We assume that the price set for the end-of-aisle item is the profit-maximizing price, that is, that the product is not a loss-leader or sale item. Then, if that is the case, we can use certain key relationships to determine the optimal new price after the elasticity change. The first is that, at the profit-maximizing level of output, the following condition holds:

• MR = MC,

where, MR is marginal revenue and MC is marginal cost.

At the profit-maximizing level of output, the price for the commodity will be read off the product demand curve. The second relationship or relevance is that between MR, product price (P) and the price-elasticity of demand for the commodity (e), which is expressed as follows:

• MR = P(1 + 1/e).

Using this relationship and the old value of e of -2, we can solve for MR and MC as follows:

• MR = MC = $10(1 + 1/-2) = $10(0.5) = $5.

So, MR and MC are both equal to $5 at the original value for e. MC, which is derived from the production and cost functions, does not change after the change in the value of e. Therefore, MR will also be $5 at the new profit-maximizing price after the change. Using this information, we can use the above elasticity relationship to calculate the new value for P as follows:

• MR = P(1 + 1/e)
• $5 = P(1 + 1/-3)
• P = $5/(0.666) = $7.5.

So, the new promotional price should be $7.50. What has happened is that the move of the product to the end-of-aisle promotional position has shifted the demand curve and made it more price elastic. This has resulted in a higher equilibrium quantity, established where MR equals the unchanged MC, and a lower price on the new demand curve at a point where e is higher in absolute value terms.