Explain the relationship between Average Product & Marginal Product, and Average Variable Cost & Marginal Cost with the help of diagrams.

Q. Explain the relationship between Average Product & Marginal Product, and Average Variable Cost & Marginal Cost with the help of diagrams.

The Relation

ship Between Average Product and Marginal Product, and Average Variable Cost and Marginal Cost

In the study of microeconomics, the concepts of Average Product (AP) and Marginal Product (MP), as well as Average Variable Cost (AVC) and Marginal Cost (MC), are fundamental to understanding production and cost behavior in the short run. These concepts play a crucial role in helping firms make decisions related to resource allocation, production levels, and pricing. Their relationships are deeply interconnected, and a clear understanding of these relationships is essential for analyzing firm behavior and efficiency.

I. Average Product (AP) and Marginal Product (MP)

1. Definition of Average Product (AP) and Marginal Product (MP)

· Average Product (AP): The average product is the output per unit of the variable input, typically labor. It is calculated by dividing total output (Q) by the number of units of the variable input (L):

$AP=Total Output (Q)Units of Variable Input (L)AP = \frac{Total\ Output\ (Q)}{Units\ of\ Variable\ Input\ (L)}$ AP=Units of Variable Input (L)Total Output (Q)

The average product reflects the efficiency with which a firm uses its variable input (e.g., labor) to produce output.

· Marginal Product (MP): The marginal product is the additional output produced by employing one more unit of the variable input, holding all other inputs constant. It is calculated by taking the change in total output (ΔQ) resulting from a small change in the variable input (ΔL):

$MP=ΔTotal OutputΔLaborMP = \frac{\Delta Total\ Output}{\Delta Labor}$ MP=ΔLaborΔTotal Output

Marginal product represents the increment in output that results from a small increase in input, indicating how much extra output is generated when an additional unit of labor is employed.

2. The Relationship Between AP and MP

The relationship between average product and marginal product is fundamental to understanding the efficiency of production. The behavior of these two variables is guided by the law of diminishing marginal returns, which states that as more units of a variable input (e.g., labor) are added to a fixed input (e.g., capital), the marginal product eventually begins to decline, while the average product initially rises, reaches a maximum, and then falls.

Here’s how the two are related:

· When MP > AP: If the marginal product is greater than the average product, it means that the additional units of labor are contributing more to total output than the average labor input, which causes the average product to rise. This occurs when each additional worker is more productive than the average of previous workers.

· When MP = AP: When the marginal product equals the average product, the average product is at its maximum. This is the point where additional labor has just enough effect to maintain the average product, and no further increases in AP occur from additional labor.

· When MP < AP: If the marginal product is less than the average product, it means that each additional worker is less productive than the average worker, leading to a decline in the average product. This typically occurs after the law of diminishing marginal returns has set in, meaning that the benefits of adding more labor diminish as the fixed input (such as capital) becomes over-utilized.

3. Graphical Representation of AP and MP

To illustrate the relationship between average product and marginal product, let’s consider a simple production function for a firm that uses labor as the variable input, holding capital constant. The typical shape of the AP and MP curves is as follows:

AP Curve: The average product curve starts at the origin, rises initially, reaches a maximum point, and then falls as more labor is added.
MP Curve: The marginal product curve starts at the origin, rises to a peak, and then falls, intersecting the AP curve at the point where the AP curve is at its maximum.

Here’s how you can visualize this:

1. Initial Increase in MP: At first, as labor is added, both average product and marginal product rise. This is because workers complement each other well with the fixed inputs, and the firm is experiencing increasing returns to labor.

2. Diminishing Returns: Eventually, however, marginal product begins to decline as more labor is added, following the law of diminishing marginal returns. After the MP reaches its maximum, the additional units of labor result in a decrease in MP.

3. AP Reaches Its Peak: The AP curve increases until it reaches its peak, where it intersects the MP curve. After this point, as MP falls, AP also begins to decrease, reflecting a reduction in the efficiency of adding more labor.

