Statistics for Business: Decision Making and Analysis, 3rd Edition

... orange juice costs the chain $1 to stock and sell. The estimated elasticity from the least squares equation is − 1.75. If we substitute the estimated elasticity into the optimal pricing formula, the estimated optimal price is

$$c\gamma /\left(1+\gamma \right)=\$1\left(-1.75\right)/\left(1-1.75\right)=\$1\left(2.33\right)=\$2.33$$

At $3, selling the predicted 18 cartons earns 18 × $2 = $36 profit. At $2.33, say, predicted sales grow to about 28 cartons and earn a bit more profit, 28 × 1.33 = $37.24 per store.

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The chain would make higher profits by decreasing the price from the current $3 to near $2.33. Even though it makes less on each, the increased volume would generate more profit. The typical store sells 18 cartons at $3, giving profits of 18 × ($3 − $1) = $36 per store. At ...