The economy was mired in stagflation, the unfortunate combination of high inflation and high unemployment. Mr. Laffer, then a professor at the University of Chicago, was a leading spokesman for a new school of economic thought, supply-side economics, that saw tax cuts as the best way to increase economic growth while reducing inflation.

The two men met for drinks with Mr. Wanniski in early December at a restaurant across the street from the Treasury Department. Mr. Wanniski also invited Grace-Marie Arnett, a Republican aide who was interested in supply-side economics.

In Mr. Wanniski’s account, Mr. Laffer grew frustrated as he tried to explain the value of tax cuts to Mr. Cheney, finally grabbing a paper napkin so he could draw a visual aid. The Laffer Curve, which looks like the nose of an airplane, is meant to show that higher tax rates can reduce tax revenues — and lower tax rates can bring in more money.

Ms. Arnett, now known as Grace-Marie Turner, said that she recalled the moment vividly because she had never seen the Laffer Curve before, and she found it illuminating.

She said she was certain that the meeting had happened after the elections because until then, she was working for a Republican House candidate in Texas. And, she added, “I absolutely know that it was a paper cocktail napkin.”

Mr. Cheney also wrote in his memoirs that the meeting had happened after the midterms.

Mr. Laffer has always said he does not have a clear recollection of the original meeting, but he said that he did not regard the Smithsonian’s napkin as the authentic original.

“There was a napkin done and I don’t know where it ended; I guess it was probably in the trash,” he said. “And Jude Wanniski wanted me to do another example of it two years later, and I believe that this is the napkin that Jude Wanniski asked me to do for him.”