Why's A's expected profit $.04?
Without criticizing the other answer, I think an alternative approach illustrates—and helps assess—Posner's legal argument that "Society is also better off" with a breach of contract. To outline A's profit, one needs to consider the proceeds A would obtain for each widget. Thus, this alternative approach consists of comparing A's profit for various sales prices (meaning sales by A) with and without breach of contract, and then find the break-even sales price from A's perspective (which turns out to be $0.14 = $0.04 + $0.10).
At $0.10 apiece, A's total cost for 100,000 widgets is $10,000.
But due to the supplier's breach of contract, A experiences a total cost of $0.1*75,000 – $1,000 = $6,500 for the 75,000 delivered units (recall that the supplier pays A $1,000 for the breach). To A, the breach results in a unit cost of $0.086667.
At A's sales price of $0.10 per unit, the scenario with no breach of contract leads to profit = ($0.10 – $0.10)*100,000 = $0.00. With breach of contract, A's profit would be ($0.10 – $0.086667)*75,000 = $1,000 (>$0.00). Therefore, A is better off with the breach.
At A's sales price of $0.12 per unit, the scenario with no breach of contract leads to profit = ($0.12 – $0.10)*100,000 = $2,000. With breach of contract, A's profit would be ($0.12 – $0.086667)*75,000 = $2,500 (>$2,000). Therefore, A is better off with the breach.
Now suppose A's sales price is $0.20 per unit. The scenario with no breach of contract leads to profit = ($0.20 – $0.10)*100,000 = $10,000. With breach of contract, A's profit would be ($0.20 – $0.086667)*75,000 = $8,500 (< $10,000). Thus, in this case, the breach hurts A's profit.
In this example, it turns out that the break-even sales price is $0.14 per unit. Indeed, the scenario with no breach leads to profit = ($0.14 – $0.10)*100,000 = $4,000, and with breach of contract, A's profit ($0.14 – $0.086667)*75,000 = $4,000. That is, at a sales price of $0.14 per unit, A is indifferent between the breach and the no-breach scenarios.
Essentially, it is a matter of solving for x the equation (x – $0.10)*100,000 = (x – $0.086667)*75,000.
Hence, x = $0.14. A benefits (loses) from the breach as long as the sales price is lower (greater) than $0.14.
Strictly speaking, it is not that a breach itself makes society better off. The so-called "enhancement" of valued use (what Posner describes as "[upgrading] widgets from a lower valued to a higher valued use") due to a breach takes place only inasmuch as B subsidizes that "enhancement" by paying a premium for the breach he incentivized.
But Posner's questionable conclusion (that society is "better off" with the breach) misses one ramification. In exchange for the aforementioned "enhancement", the breach is overall detrimental from the standpoints of subsequent formation of contracts and the predictability of their performance:
- The supplier's inability to fulfill its contract with A will tend
to make A more uncertain about future agreements; and
- in turn, A's partial inability to deliver (namely, per the missing 25,000 units) tends to have on his customers the same effect that the
supplier's breach tends to have on A with respect to the supplier.
This sort of domino effect contravenes or weakens the contract law premise that a party knowingly subjects himself to a set of circumstances.
Also, Posner's term of "expected" profit is somewhat misleading because this has nothing to do with probabilities.
Just to be clear, I don't mean any of the above in a derogatory way toward former Judge Posner. In fact, he is one of the very few members of the judiciary I consider actually honorable. Sadly, it was his integrity and his indefatigable diligence what alienated his crooked peers in judicial office.