By Philip Elmer-DeWitt
June 3, 2013

FORTUNE — One of the fears that sent Apple’s (AAPL) stock price into a seven-month tailspin was concern that the company’s enviable profit margins — which had already taken a hit when it introduced a flurry of new products last fallĀ — could be hit again if it launches a lower-priced iPhone this fall.

Not to fear, writes Morgan Stanley’s Katy Huberty in a note to clients Monday.

According to her calculations, a lower-priced iPhone should — paradoxically — raise those margins.

The way she sees it, if Apple lowers the cost of owning an iPhone, more people will buy them. And because the profit margins on even a lower-cost iPhone are so much higher than the margins on Apple’s other products, the net effect will be to lift the company’s gross margin.

“Based on a 100M C2H13 unit build (vs. our current 77M) with 50% mix of a new low-priced iPhone at a $399 starting price point,” she writes in classic analyst telegraphese, “we see 6% gross profit dollar and 10bps gross profit margin upside to our C2H13 model.” [see spreadsheet above]

Profit margins for the current quarter could show a similar effect, she writes, as Apple experiments with lower regional price points on the old iPhone 4. In the spreadsheet below she shows that although iPhone 4 discounts could lower the device’s average selling price 14%, the net effect of selling more of them would be to lift the company’s gross margin for the June quarter 0.3 percentage points.

The spreadsheet shows one more paradox: If sales of iPad minis and Macs have slowed — as her market research suggests — gross margins for the June quarter could grow by as much as 0.9 percentage points.

It all has to do with the mix of products and the fact that iPhones — even the cheap ones — are so darned profitable.

How cheap will those new phones be? Huberty is expecting $399 without a carrier subsidy — about $6 less than the $405 average selling price of the flagship phones made by the leading Chinese smartphone manufacturers.

But the company has some wiggle room. Huberty’s model shows Apple’s gross profits increasing at any price above $349 and its gross margins increasing above $393.

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