how would you prove that the average cost is a minimum at the value of x
where the average cost equals the marginal cost? shouldn't the min be where avg cost marginal cost?

Question

how would you prove that the average cost is a minimum at the value of x
where the average cost equals the marginal cost? shouldn't the min be where avg cost > marginal cost?

blacksteel · Answer

Assuming a constant marginal cost:
The marginal cost is the cost to produce one additional unit of your good or service. Hence, you cannot produce a unit of your good for less than the marginal cost. Therefore, the marginal cost is the minimum possible value for the average cost.

Hope this helps: Feel free to ask if you have any questions.

anonymous · Answer

is there a way to explain that with numbers? I have a really hard time seeing econ in words...

blacksteel · Answer

Okay, suppose the marginal cost is m, and we have a fixed cost of f. Then the cost to produce x units of a good is f + m*x. It should be clear then that the more of a good you produce, the closer the average cost gets to m, but the cost can never go below m.

In fact, in economics this is called economies of scale - in industries where f is a really big number, we see that small companies are not competitive because their average cost per unit is so high, even though their marginal cost is the same as big companies.

blacksteel · Answer

You'll also notice that if f is not 0, the average cost can never actually be the marginal cost, no matter how big x gets. So technically, if f > 0, m is a horizontal asymptote for the graph of average cost as a function of x, not actually the minimum value.