Analyzing Price Elasticity and Promotional Pricing Strategy
In this scenario, we will determine the promotional price that equates marginal revenue and marginal cost when the price elasticity of the good changes from -2 to -3 due to an end-of-aisle price promotion.
Given Information:
– Initial Price Elasticity (at normal price): -2
– New Price Elasticity (after promotion): -3
– Normal Price: $34
Initial Situation (Price Elasticity = -2):
In a competitive market, when price elasticity is -2, marginal revenue (MR) equals marginal cost (MC) for profit maximization. At the normal price of $34, MR = MC.
Calculating Initial Quantity and Revenue:
Given that initial price elasticity (ε) = -2, we know the relationship between price elasticity and marginal revenue (MR):
[ MR = P \times (1 + 1/\varepsilon) ]
Substitute the values into the formula:
[ MR = $34 \times (1 + 1/-2) = $34 \times 0.5 = $17 ]
Given that MR = MC at the normal price, MC = $17 per unit.
New Situation (Price Elasticity = -3):
When the price elasticity changes to -3 due to the promotion, we need to find the promotional price that equates MR and MC.
Calculating Promotional Price:
Given the new price elasticity (ε) = -3:
[ MR = P \times (1 + 1/\varepsilon) ]
[ $17 = P \times (1 + 1/-3) ]
[ $17 = P \times 0.67 ]
[ P = $17 / 0.67 ]
[ P ≈ $25.37 ]
Therefore, the promotional price that equates marginal revenue and marginal cost when the elasticity changes to -3 should be approximately $25.37. This pricing strategy aims to optimize profit while considering changes in consumer responsiveness to price variations. By adjusting prices strategically based on elasticity changes, businesses can enhance revenue and market competitiveness during promotional periods.
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