To plot these on a graph:

The x-axis represents the number of labor units.
The y-axis represents output (either average product or total output).
The AP curve rises, peaks, and then falls.
The MP curve rises, peaks, and then falls, intersecting the AP curve at the point where AP is maximized.

The point where MP intersects AP is significant because it marks the point of maximum average product.

II. Average Variable Cost (AVC) and Marginal Cost (MC)

1. Definition of Average Variable Cost (AVC) and Marginal Cost (MC)

· Average Variable Cost (AVC): The average variable cost is the total variable cost divided by the quantity of output produced. It shows how much the firm spends on variable inputs (e.g., labor, raw materials) per unit of output. The formula for AVC is:

$AVC=Total Variable Cost (TVC)Quantity of Output (Q)AVC = \frac{Total\ Variable\ Cost\ (TVC)}{Quantity\ of\ Output\ (Q)}$ AVC=Quantity of Output (Q)Total Variable Cost (TVC)

AVC reflects the per-unit cost of variable inputs used in production, which typically decreases as output increases due to economies of scale, and then increases as the firm faces diminishing returns.

· Marginal Cost (MC): Marginal cost is the additional cost incurred by producing one more unit of output. It is calculated as the change in total cost (ΔTC) resulting from a change in output (ΔQ). The formula for marginal cost is:

$MC=ΔTotal CostΔQuantity of OutputMC = \frac{\Delta Total\ Cost}{\Delta Quantity\ of\ Output}$ MC=ΔQuantity of OutputΔTotal Cost

Marginal cost represents the cost of producing one additional unit of output and is crucial for understanding how the cost structure of a firm changes as output increases.

2. The Relationship Between AVC and MC

The relationship between average variable cost and marginal cost is important because it reflects how costs change as output increases. The behavior of both AVC and MC is determined by the productivity of the firm’s variable inputs (e.g., labor). As output increases, both AVC and MC initially decrease due to increasing returns to scale but eventually start to increase as diminishing marginal returns set in.

Here’s how AVC and MC are related:

· When MC < AVC: When marginal cost is less than average variable cost, average variable cost is falling. This is because producing one more unit of output reduces the average cost of producing all units up to that point.

· When MC = AVC: When marginal cost equals average variable cost, average variable cost is at its minimum. This is the point where the firm has achieved the most efficient level of production with respect to variable costs, and any further increase in output will increase AVC.

· When MC > AVC: When marginal cost exceeds average variable cost, average variable cost is rising. This reflects the diminishing returns to the variable input as more output is produced. The firm is no longer benefiting from economies of scale in its production process, and each additional unit of output is becoming more expensive to produce.

3. Graphical Representation of AVC and MC

The relationship between AVC and MC can be represented on a graph as follows:

The x-axis represents the quantity of output produced.
The y-axis represents cost (either average variable cost or total cost).
The AVC curve typically has a U-shape, initially decreasing as output increases, then increasing after a certain point due to diminishing returns.
The MC curve intersects the AVC curve at the minimum point of the AVC curve. When the marginal cost is below average variable cost, AVC is falling; when MC is above AVC, AVC is rising.

The key point of intersection between the MC and AVC curves is where AVC is at its lowest, representing the most efficient level of production in terms of variable costs. The MC curve typically slopes upwards after the AVC curve reaches its minimum, reflecting the increasing costs due to diminishing marginal returns.

III. The Interrelationship Between AP and MP, and AVC and MC

The relationships between average product (AP) and marginal product (MP) on one hand, and average variable cost (AVC) and marginal cost (MC) on the other, can be understood as two sides of the same coin. The behavior of AP and MP directly impacts the shape of the cost curves, and the cost curves, in turn, reflect the productivity of the variable inputs in the production process.

1. AP and MP and Their Effect on Cost Curves:

o AP and MP affect the firm’s cost structure through their influence on the marginal cost and average variable cost. When marginal product is increasing, it leads to lower marginal costs because additional units of input are contributing more to output. When the marginal product starts to decline, the marginal cost begins to rise.

o Rising MP (increasing efficiency) corresponds to a falling MC (lower cost per additional unit of output), whereas falling MP (decreasing efficiency) corresponds to a rising MC (higher cost per additional unit of output).