If the price elasticity of demand for a firm' s product is -4, the firm's profit-maximising mark-up on price is:

Question

BlackTom AI · Accepted Answer

To approach this, we recall the relationship between monopoly pricing and demand elasticity. When a firm faces a downward-sloping demand with constant elasticity, the Lerner index L = (P − MC)/P equals −1/ε, where ε is the price elasticity of demand (a negative value in standard notation).

Option a (100%): This would imply L = 1, which corresponds to ε = −1. That is, the elasticity needed for a 100% markup is far from the given ε = −4, so this is not correct.

Option b (50%): A Lerner index of 0.50 would require ε = −2. Since the elasticity is −4, the required markup is smaller than 50%, so this option overstates the permissible markup.

Option c (33%): A 33% markup corresponds to a Lerner index of 0.33, which would imply ε ≈ −3.03. While that’s closer, the exact given elasticity is −4, so this underestimates the precision for ε = −4.

Option d (25%): Here the Lerner index is 0.25, which directly matches ε = −4 via L = −1/ε = −1/(−4) = 0.25. This yields P − MC = 0.25P, i.e., a 25% markup on price.

Putting it together, the correct interpretation for a price elasticity of −4 is a 25% markup on price, while the other options correspond to other elasticity values and do not align with ε = −4.

If the price elasticity of demand for a firm' s product is -4, the firm's profit-maximising mark-up on price is:

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