You probably would have calculated it correctly; the average cost of one toy per year is the total cost -- $1,000,001 -- divided by 1.

Once you have that one right, try this one:
For that same factory, what is the average cost of producing 2 toys per year?

You are (most probably) again Correct!; the average cost of producing 2 toys per year is 500001 i.e. the total cost -- $1,000,002 -- divided by 2.

It's easy to confuse Average Cost with Marginal cost. Marginal cost is the cost of adding or subtracting one unit of output.

Table Representation of Average Cost: I'll use the Joan's Home Care numerical example from the preceding interactive tutorials.

The average cost of serving 3 patients, for example, is  3333

The average cost can tell you whether you are breaking even -- whether your total revenue is covering your total cost.

Suppose that the firm charges all of its patients the same price. 

Try this True or False question: The firm is making a profit if, and only if, the average cost is less than this price: Answer in "True" or "False"

The answer is 4 ; the lowest output rate at which Joan's makes a profit is 4 patients per year.

And, what is the highest output rate that's profitable for Joan's?

The answer is 8; the highest output rate at which Joan's makes a profit is 8 patients per year.

If you had trouble with those, better check your definitions of Revenue, Cost, and Profit.

Revenue : Total Revenue is the total amount of money received at any given output rate. It is the price multiplied by the quantity of output.

Cost: Total Cost is the cost of maintaining any given output rate. This generally comes from a table or a calculation, because it is the sum of the fixed cost and the variable cost.

The Break Even Point: The break even point is, in the usual usage, the lowest output level at which total revenue exceeds total cost.  That's because most new business fail by selling too little, not by selling too much.  The break even point tells you the minimum you have to do to make your enterprise viable.

Profit is positive if and only if average cost is less than the price patients pay (i.e. if average cost is less than $ 3200) Thus, we can judge whether the firm breaks even either by looking at total revenue and total cost or by looking at price and average cost.

That means you have two ways that you can present a break even analysis:

We can apply this principle to show what happens to the break even point in a competitive industry if more and more firms enter the market and drive the price down.

Let's start our example with a high price: $4200.

Question: What is Joan's break even point, based on that price and the costs above?

Question: Where does Joan's average cost bottom out? At what output rate is Joan's average cost minimized? 

True or false? : A firm should always choose the output level at which its average cost is the least.

Question: What is the number of patients that gives Joan's the most profit, if the price patients pay is $4200?

Answer: 8 is the highest output rate that has a marginal cost that is less than $4200. This is the most profitable output rate, even though the average cost at 8 is higher than at 7, 6, or 5.

I'm deliberately switching back and forth between Marginal Cost and Average Cost, to better bring out the distinction between them.

Question: Now what is Joan's break even number of patients, after the price has fallen to $3200?

Question: What is the top end of the profitable range, the most patients Joan's can serve and still make a profit, if the price patients pay is $3200? 

Question: What would be a price for which the break-even or make-profit output rate range would be just 5 to 6 patients per year? 

Answer: $ 2917-$ 3000; For any price from $2917 up to $3000, output rates of 5 and 6, and only those, are profitable or break even. Joan's output decision is narrowly constrained if the price is in this $2917-$3000 range.

As new firms flood into the home care market, the price patients have to pay will be bid down further and further.

Question: What price is so low that the best Joan's can do is just break even? 

Answer: 2900; At this price, Joan's has no choice but to see 5 patients per year, and the firm just breaks even.

If competition in the industry drives the price down this low, this will squeeze the profit out of the industry, assuming that Joan's costs are typical.

If the price falls this low, and profits disappear, new firms will stop entering this market, and some established ones may fold.; This will make the supply stop growing and the price stop falling.

In an ideal theoretical competitive market, the freedom to set up a new business firm guarantees that the consumers' demands for products and services will be met at the lowest possible costs and prices.

Those prices will be at (or just above) the minimum level of average cost.

This is called consumer sovereignty.

Innovation to stay ahead, temporarily: There's another way that Joan's might deal with a low price for her product. That would be to reduce her minimum average cost below $2900. A typical way to do that would be to buy labor-saving equipment. Her fixed cost would go up (paying off the loan that enabled her to buy the equipment), but variable cost would go down (less labor means less paying less in total wages.)

Answer: Yes; Some average costs are lower than before. There are several output rates at which the average cost is less than $2900.

Question: How many patients should Joan's serve to maximize profit at the $2900 price?

Answer: 8; With these lower costs, Joan's makes the most profit at an output rate of 8. It's the highest output rate before the marginal cost gets higher than $2900.

With the new cost-cutting technology, Joan's expands her output rate to 8.

Question: If all the firms in the industry adopt the new technology, so that all the firms have costs just like Joan's, then every firm will try to expand its output just as Joan's did. Which way will the price go?

Answer: The supply expansion, and consequent competition among the sellers, should force the price down.

My analysis assumes that there is price competition in this market. By contrast, Brown, M.L., Kessler, L.G., Reuter, F.G., "Is the Supply of Mammography Machines Outstripping Need and Demand?" Annals of Internal Medicine, October, 1, 1990, 113(7), pp. 547-552, found that prices of screening mammograms stayed high despite a great increase in supply, because there was no price competition. I am assuming a textbook type of perfect competition in the market that Joan's is in.

Question: Suppose, though, that competition doesn't work, and the price stays up at $2900. In that case, the firms will want to treat 8 patients each, but there won't be enough patients to go around. Many will have to settle for fewer than 8 patients. What is Joan's minimum break even output rate?

That should be plenty on the break even output rate and the profit maximizing output rate!