Question

If the units of variable input in a production process are \(1,2,3,4,\) and 5 and the corresponding total outputs are \(10,22,33,42,\) and 48 respectively, the marginal product of the fourth unit is a. 2 b. 6 c. 9 d. 42

Short answer

The marginal product of the fourth unit is 9 (option c).

Step-by-step solution

Understand the concept of marginal product

In the context of production processes, marginal product refers to the additional output produced when one more unit of input (variable) is added. In this exercise, we are given a set of variable inputs, and their corresponding total outputs.

Identify the total outputs for 3rd and 4th units

The total output for the 3rd unit is 33, and for the 4th unit, it is 42. We now need to identify the marginal product of the fourth unit, i.e., the additional output produced when the fourth unit is added.

Calculate the marginal product of the fourth unit

To find the marginal product of the fourth unit, subtract the total output of the 3rd unit from the total output of the 4th unit: Marginal Product = Total Output(4th unit) - Total Output(3rd unit) = 42 - 33 = 9

Identify the correct option

As per our calculation, the marginal product of the fourth unit is 9. Comparing this to the given options: a. 2 b. 6 c. 9 d. 42 The correct answer is option (c), 9.

Key concepts

Production Process

The production process in economics refers to the methods and operations used to produce goods and services. It involves the combination of various inputs, such as labor, materials, and machinery, to create outputs that are valued by consumers.

Understanding the production process is crucial as it helps businesses optimize operations, reduce costs, and increase profitability.

• It begins with the selection and acquisition of inputs.
• These inputs go through operations or processing units.
• Finally, they result in outputs which can be goods or services.

In this process, businesses often analyze how changes in input levels affect output levels, a key component of understanding productivity and efficiency.

Variable Input

A variable input is an input whose quantity can be changed in the short-run to influence the level of output. Labor is a classic example of a variable input because the workforce size can be increased or decreased depending on the production needs.

In a simple production scenario, other inputs like raw materials can also be considered variable inputs. Managing these inputs effectively allows businesses to adjust their production process to meet changing demand.

• Variable inputs can be altered quickly and easily.
• They offer flexibility to scale production up or down.
• Efficient use of variable inputs leads to cost-effectiveness.

By experimenting with different levels of variable inputs, businesses can determine the most efficient input combination for desired output levels.

Total Output

Total output is the cumulative amount of product or services produced by a firm or production process over a certain period. It reflects the aggregate production capability of the business when all inputs are utilized.

In the given exercise, total output is measured for varying levels of input, highlighting how output increases with additional input. Understanding total output helps businesses:

• Measure overall productivity and efficiency.
• Identify optimal output levels for maximum profitability.
• Evaluate the impact of scaling resources on production.

Calculating total output involves summing up all produced units, providing a clear picture of a company's performance and operational capacity.

Marginal Analysis

Marginal analysis is a decision-making tool used in economics to evaluate the benefits and costs of adding an additional unit of input or output. It plays a fundamental role in optimizing resource allocation and maximizing profits.

The exercise illustrates marginal analysis through the calculation of the marginal product, highlighting how each additional unit of input impacts total output.

• Marginal analysis helps in determining the efficiency of resource usage.
• It aids in understanding the diminishing returns as more inputs are added.
• Businesses use it to make informed production and investment decisions.

By focusing on the incremental changes, marginal analysis provides insights into the optimal level of resource deployment, guiding strategic choices in production and operations.