Born in Seattle, Washington, Cagan and his family moved to Southern California shortly thereafter. Cagan joined the U.S. Navy at age 17 and fought in World War II. After the war, Cagan decided to go to college, and earned his B.A. from UCLA in 1948. Cagan received his M.A. in 1951, and his Ph.D. in Economics in 1954 from the University of Chicago.

After graduate school, Cagan joined the National Bureau of Economic Research (NBER) in New York where he worked for two years. Then Cagan re-entered academia, teaching at the University of Chicago for three years, and at Brown University for seven years. In 1966 Cagan was hired by Columbia University, where he taught economics for nearly thirty years — save for fifteen months spent in Washington, D.C., when he was on the staff of the Council of Economic Advisors (CEA).

During his time at Columbia, Cagan was also associated with the American Enterprise Institute (AEI) in Washington, D.C., writing on public policy issues.

Cagan lived later in life in Palo Alto, California.

Cagan's work focused on monetary policy and the control of inflation. Cagan published over 100 books, journal articles, reviews, reports, and pamphlets on these and other topics in macroeconomics. He is perhaps best known for Determinants and Effects of Changes in the Stock of Money, 1875 - 1960, a work that sought to identify the "causal relationships between changes in money, prices and output." The book, part of the NBER series that contained Milton Friedman and Anna J. Schwartz's Monetary History of the United States, 1867 - 1960, was praised for its "careful empirical work" and called "the most complete study in the area."

Cagan's most important contribution to economics, however, is the article included in Milton Friedman's edited volume Studies in the Quantity Theory of Money (1956), entitled "The Monetary Dynamics of Hyperinflation," a work that became an "instant classic" in the field.

The article, which contained "extensive manipulation of differential equations and an ingenious use of exponentially weighted averages", analyzed seven hyperinflations and found that "the parameters of money demand functions estimated during hyperinflation generally satisfy the condition of dynamic stability that precludes the inflation from being self - generating, or displaying period - to - period oscillations."

After its publication, Cagan's article generated a significant body of work, as a number of leading macroeconomists either reexamined or extended Cagan's model, most notably "Barro (1970), Sargent and Wallace (1973), Frenkel (1975, 1976a, 1976b, 1977, 1979), Sargent (1977), Abel et al. (1979), Salemi (1979), and Salemi and Sargent (1979)." In addition, monetary economists today often refer to a "Cagan demand function" when modeling the real value of money.

Because of the impact that this groundbreaking work had upon the economics profession, Cagan was elected Fellow of the Econometric Society (the most prestigious society in the field), and had been mentioned as a possible candidate for the Nobel Prize in Economics.