Shapes of Total Product Marginal Product and Average Product Curves

Total product, marginal product, and average product are fundamental concepts used to analyze the relationship between inputs and outputs in the production process. Understanding how these curves behave helps firms make optimal production decisions and resource allocation choices.

Formulas

The three key production measures are calculated as follows:

• Total Product (TP) The total quantity of output produced using all units of variable input
• Marginal Product (MP) $$\mathrm{MP = \frac{\Delta TP}{\Delta L}}$$
• Average Product (AP) $$\mathrm{AP = \frac{TP}{L}}$$

Where:

• ?TP Change in total product
• ?L Change in variable input (labor)
• L Units of variable input used

Example Calculation

Consider a bakery where labor is the variable input. With capital fixed at 2 ovens:

For the 3rd worker: $$\mathrm{MP = \frac{35 - 25}{3 - 2} = 10}$$ and $$\mathrm{AP = \frac{35}{3} = 11.7}$$

Shape of Total Product Curve

The total product curve exhibits three distinct stages:

Stage I: Increasing Returns

Initially, TP increases at an increasing rate due to efficient resource utilization and specialization. The curve shows a steep upward slope as each additional input unit contributes significantly to output.

Stage II: Diminishing Returns

TP continues to increase but at a decreasing rate. The law of diminishing returns sets in as fixed inputs become constraining factors. The curve maintains an upward slope but flattens progressively.

Stage III: Negative Returns

Beyond the maximum point, additional input units actually reduce total output due to overcrowding and coordination problems. The TP curve begins to slope downward, indicating negative productivity.

Shape of Marginal Product Curve

The MP curve is derived from the slope of the TP curve and follows a characteristic inverted U-shape:

Initially, MP rises as specialization and efficient input utilization increase productivity. The curve reaches its maximum when the TP curve has its steepest slope. After this peak, MP declines due to diminishing returns but remains positive while TP continues growing. Eventually, MP becomes negative when additional inputs reduce total output, corresponding to the declining portion of the TP curve.

Shape of Average Product Curve

The AP curve also follows an inverted U-shape but with specific relationships to the MP curve:

AP initially rises as total product increases faster than input quantity. The curve reaches its maximum at the point where AP equals MP. After this intersection, AP declines because MP falls below AP, pulling the average down. The AP curve always intersects the MP curve at AP's maximum point.

Key Relationships Between Curves

• When MP > AP Average product is rising
• When MP = AP Average product is at maximum
• When MP Average product is falling
• MP reaches maximum before AP This occurs at the inflection point of TP curve

Real-World Applications

Understanding these curve shapes helps businesses optimize production by identifying the most efficient input levels. Manufacturers use this analysis to determine optimal workforce size, farmers apply it to fertilizer usage decisions, and service companies use it for staffing optimization. The curves also guide capacity planning and help avoid the inefficient negative returns stage.

Conclusion

The shapes of TP, MP, and AP curves reveal crucial insights about production efficiency and optimal resource allocation. These relationships help firms maximize output while minimizing costs through informed decision-making about input levels.

FAQs

Q1. What is meant by total product?

Total product refers to the total quantity of output produced by a firm using all available inputs during a specific time period.

Q2. What is the shape of the marginal product curve?

The MP curve initially rises, reaches a maximum, and then declines before becoming negative, forming an inverted U-shape.

Q3. What is the shape of the average product curve?

The AP curve initially rises, reaches a peak where it intersects with MP, and then gradually declines.

Q4. Why does the marginal product eventually become negative?

Marginal product becomes negative when additional input units create inefficiencies, overcrowding, or coordination problems that actually reduce total output.

Q5. At what point do AP and MP curves intersect?

The AP and MP curves intersect at the maximum point of the average product curve, where AP = MP.