In his book, Prophet of Innovation: Joseph Schumpeter and Creative Destruction, business historian Thomas K. McCraw lays out a numerical example of economies of scale. Unfortunately, in doing so he confuses marginal and average cost. McCraw writes (pp. 52-53):
Let us assume that a steel mill turns out ten pounds per day. Because the mill’s furnace must use a great deal of fuel to generate the heat needed to produce any steel at all, the cost of producing the first pound might be, say, $10. But once the furnace is sufficiently hot, the mill’s operator can make additional steel by using just a little more fuel. So the average cost of producing the second pound might fall to $9, the third to $8, and so on, until the cost of the tenth pound is $1. The average cost of all ten pounds would then be the sum of $10 + $9 + $8 + $7 + $6 + $5 + $4 + $3 + $2 + $1 (which equals $55), divided by 10–that is $5.50.
You can get an average cost of 10 pounds being $5.50 if the marginal costs are $10, $9, etc., but then he should have said “marginal,” not “average.” Alternatively, he could have the cost of the first pound being $10 and then additional pounds after that having a constant marginal cost of, say, $5. Then the total cost of the 10 pounds would be $10 + 9*$5, for a total of $55. In other words you have constant marginal costs from 2 pounds on and the declining average cost throughout that McCraw needs for his argument. Indeed, this second alternative is more fitting with his verbal reasoning. It makes sense for the first pound to have a big cost and then have additional units cost a constant amount each.
READER COMMENTS
robert arbon
Jun 12 2009 at 3:09am
Funny, I read it differently. I took ‘average cost of producing the second pound’ to mean the cost of the second pound (the marginal cost in the sense that it’s the cost of producing the second one after the the first) will be on average $9. Surely whenever someone reports marginal costs it will be, in some sense, an average from analysing a production process on many different occaisions to determin said costs?
Put another way, if you looked at the true marginal costs each day they might well be stochastic and so averaging each marginal costs would be appropriate to calculate the marginal cost of the steel mill.
William
Jun 12 2009 at 9:15am
Robert’s right. This isn’t a mistake.
Greg
Jun 12 2009 at 1:23pm
I’ll buy the other commenters’ perspective on the use of average versus marginal. From a business perspective, the passage still comes off as a little economically illiterate. There’s no way costs would vary from $9 to $1 for the additional production. He should have broken the example down explicitly into fixed costs and variable costs rather than pulling decreasing numbers out of a hat.
Then if you want to get really fancy, also consider experience effects (i.e., supposedly every time total cumulative production doubles, you should be able to cut 10-30% of average cost because you just get better at figuring out how to manufacture product X efficiently).
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