Agents demand money for three motives: transactions (to facilitate exchange), precautionary (to handle unexpected needs), and speculative (to take advantage of expected changes in asset prices). The transactions and precautionary demands increase with income, while speculative demand depends on interest rates and expectations of future interest rate movements. The aggregate money demand function M_d/P = L(Y, i) is increasing in output and decreasing in the nominal interest rate.
From your prerequisite study of money and its functions, you know that money serves as a medium of exchange, a store of value, and a unit of account. But this raises a puzzle: why do people hold money at all when they could hold interest-bearing assets like bonds? Holding money has an opportunity cost — the interest you forgo by keeping wealth in cash rather than invested. The theory of money demand is essentially an answer to the question: given this cost, why do rational agents still demand money, and how much of it?
Keynes identified three distinct motives, each driven by a different logic. The transactions motive is the most intuitive: you need money to buy things. Between paychecks or income receipts, you hold a buffer of cash to cover everyday purchases. The size of this buffer grows with your income — higher-income people make larger and more frequent transactions and need proportionally more money on hand. This motive treats money purely as a medium of exchange, demanded because exchange requires it. The precautionary motive extends this: beyond planned transactions, people hold extra money to handle unexpected needs — a sudden medical expense, a car repair, an unexpected opportunity. Like transactions demand, precautionary demand rises with income, because larger income implies larger potential unexpected expenses and larger precautionary reserves.
The speculative motive introduces the interest rate as a key determinant. Bond prices move inversely with interest rates — when rates rise, existing bond prices fall. If you expect interest rates to rise (bond prices to fall) in the near future, holding bonds means capital losses, and you'd prefer to hold money instead until the price decline occurs. Conversely, if rates are expected to fall (bond prices to rise), you'd rather hold bonds and capture the capital gain. In aggregate, the higher the current interest rate, the more likely it is that rates will fall in the future, so the more attractive bonds become and the less money people wish to hold speculatively. This generates the inverse relationship between speculative demand and the current interest rate.
Combining all three, the aggregate money demand function is written L(Y, i): demand for real money balances rises with real output Y (through transactions and precautionary motives) and falls with the nominal interest rate i (through the speculative motive). This function is the foundation for the LM curve in IS-LM analysis and for understanding monetary policy transmission. When the central bank changes the money supply, it shifts the equilibrium on the money market — and since money demand slopes downward in the interest rate, the adjustment clears through interest rate changes that then propagate to investment, consumption, and output. The three-motive framework thus connects the microeconomics of portfolio choice to the macroeconomics of monetary policy.