Story about costs

1. Story about costs Let’s say I am thinking about buying a pizza oven that costs $1000. Also say that for every pizza I make it will cost me $1 in ingredients and electricity and labor. The last point I would make is that I can sell each pizza for $2. Let’s look at total revenue TR, total cost TC and profit ∏ at various levels of output Q. As we look at an example I want to point out some ideas that we might find useful later as well.

2. $ TR TC ∏ Q Q = 1000

3. You can see that if I can get sales up to 1000 units that I will get to a point of zero profit. At that point I would have covered the cost of each pizza ($1) and the price of the oven ($1000). If I can not sell 1000 units I will lose money and if I sell more than 1000 units I will make profit. If I am a profit maximizer I would try to sell as many units as possible. Now, instead of looking at the total amounts, let’s look at some concepts that are called marginal values. Marginal revenue MR equals the change in total revenue divided by the change in quantity as we change quantity 1 unit at a time. Marginal cost MC equals the change in total cost divided by the change in quantity as we change quantity 1 unit at a time.

4. Note that the MR as we go from 1 to 2 units is (4-2)/(2-2=1) = 2. As we go from 500 units to 501 units the MR is (1002 – 1000)/(501 – 500) = 2. So, the MR is always 2 in this example. I think you will see that the MC is always 1 in this example. $ MR MC Q Now, as we look at the marginal ideas here we do not see the curves cross. If I can sell additional units of pizza I add more to my revenue than my cost and thus my profit will increase (although until my output gets to 1000 units my profit, while increasing, will still be negative.)

5. Next I want to look at some concepts called average values. At any quantity level of output we can calculate average values. Average revenue AR at a quantity is the total revenue divided the quantity. In our example you can see the AR is always equal to $2 at every quantity. In fact, here the AR = price. Average total cost ATC is the total cost divided by the quantity. At Q = 1 ATC = 1001/1 = (1000 + 1)/1 = (1000/1) + (1/1) = 1001 At Q = 2 ATC = 1002/2 = (1000 + 2)/2 = (1000/2) + (2/2) = 501 At Q = 3 ATC = 1003/3 = (1000 + 3)/3 = (1000/3) + (3/3) = 334.33 AFC AVC

6. In the example you can see the ATC falls quickly. But I also separated out the cost of the oven and the cost of making each pizza. You can see that at each level of output the cost of the oven is fixed at $1000. When a cost does not change as the level of output changes we say the cost is a fixed cost. So the oven cost is a total fixed cost TFC and the AFC = TFC/Q and this is what is falling quickly as Q is added. The other cost “inside” the TC is the total variable cost TVC. This is the result of the cost of the ingredients and electricity and labor to make each pizza. The average variable cost AVC turns out to always by $1 here. With this TC broken up into TFC and TVC and the average cost concepts I want to show you some more graphs.

7. $ $ TC TVC TFC ATC AVC Q AFC Q Here I have broken down the TC into TFC and TVC. Here I have indicated what each average curve would look like. Note the difference between the ATC and AVC is the AFC. In econ we know that ATC = AFC + AVC, so we often only show the ATC and AVC curves and note AFC = ATC – AVC.

8. $ ATC MR = AR = P AVC = MC Q In this graph I have put the average concepts and the marginal concepts in one graph. One thing we note is that P > AVC all the time. But, profit is only positive if we can get above 1000 units of output. In this example P = 2 and AVC = 1. This means on average that revenue can cover variable cost and have some left over to cover fixed cost. Cover the variable cost first.

9. In my example, if I changed the price I could sell the pizza at to 80 cents then I would have P = 0.80 and AVC = 1 (AVC is still 1 because that value is determined by ingredient, electricity and labor cost.) I hope you can see that I could never make positive profit here. If I sell 1250 units I will have TR = 1000 and that would cover my TFC, but again, I can never make positive profit. The reason profit can never be positive is because when I put the ingredients, electricity and labor into a pizza I have an AVC = $1 and the price is only 80 cents. So, the revenue doesn’t cover all the variable cost and this means revenue can not make any contribution to fixed cost. The goal is to have revenue cover all costs. But in econ we worry about covering variable cost first and then covering the fixed cost. In the short term if P > AVC we operate, even if losing money in total. If P < AVC, don’t bother.

10. Now I want to add to the story by first mentioning another story. Let’s call this story THE PRINCIPLE OF LOW HANGING FRUIT. Say you want to fill up bushel baskets with fruit at a fruit farm. The idea here is that the first baskets are filled with the fruit that may already be on the ground and on the low hanging limbs. But to get additional bushels one must get higher and higher into the tree. Because of this the time it takes to fill each basket gets longer and longer, which really means the additional baskets have higher and higher costs! In my pizza example I had each pizza cost the same amount. But maybe the more we try to make in a certain period of time the costs per pizza will rise. In economics we say that maybe there are diminishing returns to the variable input and thus marginal and average variable cost behave differently than I have shown here.

11. $ MC ATC AVC Q This graph is a more general way to express all the cost concepts I have mentioned so far.

12. The last point I would make is that when we try to explain happenings in the world we will come up with theories. Folks like theories to be as simple as possible and still get the point across. Sometimes this means make assumptions about the world that may not be totally accurate or true, but by making the assumption does not change the basic true understanding of the world. In sports econ we may say some cost concepts are constant when in fact they probably aren’t. But we can get through the story we want to tell with easier details and still get the same basic understanding of the world!!