Chapter 6, Promotional Pricing Question

QUESTION:  In a supermarket, an end-of-aisle promotional display typically makes the demand more elastic (see link) by making customers more aware of price differences between products.  

Specifically, suppose that a promotional display changes the price elasticity of demand for a good from -2 to -3. If the normal price is $10, what should the promotional price be? 

ANSWER: 

• STEP 1: Use the optimal pricing formula from Chapter 6 to solve for Marginal Cost (MC) at the pre-promotional elasticity of -2.  
• (PRICE-MC)/PRICE=1/|Elasticity| 
• Margin=Target Margin 
• ($10-MC)/$10=1/2 
• $10-MC=$5 
• MC=$5 
• STEP 2: Use the optimal pricing formula to solve for the new price at elasticity of -3
• (Price-$5)/Price=1/3 
• 3*(Price-$5)=Price
• 2*Price=$15
• Price=$7.50
• CHECK ANSWER:  
• ($7.50-$5)/$7.50=1/3
• $2.50/$7.50=1/3
• 3*$2.50=$7.50
• $7.50=$7.50