What is the relationship between average cost and marginal cost in production?

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In summary, the conversation discusses the relationship between the total cost of manufacturing a certain commodity, the average cost per unit, and the marginal cost. The speaker mentions taking the derivative of the cost function to find the minimum average cost per unit, but notes that it doesn't make sense for the value of x to be negative. They also mention their lack of knowledge in economics and ask for clarification on the term "marginal cost." Another person explains that average cost is the cost divided by the quantity produced, and marginal cost is the derivative of the cost function. They suggest setting the equations equal to each other to find the value of x when the average cost per unit is equal to the marginal cost. The conversation ends with the note that this
  • #1
pattiecake
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Suppose the total cost (in dollars) of manufacturing x units of a certain commodity is C(x)= 3x^2+ 18x + 243. At what level of production is the average cost per unit the smallest? At what level of production is the average cost per unit equal to the marginal cost?

So I thought if you want the average cost per unit to be the smallest- all you have to do is take the derivitave of C(x)= 3x^2+ 18x + 243, then solve for the minima which is at x=-3. But in this case, it doesn't make sense for the x value to be negative.

But for the second part, i lack knowledge in the area of economics, so I'm not sure what value they want when they ask for "what level of production is the average cost per unit equal to the marginal cost". Are they talking about inflection points? Help!
 
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  • #2
differential cost

n : the increase or decrease in costs as a result of one more or one less unit of output [syn: marginal cost, incremental cost]
 
  • #3
marginal cost, from my damn economics teacher pounding into my head, is the one extra unit of whatever and its effects... But really, from that definition I have nothing to work with mathamatically, just parroting the book.. Damn teacher... Hope you can find what you need...


If you are studying to become an economist, this can be much of a problem...
 
  • #4
This makes me happy to be a double major in math and economics :)

Average cost is the cost divided by the quantity produced, or in your notation, C(x)/x . Do you see why? x is the number of units produced and C(x) is the cost. Thus you get C(x)/x = 3x + 18 + 243/x. Now to get this minimized you have to differentiate, then set it equal to zero. This shouldn't be too hard. You get 9 as an answer, but work it out for yourself.

Marginal cost is definitely your cost function differentiated, so I also don't see how x could be negative... could you have maybe copied down the problem wrong? For instance, if it was -18x instead of +18x, you'd get the same answer for your first question, and the other two questions would make more sense.
 
  • #5
*shakes head* nevermind, I forgot the exact wording of the question before. Marginal cost is the derivative of C(x). Thus, to get the second question correct, you simply set the equation we got in the first part equal to C'(x). Solving for x, you should get an answer of 9 once again.

Translated to economic terms, this makes perfect sense. If you ever take a college microeconomics course, you'll learn that the marginal cost curve always intersects the average total cost curve at its minimum.
 
  • #6
Heh... someone needs to review their stuff again... :( sorry I was no help.
 

What is the concept of minimum cost and marginal cost in economics?

In economics, minimum cost refers to the lowest possible cost necessary to produce a good or a service. It takes into account all the factors of production, such as labor, materials, and overhead costs. On the other hand, marginal cost is the change in total cost that results from producing one additional unit of a good or service. It is calculated by dividing the change in total cost by the change in the quantity produced.

How are minimum cost and marginal cost related?

Minimum cost and marginal cost are closely related because the minimum cost is the lowest amount a company can produce a good or service for, while marginal cost represents the cost of producing one additional unit. As a company increases its production, the marginal cost will eventually equal the minimum cost, indicating that the company is maximizing its production efficiency.

Why is it important for a company to understand minimum cost and marginal cost?

Understanding minimum cost and marginal cost allows a company to make informed decisions about production and pricing. By knowing the minimum cost, a company can determine the lowest price at which it can sell its goods or services, ensuring profitability. Marginal cost helps companies determine the optimal level of production and avoid overproduction, which can lead to unnecessary costs.

How can a company reduce its minimum cost and marginal cost?

There are several ways a company can reduce its minimum cost and marginal cost. One way is to increase efficiency in production by using technology or improving processes. Another way is to negotiate better prices with suppliers or find cheaper alternatives. Additionally, a company can reduce its labor costs by hiring more efficient workers or outsourcing certain tasks.

Are there any limitations or drawbacks to using minimum cost and marginal cost in decision-making?

While minimum cost and marginal cost can be helpful in decision-making, there are some limitations and drawbacks to consider. These measures do not take into account external factors, such as market demand or competition, which can impact a company's pricing and production decisions. Additionally, marginal cost assumes that all units are identical, but this may not always be the case in real-world production. It is important for companies to use these measures in conjunction with other factors when making decisions.

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