If the amount of money that people are willing to spend on a good stays the same when its price doubles, then demand for that good must have a price elasticity of demand smaller in absolute value than 1.

If the amount of money people are willing to spend on a good remains the same when its price doubles, it indicates that the quantity demanded decreases proportionally to the price increase, which is characteristic of unitary price elasticity of demand, where the price elasticity of demand equals 1 in absolute value.