6) Calloway Shirt Manufacturers sells knit shirts in two sub-markets. In one sub-market, the shirts carry Calloway's popular label and breast logo and receive a substantial price premium. The other sub-market is targeted toward more price conscious consumers who buy the shirts without a breast logo, and the shirts are labeled with the name Archwood. The retail price of the shirts carrying the Calloway label is $42.00 while the Archwood shirts sell for $25. Calloway's market research indicates a price elasticity of demand for the higher priced shirt of -2.0, and the elasticity of demand for the Archwood shirts is -4.0. Moreover, the research suggests that both elasticities are constant over broad ranges of output.

a. Are Calloway's current prices optimal?

b. Management considers the $25 price to be optimal and necessary to meet the competition. What price should the firm set for the Calloway label to achieve an optimal price ratio?