If the key to a financial analyst's heart is profit margin, then Apple did a good job yesterday of reassuring Wall Street with its roll out of new products. That's because it introduced new iPads with higher prices.

Apple's stock moved up this morning by about a half a percent, trading near $522, despite a falling broader market. This comes after Wall Street analysts had generally positive responses to yesterday's new product announcements.

Apple's product announcements focused on MacBooks and iPads, but the future of the iPad — and particularly the iPad mini — is the most important component for Apple. Analysts say that keeping pricing and boosting margins in the iPad and iPad Mini is crucial because that is the area in which Apple has been hurt the most in the past couple of years.

With the announcement of the iPad Mini 2, which will begin shipping in November at list price of $399, Apple has raised the bar in its smaller tablet product. That should improve its margins and that's what many analysts liked.

Best Possible Move

"People are missing that there's a real margin story here," said Cowen & Co. analyst Tim Arcuri in an interview this morning. "When you look at the bugaboo in the margins, the iPad Mini margins were horrible. By raising the price on the Mini and fixing the Retina yield issue, they are bringing up margins on the worst margin product."

While phones are still 70 percent of Apple's growth profit and tablets only 15 percent, Arcuri said that fixing the iPad Mini margins will be the best move to stabilize the company's overall profit margin — and support the stock price. Analysts say a large reason Apple had such a steep decline in share price from 2011 into early 2013 was because its overall margins were declining, and there were growing fears that it was losing in the tablet market.

"The mini is more important than the [iPad] Air because the mini had relatively low margins," said Arcuri. "What's new in this launch? The Air is great, but the Mini having a higher price is the most higher."

Dealing with Competitors

Here's another factor: There is no doubt Samsung's tablet assault has hurt Apple. But by reducing the overall size of the iPad Mini, as Apple has done, it has a more competitive entry in the 7" tablet market. 

Apple was able to shrink the overall product but maintain the screen size -- 7.9" -- by having the screen extend all the way to the edge of the form factor. This is important because Google's new Android tablet product, the Nexus 7, also comes in to the market in the 7" form.

Apple has basically said, "We'll give you a product that's only 1-inch bigger (7.9" instead of 7"), with a larger and better screen."  Although the iPad mini is now much more expensive than the Nexus 7 and Samsung Galaxy Note 8.0, it may have more appeal to higher end customers that want a better screen experience.

All of this has made Apple's position in the small tablet market more clear: The Cupertino-based company is going to focus on the high end.

Wall Street Reaction

Piper Jaffrey analyst Gene Munster, a closely followed Apple analyst, liked the idea that iPad has introduced a more expensive tablet product, the iPad Air, which starts at $499, but can run all the way up to $900 depending on the features installed.

Aside from the margin detail, we believe the new iPad gives us comfort that growth can reaccelerate in the December quarter," wrote Munster in a research note issued this morning.

Munster expects the iPad pricing to keep Apple's margins in the 36-38% range. If anything has hit Apple's stock in recent years, it was declining margins caused by the introduction of lower-priced products. If Apple can introduce enough premium products and stabilize margins, that may be the key to future share-price growth.

Several analysts commented that they liked the new name of the iPad, the iPad Air, because it gives consumers the idea that they are getting something new, rather than just another iPad.

Overall, the news gave investors confidence in Apple's tablet growth story. The company announced yesterday that it has now shipped more than 170 million iPads since they were launched in April 2010. That's an increase from the 100 million iPads sold last year when the iPad Mini was launched.

(Disclosure: The author owns Apple stock in a retirement account.)