The $31-a-share bid of cash or Microsoft stock is 62 percent more than Yahoo's closing price yesterday. Before today, Yahoo had dropped 18 percent this year in Nasdaq Stock Market trading, and said this week that fourth-quarter profit fell 23 percent.

Microsoft Chief Executive Officer Steve Ballmer is attempting the biggest-ever technology takeover after failing to compete with Google in a market that may almost double to $80 billion by 2010. Google has grown faster than Microsoft in every quarter since Google's 2004 initial public offering as its search engine won more users.

``Microsoft is under massive pressure to expand its Internet business to fend off competition from rivals such as Google and this deal shows how desperate they are,'' said Thomas Radinger, a fund manager at Pioneer Investments in Munich, which oversees about $95 billion, including Microsoft shares. ``It's a huge gamble as the price is very steep and it will take years to successfully integrate such a massive acquisition.''

Yahoo rose $8.58, or 45 percent, to $27.76 at 10:46 a.m. in Nasdaq trading. Microsoft, based in Redmond, Washington, fell $2.02, or 6.2 percent, to $30.58, while Google dropped 9.5 percent to $510.75.

Cost Savings

Microsoft said the transaction may cut costs by $1 billion annually for the combined company. Yahoo, based in Sunnyvale, California, said it plans to evaluate the proposal ``promptly.''

``This is kind of a gift from heaven for the Yahoo shareholders who have really been suffering for the last couple years,'' said Georges Yared, chief investment strategist for Yared Investment Research in Wayzata, Minnesota. ``This allows the shareholders to be bailed out.''

Yahoo's inability to crack Google's dominance in search has led to eight straight quarters of declining profit and a stock that, before today, had lost half its value in the past two years.

``It shows how serious the threat is from Google,'' Jordan Rohan, an analyst at RBC Capital Markets in New York, said in an interview. ``Yahoo is vulnerable. Investors are losing patience with the Yahoo management team.'' The New York-based analyst rates the stock ``outperform.''

Google yesterday reported a 52 percent increase in fourth- quarter sales growth, its 14th straight quarter exceeding 50 percent. Still, profit and revenue trailed analysts' estimates as it received less money than expected from ad deals with social- networking sites like News Corp.'s MySpace.

Losing Share

Google, based in Mountain View, California, captured 56 percent of U.S. Web queries in December, almost double the combined share for Yahoo and Microsoft, which attracted 18 percent and 13 percent, according to New York-based Nielsen Online. Searches will account for 37 percent of the $27.5 billion U.S. online advertising market in 2008, estimates research firm EMarketer Inc.

Yahoo has also lost sales in the market for graphical, or display, ads to social sites like Facebook Inc. and MySpace. Co- founder Jerry Yang replaced Terry Semel as chief executive officer in June to reignite sales growth. Microsoft increased competition with Google by agreeing to buy a 1.6 percent stake in Facebook, the second-most visited social-networking site.

Before today's stock gain, about half of Yahoo's market value came from its investments in China's Alibaba Group and Alibaba.com, Yahoo Japan and South Korea's Gmarket Inc. The company said this week that the value of those investments was more than $10 a share in the latest quarter.

Yahoo Rejection

Microsoft was advised by Morgan Stanley and Blackstone Group LP. Yahoo hasn't disclosed its bankers. Microsoft and Yahoo explored ways to work together in late 2006 and early 2007, according to a letter Ballmer sent to the Yahoo board. Yahoo rejected the idea of being taken over by Microsoft a year ago, the letter said.

``This combination provides value to advertisers in the form of more scale and more inventory,'' Kevin Johnson, who runs Microsoft's Windows and Internet group, said in an interview. ``It provides value to publishers, in terms of integrating the ad platform.''

Yahoo was founded by Yang and David Filo while the two were graduate students at Stanford University in 1995. The co- founders, who own a combined 9.8 percent of Yahoo's stock, took the company public a year later. After a three-year jump in the stock price, they were each worth $4 billion, according to Forbes Magazine. Then the market crashed in 2000, wiping out 86 percent of Yahoo's market value.