be calculated as follows:

$\begin{array}{c}\text{Revenue of the firm}=\text{Number of units produced}\times \text{Per unit price}\\ =3\times 3\\ =9\end{array}$

The cost of production technique can be calculated as follows:

Resource	Price per unit of resource	Technique 4
		Unit	cost
Labor	$2	1	$2
Land	1	1	1
Capital	3	1	3
Entrepreneurial ability	3	1	3
Total cost of $15 worth bar soap			$9

Thus, from the above calculations, we can easily summarize that the new production technique involves the total cost of $9 and the total revenue of $9. . Thus, there is no economic profit for the firm to carry on its production using the technique 4. But the use of the technique 2 provides the firm with economic profit and thus, the firm will continue its production using the technique 2.

Economics Concept Introduction

Concept Introduction:

Profitability of production: The profitability of production takes place when the total revenue is greater than the total cost of the production. The difference between the total revenue and the total cost in this situation is known as profit. When the total cost is higher than the total revenue, then the difference between the total cost and the total revenue is known as loss.