Lesson Note on Production Possibility Curve: Productivity and Law of Variable Proportion for SS 2

Class: Senior Secondary School 2 (SS2 / SSS2)
Term: 1st Term
Week: 6
Age: 16 years
Duration: 45 minutes
Subject: Economics
Curriculum Theme: Production
Previous Lesson: Production Possibility Curve: Meaning, Plotting and Productivity.
Topic: THE PRODUCTION POSSIBILITY CURVE
Subject Matter: Concept of total productivity, concept of average productivity, concept of marginal productivity, laws of variable proportion

Specific Objectives

By the end of the lesson, pupils should be able to:

Cognitive Domain:

• Define total, average, and marginal productivity.
• State the formulas for calculating total, average, and marginal productivity.
• Explain the relationship between total, average, and marginal productivity.
• State and explain the Law of Variable Proportions.
• Identify the stages of production under the Law of Variable Proportions.

Affective Domain:

• Appreciate the importance of efficient resource allocation in production.
• Participate actively in discussions about productivity concepts.

Psychomotor Domain:

• Calculate total, average, and marginal productivity from given schedules.
• Sketch and interpret simple productivity curves (TP, AP, MP).

Social Domain:

• Collaborate with peers to solve problems related to productivity calculations.
• Communicate their understanding of productivity concepts clearly to others.

Reference Materials

The following resources were used in planning this lesson:

• Senior Secondary Schools Education Curriculum
• State Unified Scheme of Work
• Any standard Economics textbook for Senior Secondary Schools (e.g., Alika, I. J. (2018). Essential Economics for Senior Secondary Schools. Tonad Publishers.)
• https://www.economicsdiscussion.net/production-function/law-of-variable-proportions/31804
• https://www.investopedia.com/terms/p/production-possibility-frontier.asp

Instructional Materials

The teacher will teach this lesson with the aid of:

• Graphs illustrating productivity curves
• Tables/schedules showing input and output data
• Whiteboard/chalkboard
• Markers/chalk

Rationale for the Lesson

This lesson helps pupils understand how output changes when variable inputs are combined with fixed inputs. Understanding productivity concepts and the Law of Variable Proportions enables pupils to grasp fundamental principles of production and resource management in economics.

Prerequisite/Previous Knowledge

Pupils have a basic understanding of factors of production, production processes, and simple graphical representation.

Lesson Content/Board Summary

Concepts of Productivity and the Law of Variable Proportion

Introduction to Productivity

Productivity refers to the efficiency of production, typically measured as the amount of output produced per unit of input. It shows how effectively resources are utilized in the production process.

Total Productivity (TP)

Total productivity is the total amount of output produced by all units of a variable input combined with a fixed input. It represents the overall output level achieved.

Formula: TP = Total Output

Average Productivity (AP)

Average productivity is the output per unit of the variable input. It is calculated by dividing the total output by the number of units of the variable input used.

Formula: AP = Total Productivity (TP) / Units of Variable Input

Marginal Productivity (MP)

Marginal productivity is the additional output produced when one more unit of a variable input is added, while all other inputs remain constant. It measures the change in total output due to the last unit of input.

Formula: MP = Change in Total Productivity (ΔTP) / Change in Units of Variable Input (ΔVariable Input)

Relationship Between TP, AP, and MP

The relationship between TP, AP, and MP is important for understanding the stages of production:

• When MP is increasing, TP increases at an increasing rate. AP also increases.
• When MP is decreasing but positive, TP increases at a decreasing rate. AP may still be increasing initially, then starts to fall after intersecting MP.
• When MP is zero, TP is at its maximum.
• When MP is negative, TP starts to fall. AP continues to fall.
• MP intersects AP at the maximum point of AP.

Law of Variable Proportion (Law of Diminishing Returns)

The Law of Variable Proportion states that as more and more units of a variable input (e.g., labour) are added to a fixed input (e.g., land or capital), the total output will initially increase at an increasing rate, then increase at a diminishing rate, and eventually decline.

Assumptions:

• One input is variable, while others are fixed.
• Technology remains constant.
• The units of the variable input are homogeneous (identical).
• It applies to the short run.

Stages of Production:

1. Stage I: Increasing Returns

   In this stage, TP increases at an increasing rate, and MP is rising. AP is also rising. This occurs because the fixed input is underutilized, and adding more variable input leads to greater specialization and efficiency.

2. Stage II: Diminishing Returns

   In this stage, TP continues to increase but at a diminishing rate. MP starts to fall but remains positive. AP is still rising initially, then falls after intersecting MP. This is the most rational stage of production for a firm.

3. Stage III: Negative Returns

   In this stage, TP starts to decline, and MP becomes negative. AP continues to fall. Adding more variable input beyond this point leads to overcrowding, inefficiency, and a reduction in total output.

Worked Example: Calculating Productivity

Consider a firm with a fixed amount of land, adding labour:

Calculations:

• MP: For 1 unit of labour, MP = 10 – 0 = 10. For 2 units, MP = 25 – 10 = 15. For 3 units, MP = 45 – 25 = 20.
• AP: For 1 unit of labour, AP = 10 / 1 = 10. For 2 units, AP = 25 / 2 = 12.5. For 3 units, AP = 45 / 3 = 15.

