This paper provides a non-steady state general equilibrium foundation for the transactions demand for money going back to Baumol (1952) and Tobin (1956). In our economy, money competes against real capital as a store of value. We prove existence of a monetary general equilibrium in which both real capital and fiat money are voluntarily held over time. The demand for money is generated by fixed transactions costs. More precisely, we assume that house-holds have two physically separated accounts. On the first account they finance consumption and might want to hold money over time. On the second account households receive their wages, hold claims on capital and earn interest income from renting capital to firms. Every transfer of wealth between the two accounts requires fixed resources. In equilibrium, households space apart the transaction dates in time. Between these transaction dates, money is held as a store of value on the first account for transactions purposes. The number of periods over which money is held is endogenous and the nonconvexity of the problem is explicitly taken into account.
