One way to maintain exclusivity for a brand is to raise its price. That's what luxury fashion and leather goods maker Louis Vuitton did. The company did not want the

brand to become overexposed and too common, so it raised prices $15$ percent and is slowing its expansion in China. The Louis Vuitton brand is the largest contributor

to the company's $$13\mathrm{.}3$ billion revenue from its fashion and leather division, accounting for $$8$ billion of those sales. It might seem counterintuitive to want to encourage

fewer customers to purchase a company's products, but when price increases, so does the product's contribution margin, making each sale more profitable. Thus,

sales can drop and the company can still maintain the same profitability as before the price hike. If a company's original contribution margin was $45\%,$ calculate the

new contribution margin if price is increased $15\%.$

Set the initial price equal to $$1\mathrm{.}00.$ Then the variable cost is $$0\mathrm{.}55.($Round to the nearest cent.$)$

The new price will be $$1\mathrm{.}15.($Round to the nearest cent.$)$

The new contribution margin is $52\%.($Round to the nearest percent.$)$