Teaching Methods/Instructional Techniques

Discussion, Lecture, Demonstration, Question and Answer, Visual Aids

Instructional Procedures

Step 1: Introduction

Time: 5 minutes
Teaching Skill: Set Induction
Teacher’s Activity: The teacher greets the pupils and asks them to recall the factors of production and how they are combined to produce goods and services. The teacher then introduces the lesson by explaining that today’s lesson will focus on how efficiently these factors are used.
Pupils’ Activity: Pupils respond to the teacher’s questions and listen attentively.
Learning Point: Pupils are prepared for the new lesson and connect it to prior knowledge.

Step 2: Concept of Total Productivity

Time: 5 minutes
Teaching Skill: Explanation/Definition
Teacher’s Activity: The teacher defines Total Productivity (TP) and explains its significance as the total output produced. The teacher writes the definition and formula on the board.
Pupils’ Activity: Pupils listen, copy the definition and formula into their notes, and ask questions for clarity.
Learning Point: Pupils understand the concept and formula of Total Productivity.

Step 3: Concept of Average Productivity

Time: 5 minutes
Teaching Skill: Explanation/Calculation
Teacher’s Activity: The teacher defines Average Productivity (AP) and shows how it is calculated using the formula. The teacher uses a simple numerical example to demonstrate the calculation.
Pupils’ Activity: Pupils listen, copy the definition and formula, and attempt the example calculation.
Learning Point: Pupils understand the concept and calculation of Average Productivity.

Step 4: Concept of Marginal Productivity

Time: 5 minutes
Teaching Skill: Explanation/Calculation
Teacher’s Activity: The teacher defines Marginal Productivity (MP) as the additional output from one more unit of input. The teacher explains its formula and uses another simple numerical example to demonstrate its calculation.
Pupils’ Activity: Pupils listen, copy the definition and formula, and follow the example calculation.
Learning Point: Pupils understand the concept and calculation of Marginal Productivity.

Step 5: Relationship Between TP, AP, and MP

Time: 7 minutes
Teaching Skill: Diagram/Analysis
Teacher’s Activity: The teacher uses a table (like the one in the board summary) to illustrate the relationship between TP, AP, and MP. The teacher guides pupils to observe how changes in one affect the others, especially when MP is increasing, decreasing, zero, or negative.
Pupils’ Activity: Pupils study the table, observe the relationships, and ask clarifying questions.
Learning Point: Pupils grasp the interconnectedness of total, average, and marginal productivity.

Step 6: Law of Variable Proportion (Law of Diminishing Returns)

Time: 10 minutes
Teaching Skill: Explanation/Illustration
Teacher’s Activity: The teacher states the Law of Variable Proportion, explains its underlying assumptions, and describes the three stages of production (increasing returns, diminishing returns, negative returns) using the example table from the board summary. The teacher emphasizes why Stage II is considered the rational stage.
Pupils’ Activity: Pupils listen, take notes on the law, its assumptions, and the stages, and ask questions for deeper understanding.
Learning Point: Pupils understand the Law of Variable Proportion and its implications for production.

Step 7: Evaluation/Review

Time: 5 minutes
Teaching Skill: Questioning/Assessment
Teacher’s Activity: The teacher evaluates the learning by asking the following questions:

1. Define Total Productivity (TP), Average Productivity (AP), and Marginal Productivity (MP).
2. State the formula for calculating each type of productivity.
3. Explain the relationship between MP and TP when MP is zero.
4. State the Law of Variable Proportion and mention two of its assumptions.

Pupils’ Activity: Pupils answer orally and in writing.

Learning Point: Pupils demonstrate understanding of the lesson.

Step 8: Conclusion

Time: 3 minutes
Teaching Skill: Summarization
Teacher’s Activity: The teacher summarizes the key points of the lesson, reiterating the definitions of the productivity concepts and the stages of the Law of Variable Proportion. The teacher assigns homework: “Create a production schedule with at least 5 units of variable input and calculate TP, AP, and MP. Identify the stages of production.”
Pupils’ Activity: Pupils listen to the summary, ask any final questions, and note down the homework.
Learning Point: Pupils consolidate their learning and apply it in practice.

Lesson Keywords

• Total Productivity – The total output produced by all units of a variable input.
• Average Productivity – The output per unit of the variable input.
• Marginal Productivity – The additional output from adding one more unit of a variable input.
• Law of Variable Proportion – Economic principle stating that adding more variable input to a fixed input will eventually lead to diminishing returns.
• Diminishing Returns – A point at which the addition of an input leads to a decrease in the marginal output.

Differentiation

For pupils who grasp the concepts quickly, the teacher can challenge them to draw and interpret the productivity curves (TP, AP, MP) from the example schedule. For pupils needing more support, the teacher will provide additional guided examples and one-on-one assistance to ensure they understand the calculation of each productivity measure.

Note for teachers using this lesson plan

Ensure that pupils clearly understand the difference between fixed and variable inputs before introducing the Law of Variable Proportion. Emphasize the practical implications of diminishing returns in real-world production scenarios. Encourage pupils to use graph paper to plot the curves for better visualization.