initial $36 price for a new spring line of blouses, Betty's added a 50 percent markup on cost. Costs were estimated at $24 each: the $12 purchase price of each blouse, plus $6 in allocated variable overhead costs, plus an allocated fixed overhead charge of $6. Customer response was so strong that when Betty's raised prices from $36 to $39 per blouse, sales fell only from 54 to 46 blouses per week. Was Betty's initial $36 price optimal? Is the new $39 price suboptimal? If so, what is the optimal price?

At first blush, Betty's pricing policy seems clearly inappropriate. It is always improper to consider allocated fixed costs in setting prices for any good or service; only marginal or incremental costs should be included. However, by adjusting the amount of markup on cost or markup on price employed, Betty's can implicitly compensate for the inappropriate use of fully allocated costs. It is necessary to carefully analyze both the cost categories included and the markup percentages chosen before judging a given pricing practice.

To determine Betty's optimal markup, it is necessary to calculate an estimate of the point price elasticity of demand and relevant marginal cost, and then apply the optimal markup formula. Betty's standard cost per blouse includes the $12 purchase cost, plus $6 allocated variable costs, plus $6 fixed overhead charges. However, for pricing purposes, only the $12 purchase cost plus the allocated variable overhead charge of $6 are relevant. Thus, the relevant marginal cost for pricing purposes is $18 per blouse. The allocated fixed overhead charge of $6 is irrelevant for pricing purposes because fixed overhead costs are unaffected by blouse sales.

The $3 price increase to $39 represents a moderate 7.7 percent rise in price. Using the arc price elasticity formula, the implied arc price elasticity of demand for Betty's blouses is

If it can be assumed that this arc price elasticity of demand eP = -2 is the best available estimate of the current point price elasticity of demand, the $36 price reflects an optimal markup of 100 percent on relevant marginal costs of $18 because

Optimal Markup _ -1

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