Question

If \(\mathrm{AVC}\) is declining, then _____. a) marginal cost must be less than AVC b) marginal cost must be greater than ATC c) AVC must be greater than AFC

Short answer

If the AVC is declining, then the marginal cost must be less than AVC. Hence, the correct answer is option 'a'.

Step-by-step solution

Examine the first option

The first option suggests that the MC must be less than AVC. As already stated, if an average (in this case, AVC) is decreasing, the next number (in this case, the MC) must be less than the current average. Therefore, the first option is correct.

Evaluate the second option

This option proposes that the MC must be greater than ATC. However, we only know that the AVC is declining, no information about ATC's behavior is given. Hence, we cannot infer anything about the relationship between MC and ATC solely from the declining AVC. Therefore, option 2 does not necessarily hold and is incorrect.

Assess the third option

The third option posits that AVC must be greater than AFC. The AFC tends to decrease as output increases, and it is not influenced by the AVC. As such, without additional information, it's impossible to establish a relationship between AVC and AFC solely based on the AVC's decline. Therefore, option three is incorrect. In conclusion, the correct answer is: "If the AVC is declining, then the marginal cost must be less than AVC." Thus option 'a' is the right answer.

Key concepts

Marginal Cost

Marginal cost (MC) is a fundamental concept in economics that represents the additional cost incurred by producing one more unit of a good or service. It's crucial to understand that MC is dynamic and changes with the level of production. When studying the behavior of MC in relation to average variable cost (AVC), we see a direct relationship. If the AVC is declining, this typically indicates that the MC must be lower than the AVC. This occurs because the addition of the MC, which is lower, brings down the average of the variable costs.

It is important for students to recognize that the MC can help predict the behavior of AVC. When the MC is below the AVC, we anticipate the AVC will continue to decrease with additional production, until the point where MC equals AVC. After that point, if MC begins to rise above AVC, the AVC will start to increase as well.

Average Total Cost

Average total cost (ATC) is the sum of all production costs divided by the quantity of goods produced. It includes both variable and fixed costs. Variable costs change with the level of output, whereas fixed costs remain constant regardless of output levels. The ATC curve typically starts high, decreases as production increases, and eventually rises again, creating a U-shaped curve.

Understanding the relationship between ATC and other cost measures is essential. The ATC is equal to the sum of AVC and average fixed cost (AFC). Therefore, when AVC is declining, it could impact the ATC depending on the behavior of AFC. If AVC is declining because of increasing production efficiency and if AFC is also decreasing (which it does as production increases), the ATC will likely follow a downward trend as well. However, one must always remember that without specific data on AFC or MC, one cannot make definitive statements about ATC based solely on the behavior of AVC.

Average Fixed Cost

Average fixed cost (AFC) is the fixed costs of production (costs that do not change with the level of output) divided by the quantity of output. As output increases, AFC decreases because the same amount of fixed costs is spread over a larger number of units, diminishing the cost per unit.

Because AFC is solely dependent on the output quantity and fixed costs, it does not directly relate to the AVC's behavior. Thus, a declining AVC does not imply a relationship with AFC. In the context of our exercise, this understanding helps to clarify why AFC is not necessarily greater than AVC when AVC is declining. Over time, with increased production and efficiency gains, both AVC and AFC may trend downward, which can lead to a decrease in ATC.