That evil sparrow with his bow and arrow claimed credit for killing Cock Robin of nursery rhyme fame.

But the grief over the bird's demise is nothing compared with the coming catastrophe of McDonalds (MCD) Dollar Menu, especially the $1 double cheeseburger.

McDonalds, purveyor of fine fast food, faces a basic problem to maintain its profit margins: Raise prices or slice portions. You can bet Burger King (BKC), Wendy's (WEN) and Chipotle (CMG) face a similar choice.

Raising prices defeats the catchy "Dollar Menu" marketing theme. But cutting portion size risks alienating loyal customers.

Some McDonalds stores are selling the famous $1 double cheeseburger with 1 slice of cheese instead of 2, calling it a "double hamburger with cheese." Others offer a double hamburger without cheese, while some continue to offer the familiar double cheeseburger at prices ranging from $1.09 to $1.19.

Bumping the cheeseburger's price above a buck may not be a problem in the land of the "free gift." Pedants ask: If it's not free, how can it be a gift? Similarly, what's an extra $0.09 to $0.19 tacked on to the Dollar Menu, metaphorically speaking?

But this is serious stuff at McDonalds, where the double cheeseburger drives sales on the 8-item Dollar Menu. Higher production costs have increased the price of cheese and the price of beef is almost certain to rise. Both increases are in part driven by higher demand for corn to make ethanol.

McDonalds may move the double cheeseburger off the $1 menu and replace it with another, slightly less splendiferous version.

However this weighty problem sakes out, Federal Reserve Chairman Ben Bernanke doesn't want to be immortalized in doggerel this way:

Who killed McDonald's $1 double cheeseburger?

I, said the Federal Reserve's Grand Pooh-bah,

With my reluctance to raise interest rates to curb inflation,

I killed the $1 double cheeseburger.