What's the price of corn in your meat? Less than you think.

In my OpEd last week I had a lot of back and fourth with the editor.  I probably had too many statistics and my first draft was just too long.  I also should have provided background information up front for the statistics I wanted to present.

One thing that got dropped in the process was an explanation for why retail food prices will rise so little even though corn prices have increased 60 percent.  So much of our food is ultimately derived from corn, or from other commodities like wheat and soybeans whose prices track corn prices fairly closely.  But it still makes little difference.

Take meat, for example.  There are only 3-5 pounds of corn used to make an additional pound of beef, and between 2 and 3 pounds of corn for a pound of chicken or pork.   The calculation isn't particularly straightforward, but these numbers are probably about right ``on the margin," as economists like to say. This can vary a bit from operation to operation or how it's measured, but feed use efficiency has risen a lot over the last couple decades with the growth of confined animal feeding operations, or CAFOs.

Let's says 5 pounds of corn per pound of meat.  There are 56 pounds of corn in a bushel and since June prices have increased from about $5 to about $8 per bushel.  This means the amount corn in your quarter-pound burger have increased from about 11 cents to about 18 cents.  If there is market power by processing companies or retailers, retail prices would go up by less than this amount (this is basic microeconomics, but I'll save the details for another time).  So, you'll have to squint to see the effect of this year's drought on prices at grocery stores and restaurants.

There are lots of complaints about CAFOs being inhumane for animals.  That may be, but they are also extremely efficient at using resources.  Without CAFOs, you would see bigger prices in all kinds of food, and this year's heat and drought would have caused a larger price spike.  We would also be using more land in crop production globally, and be using more fertilizers that pollute water and all manner of other environmental problems that follow from crop production.  Many environmentalists don't like CAFO's but they may well be doing more good for the environment than eating grass-fed beef, unless the high price of grass fed beef causes you to eat less.  (Granted, grass-fed beef is probably healthier.)

Anyhow, the main point is that commodities are a tiny share of retail prices in developed economies.  Prices of most everything, including food, is made up primarily of labor and capital costs, plus rents to producers and retailers with market power.  The big concern for high commodity prices in the developed world where the commodity share of food expenditures is much, much greater and people spend a much larger share of their income on food.

(cross posted at G-FEED)

Comments

  1. You may like to see What happened to global food prices which thinks about the consequences of the phenomenon described above, for the volatility of food prices.

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  2. "This means the amount corn in your quarter-pound burger have increased from about 11 cents to about 18 cents. If there is market power by processing companies or retailers, retail prices would go up by less than this amount (this is basic microeconomics, but I'll save the details for another time)."

    Details, please? If you work out a numerical example with linear demand curves then you'll get pass-through less than one, and with constant elasticity curves you'll get pass-through more than one.

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  3. Anonymous: If the slope of the MR curve is steeper than the demand curve, then this statement is true. We know MR is always below demand, and they both start at the same vertical intercept, so typically it will also be that the slope of the MR curve is steeper. I don't know of an example where this is not true. In the case of constant elasticity of demand, the slope of the MR curve is steeper than the demand curve by the ratio (1+e)/e where e is the elasticity of demand. You may want to double check your math.

    In any case, this also seems to roughly fit the facts

    http://www.ers.usda.gov/amber-waves/2011-june/food-commodity-cost-pass-through.aspx

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    Replies
    1. I'll buy the empirical argument, but I'm pretty confident in my math regarding constant elasticity demand curves. In the case of constant elasticity demand, the height of the MR curve is just a constant fraction of the height of the demand curve, and so the slope is a constant fraction as well. The fraction is between 0 and 1. Math below.

      Before I do any marginal revenue math, think about it this way. The monopoly mark-up equation for a general demand curve is P = MC / (1-1/|e|), where |e|>1 is the magnitude of the elasticity. (We have to have elastic demand or else you'd raise price to infinity). For constant elasticity of e=-2, then, the pricing rule would be P = 2 * MC. So when costs go up by a dollar, price goes up by two dollars.

      OK, math. Up to a constant factor, constant elasticity demand is of the form Q = P^e for elasticity e<-1, or -- writing price as a function of quantity -- P = Q^(1/e). (Here is a reference just so that we're on the same page about conventions for how we write elasticity: http://wpscms.pearsoncmg.com/aw_perloff_microecon_3/9/2365/605606.cw/index.html )
      Revenue is P * Q = Q * Q^(1/e) = Q^(1+1/e). Marginal revenue is the derivative of this with respect to Q, or (1+1/e) * Q^(1/e) = (1+1/e) * P. Recalling once again that e<-1, we have that 1+1/e is some number between 0 and 1. So marginal revenue is price, scaled down by a constant factor. The slope of MR at a given quantity is a factor (1+1/e) = (1-1/|e|)<1 of the slope of price.

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    2. Hmmm. Keep in mind what's on the vertical axis and what's on the horizontal axis. We economists are dyslexic and put our dependent variable on the horizontal axis ;-)

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    3. Quantity is on the horizontal axis, dollars (MR or Price) is on the vertical axis. Don't worry, I got that. As a function of quantity, P = Q^(1/e) and MR = k*Q^(1/e) for k = (1-1/|e|)<1 .

      Let's do this even more slowly. Tell me which step you disagree with. (1) Do you agree that if you as a monopolist face constant elasticity demand, where demand is elastic, you will set price equal to MC times a constant? (2) Do you agree that this constant is greater than one? (3) Do you agree that if MC then goes up by $1, you will increase price by more than $1?

      You don't seem to believe my math, but to confirm that I'm not crazy you can look at Question #1 of this random pdf I just googled: http://www.uh.edu/~ghong/fina6387/sol_10.PDF

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  4. Okay Anonymous (you should really use your real name): you're right, and I apologize. I'll admit I started from intuition and glossed over my math very quickly. Actually, my math was right, but then I interpreted it wrong. Here are my steps:

    Q = AP^e
    P = (Q/A)^(1/e)
    R = (1/A)^(1/e) Q^{(1+e)/e}
    MR = (1+e)/e (Q/A)^(1/e)
    = P (1+e)/e
    MC = MR
    so
    P = MC e/(1+e)

    And then I goofed by forgetting e was negative (and less than 1), so the numerator is in fact bigger than the denominator in e/(1+e).

    Now, let's check this against my earlier intuition: here neither the demand curve nor the MR curve ever intersect the vertical axis. And in the limit as Q goes to 0, MR is always the same proportion below the demand curve.

    In my defense, I would argue the constant elasticity is a dubious assumption in cases of imperfect competition. If a brand is priced reasonably close to the competition, then loyalty can matter. But I rather imagine substitution away from a good would accelerate the more a firm deviates from competitors' prices. This would imply a concave demand, not a super convex one. And if demand is weakly concave, or even a little convex, MR will be steeper than demand.

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    Replies
    1. Alright, we're finally on the same page. I get defensive when an economist makes a claim about "basic microeconomics" that I don't understand! (Meanwhile, you could say anything you want about basic macro and I'd believe it).

      Fun fact 1: log-linear demand has a constant markup, in dollars. That makes constant elasticity and log-linear demand good for problem set questions.

      Fun fact 2: your captchas are very difficult for me.

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