## Saturday, September 08, 2007

### Who Gets the Surplus?

Defs:

TR = total revenue to the firm
CS = consumer surplus (Wiki)
PS = producer surplus (Wiki)

1. If the price is set at \$600:

CS = A
PS = B + C + E
TR = B + C + E +G

2. If the price is set at \$400:

CS = A + B + C + D
PS = E + F
TR = E + F + G + H

3. If the price is set at \$600, then dropped to \$400:

CS = A + D
PS = B + C + E + F
TR = B + C + E + F + G + H

4. If there is a \$100 rebate to those who paid \$600:

CS = A + B + D
PS = C + E + F
TR = C + E + F + G + H

Change due to two-part pricing strategy (compare 2 to 3):

ΔCS = -(B+C)
ΔPS =  +((B+C)

Change due to rebate (Compare 3 to 4):

ΔCS = +B
ΔPS = -B

The dynamic two-part pricing strategy captures B+C for producers, and the rebate gives B back to consumers. For numbers, this article says iPhone sales at the end of September are projected to be 600,000-720,000, optimistically a million, and will reach 4,500,000 by the end of the year. I can't vouch for the accuracy of the projections, but based on those numbers, and the reports that the price cuts are in anticipation of the Holiday season, Q1=500,000 and Q2=4,500,000 seems reasonable. This then gives B = \$50,000,000, and B+C = \$100,000,000.

The pricing strategy could have been planned from the start, but it could also be that none of this is intentional, i.e. that demand was projected to be higher and the price cut is in recognition of the faulty forecast. The Street says:

Steve Jobs got up at a press conference, unexpectedly said that he was slashing the price of the iPhone and promptly declared victory, saying that the the move was one made out of strength and that it would push sales. ...

Now, if you can name a product in the annals of commerce that was introduced to great fanfare and shortly afterward had its price slashed to ribbons where that worked out to be a good thing, well, do let me know.

Investor's Business Daily highlights the thoughts -- and I use that term lightly -- of an analyst who essentially says: This was the plan all along, to take an ax to the price by a factor of a third. Uh, dude, if it was the plan all along, they sure didn't account for the rebellion of the loyal Apple customers who waited in line for the higher-priced iPhone weeks back. Jobs had to rush out an apology and store credit to those suckers.

Clearly this analyst does not believe it was not an intentional strategy, though I'll note that the explanation above shows that an intentional price cut doesn't necessarily make the company worse off, though the \$50 million dollar gain after the rebate would have to be balanced against any future costs due to unhappy customers.

[Note: the measurement of producer surplus depends upon the assumption that \$400 is the competitive equilibrium price. The actual equilibrium price could be lower, e.g. there could be a three-part strategy where the price falls to \$350 in a few months. It's easy to see how to extend the analysis to handle these cases and the basic message is the same, the price discrimination captures surplus for producers, and the rebate transfers some of the surplus back to consumers.]

[Update: See William Polley who predicted this might happen, and he says a bit more about the nature of the price discrimination.]

Posted by on Saturday, September 8, 2007 at 12:33 AM in Economics | Permalink  TrackBack (0)  Comments (12)

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