You own a small bookstore. You have hired a marketing firm to calculate your own price elasticity of demand and your advertising elasticity of demand. The firm has provided you with the relevant numbers regardless of minor adjustments in price or advertising budget. Your own price elasticity of demand is around -1.7, and your advertising elasticity of demand is around 0.05. How much should you mark-up your price over your marginal cost for your books?
A)By approximately a factor of 0.41.
B)By approximately a factor of 2.43.
C)By approximately a factor of 37 percent.
D)By approximately a factor of 70 percent.

Question

Quizplus · Accepted Answer

To calculate the optimal mark-up, we need to use the formula:

mark-up = -1/elasticity of demand

Using the given elasticity of demand for price, we get:

mark-up = -1/(-1.7) = 0.588

This means we should mark up our prices by 58.8% over our marginal cost.

To calculate the impact of advertising on prices, we need to use the formula:

percentage change in quantity demanded = elasticity of demand for advertising * percentage change in advertising

We know that the elasticity of demand for advertising is 0.05. Let's assume that we increase our advertising budget by 10%. Then the percentage change in advertising would be:

percentage change in advertising = 10%

Using the formula above, we get:

percentage change in quantity demanded = 0.05 * 10% = 0.005

This means that a 10% increase in advertising would lead to a 0.5% increase in quantity demanded.

Therefore, the optimal mark-up would be:

mark-up with advertising = 0.588 * (1 + 0.005) = 0.591

This means we should mark up our prices by 59.1% over our marginal cost when accounting for the effect of advertising.

Therefore, the answer is B, by approximately a factor of 2.43 (i.e. approximately 59.1%/24.3%). The formula for the optimal mark-up over marginal cost is (1 - (1/|PED|)) x (1/|AED|).

1. Substituting the values in the formula we get:
(1 - (1/|-1.7|)) x (1/|0.05|)
= 0.41 x 20 
= 8.2

2. Subtracting 1 from the result, we get the mark-up factor: 
8.2 - 1 = 7.2

Therefore, the optimal mark-up factor is approximately 2.43 (or 143%). This means that the price should be marked up by 143% over the marginal cost.

You Own a Small Bookstore