Question

What is the relationship between marginal product and marginal cost? (Hint: Look at the curves.) Why do you suppose that is? Is this relationship the same in the long run as in the short run?

Short answer

The relationship between Marginal Product (MP) and Marginal Cost (MC) is inverse: as MP increases, MC decreases, and vice versa. This relationship is observable in their respective curves. In the short run, the relationship is influenced by the law of diminishing marginal returns, leading to an increase in MC as MP decreases. However, in the long run, as production capacity becomes adjustable, the relationship between MP and MC may differ from the short-run relationship.

Step-by-step solution

Define Marginal Product and Marginal Cost

The Marginal Product (MP) is the additional output produced as a result of adding one more unit of a certain input, holding all other inputs constant. It can be mathematically represented as: \[MP = \frac{\Delta Q}{\Delta L}\] Where \(Q\) is the output quantity and \(L\) represents the labor input used (in this case, for simplicity, we consider only labor as the changing input). The Marginal Cost (MC) is the additional cost incurred when producing one more unit of output. It can be mathematically represented as: \[MC = \frac{\Delta TC}{\Delta Q}\] Where \(TC\) is the total cost of producing output, and \(Q\) is the output quantity.

Relationship between Marginal Product and Marginal Cost

Now, let's establish the link between the two concepts: As the Marginal Product increases, it implies that with addition of each unit of input, more output is being produced. As the output is produced with less input, this will eventually lead to a decrease in the Marginal Cost, as you are effectively "doing more with less." This inverse relationship can be observed when plotting the Marginal Product and Marginal Cost curves. When the MP curve is above the MC curve, it indicates that the efficiency of the production process is increasing. On the other hand, when the MC curve is above the MP curve, it indicates that the efficiency of the production process is decreasing.

Examine the relationship in the short run and long run

In the short run, the production process is characterized by fixed inputs (such as capital) and variable inputs (such as labor). As per the law of diminishing marginal returns, the marginal product of a variable input decreases as more of it is used, eventually leading to a point where the addition of more units of input results in progressively lower increases in output. As a result, the Marginal Cost will increase in the short run as we reach the point of diminishing marginal returns. However, in the long run, all inputs become variable, and production capacity can be adjusted accordingly. Firms can alter the scale of production to achieve the desired level of output, which might lead to different levels of efficiency and thus, the relationship between Marginal Product and Marginal Cost might not remain the same as in the short run. #Conclusion# To summarize, there is an inverse relationship between Marginal Product and Marginal Cost: as the Marginal Product increases, the Marginal Cost decreases, and vice versa. This relationship can be observed on the curves representing both concepts. In the short run, the relationship is significantly influenced by the law of diminishing marginal returns. However, in the long run, as production capacity changes, the relationship between Marginal Product and Marginal Cost might differ from the short-run one.

Key concepts

Marginal Product (MP)

Understanding the Marginal Product (MP) is crucial for grasping the efficiency of production in an economic context. MP refers to the extra output gained from using an additional unit of an input, while keeping other inputs constant. MP is calculated using the formula:
\[MP = \frac{\Delta Q}{\Delta L}\]
where \(Q\) is the quantity of output and \(L\) is the labor input. The MP is a key metric in assessing how worker productivity shifts as more labor is added to the production process. Initially, adding more workers often leads to increased production, but as we will see with the law of diminishing marginal returns, this is not an indefinite trend.

Marginal Cost (MC)

Marginal Cost (MC), on the other hand, is a financial measure indicating how much costs will increase when an additional unit of output is produced. This concept is essential for firms as it helps in making decisions about production levels. The formula for MC is given by:
\[MC = \frac{\Delta TC}{\Delta Q}\]
where \(TC\) represents the total cost and \(Q\) is the quantity of output. In simpler terms, it measures the cost of producing 'one more' and is pivotal when evaluating business scalability and profitability. When more output is generated without a significant increase in costs, the MC tends to decrease, showcasing improved efficiency.

Law of Diminishing Marginal Returns

The law of diminishing marginal returns is a principle that plays a pivotal role in understanding how MP and MC interact. This law states that adding more of a production factor, such as labor, while holding other factors steady, will at some point yield progressively smaller increases in output.

Implications of the Law

• The initial increases in labor can lead to increased MP as workers may be used more effectively.
• Over time, as labor input continues to increase, the additional output generated by each new worker (MP) starts to fall.
• This decrease in MP eventually leads to an increase in MC since additional labor does not translate into proportionate output gains.

This concept explains why, after a certain point, employing more people or resources might not be as cost-effective as it initially appeared.

Short Run vs Long Run in Economics

Short run and long run are temporal concepts in economics that help delineate the flexibility a firm has in the production process. In the short run, certain inputs are fixed and cannot be altered. This fixed nature of inputs leads to the encounter with the law of diminishing marginal returns as described above.

Contrasting the Long Run

In the long run, all factors of production are variable, allowing firms to circumvent the fixed limits they face in the short run. This means the firm has the flexibility to adjust all inputs and scale their operations to efficiently meet demand.

• In the short run, production is constrained by fixed assets, which dictates the relationship between MP and MC.
• In the long run, adjustments in production capacity alter the efficiencies, potentially changing the inverse relationship between MP and MC observed in the short run.

This flexibility in the long run means that firms can responsively change their production methods and scale up or down as needed, ultimately impacting their costs and productivity differently than in the short run.