Why Does the Lowest Point of an Average Total Cost Curve Cross the Marginal Cost Curve?
In economics, understanding the relationship between the average total cost (ATC) and marginal cost (MC) is crucial for businesses and managers to optimize their production processes. The lowest point of the ATC curve, where the ATC is at its minimum, always intersects the MC curve. This intersection reveals an important relationship between costs, which is essential for cost analysis and decision-making in production.
Key Concepts
Average Total Cost (ATC)
ATC is calculated as the total cost divided by the quantity of output produced.ATC Total Cost / Quantity of Output It reflects the per-unit cost of production. ATC can be expressed as a direct function of production volume: ATC (Total fixed cost Total variable cost) / Quantity of Output.
Marginal Cost (MC)
MC is the additional cost incurred from producing one more unit of output.MC Change in Total Cost / Change in Quantity of Output It measures the instantaneous rate of increase in total cost as production increases by one unit.
Explaining the Relationship
The basis of the relationship between ATC and MC lies in their respective definitions and how they interact with each other during the production process.
When MC is Less Than ATC
When the marginal cost is lower than the average total cost, producing one more unit of output reduces the ATC. For example, if you are producing toys, and the cost of producing one more toy is lower than the average cost of all toys produced so far, the average cost decreases. This is because the additional cost does not raise the average as much as the existing average.When MC is Greater Than ATC
When the marginal cost is higher than the average total cost, producing one more unit increases the ATC. If the cost of producing one more toy is higher than the average cost of all toys produced so far, the average cost goes up. This is because the additional cost has a greater impact on the average compared to existing average costs.The Point Where MC Equals ATC
The minimum point of the ATC curve is reached at the point where MC equals ATC. At this point, the additional cost of producing one more unit (MC) is exactly equal to the average cost of all produced units (ATC). Therefore, the ATC is neither increased nor decreased by the production of one more unit. This equilibrium means that the ATC is at its lowest point. Beyond this point, producing additional units would cause an increase in the average total cost.Example Analogy
To illustrate, imagine you roll a die. Initially, you might roll 1s, 2s, and 3s several times, and the average roll might be 2.5. If you then roll a 6, the average increases. Conversely, if you roll a 1, the average decreases. This is similar to the relationship between MC and ATC, where each additional unit of production affects the average cost.
If the last unit produced cost the same as the current average, then the average remains unchanged. If the last unit produced costs more, the average increases. If the last unit produced costs less, the average decreases.
Conclusion
The lowest point of the ATC curve intersects with the MC curve because, at this point, the cost of producing one more unit (MC) is exactly equal to the average cost of all units produced (ATC). Beyond this point, producing additional units will lead to an increase in the average total cost.
Understanding this relationship helps businesses to make informed decisions about production levels and cost optimization. By identifying the point at which ATC is minimized, businesses can ensure efficient production processes and cost management.