Betty's Boutique is a small specialty retailer located in a suburban shopping mall. In setting the regular $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.

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 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 the appropriateness of a given pricing practice.

A. Use the arc price elasticity formula to estimate the price elasticity of demand for Betty's blouses

B. Determine Betty's optimal markup on cost using the arc price elasticity as an estimate of the point price elasticity of demand. Based upon relevant marginal costs, calculate Betty's optimal price. Explain.