Many individuals simultaneously have significant credit card debt and money in the bank. The credit card debt puzzle is as follows: given high interest rates on credit cards and low rates on bank accounts, why not pay down debt? While some economists go to elaborate lengths to explain this, we argue it is a special case of the rate of return dominance puzzle from monetary economics. We extend standard monetary theory to incorporate consumer debt, which is interesting in its own right since developing models where money and credit coexist is a long-standing challenge. Our model is quite tractable—for example, it readily yields nice existence and characterization results—and helps put into context recent discussions of consumer debt.

Reverse mortgage loans (RMLs) allow older homeowners to borrow against housing wealth without moving. Despite rapid growth in this market, only 1.9% of eligible homeowners had RMLs in 2013. In this paper, we analyze reverse mortgages in a calibrated life‐cycle model of retirement. The average welfare gain from RMLs is $252 per homeowner, and $1,770 per RML borrower. Bequest motives, uncertainty about health and expenses, and loan costs account for low demand. According to the model, the Great Recession's impact differs across age, income, and wealth distributions, with a threefold increase in RML demand for lowest income and oldest households.