The "elasticity of money" is a term from economics that was developed by James Tobin and William Baumol in the 1950s. It was the first attempt to formalize the analysis of the effect of the money supply on the economy and spawned an entire field of economic theory called monetary theory. People had begun to realize that the Great Depression was caused in part by what we now refer to as "tight monetary policy" by the federal reserve. The basic idea was, if it is expensive to hold cash (i.e., if short-term interest rates are high, for example), then people will hold less cash. Less cash, less spending. Less spending, slower economy.
Technically, what we think of as the "money supply" (ie the total amount of cash and cash equivalents held by people and businesses) is really the intersection of the money supply curve and the money demand curve, just like everything else in economics.
Tobin and Baumol developed a mathematical model to describe the demand for money. Back in the 1950s, when savings accounts paid interest, checking accounts didnt pay interest, and you had to go to the bank to take money out or move it from savings to checking, they reasoned that people's desire to hold cash (i.e. the "demand" for money) would be based on (1) the amount of money you plan to spend (the more you spend, the more cash you carry, all else being equal); (2) short term interest rates (if short term interest rates are high, you'll tend to leave more money in the bank and carry less cash, all else being equal); and (3) what Tobin quaintly called "shoe leather costs" - the pain in the neck factor of going to the bank to withdraw cash.
In other words, if interest rates are close to zero, then there's no real incentive to leave money in a savings account; everyone will just put it in a checking account (considered a "cash equivalent") or carry cash. If interest rates are high, people have an incentive to leave money in their savings account. But then they have to go to the bank whenever they want to spend it, which is a pain in the neck. Their conclusion was that people will optimize the amount of money they carry (or leave in their checking account) based on a rational balancing of the interest they'd earn vs. the amount they want to spend and how money times they want to go to the bank each month.
The "elasticity of the demand for money" (or just the elasticity of money) is Tobin and Baumol's measurement of how much each of these factors affects the overall demand for money. For example,
- if interest rates double, then the demand for money will be half of what it otherwise would be. Higher interest rates = lower demand. The "elasticity of money with respect to interest rates" = the change in money supply caused by a change in interest rates.
- if people spend more, then the demand for money will be higher. The elasticity of money with respect to GDP (total spending in the economy) = the change in the money supply caused by a change in GDP.
- if the costs of going to the bank decrease, then people will carry less money and the demand for money will be lower. The elasticity of money with respect to "shoe leather costs" = the change in the money supply caused by a change in the cost of "going to the bank". Note that it might seem strange to think of the "cost" of going to the bank, but realize that since their original article was written, the "cost of going to the bank" has decreased radically. Credit cards, debit cards, interest-bearing checking accounts, online banking & ATM machines have made it virtually "free" to go to the bank - nowadays, most people have their money in interest bearing checking accounts all the time, and can transfer money between savings, checking and cash with very little effort, and dont even use cash to pay for most purchases.