The correct answer is: B. a vertical demand curve
A vertical demand curve is a special case of a demand curve where the quantity demanded is perfectly inelastic. This means that the quantity demanded does not change at all in response to a change in price. As a result, the elasticity of demand is zero at all points on a vertical demand curve.
A downward-sloping demand curve is a more common type of demand curve. On a downward-sloping demand curve, the quantity demanded decreases as the price increases. The elasticity of demand is not constant on a downward-sloping demand curve, but it is always negative. This means that the quantity demanded is always inversely related to the price.
A rectangular hyperbola demand curve is a type of demand curve that is shaped like a rectangular hyperbola. On a rectangular hyperbola demand curve, the quantity demanded is inversely proportional to the price. This means that the elasticity of demand is equal to -1 at all points on a rectangular hyperbola demand curve.
A horizontal demand curve is a type of demand curve where the quantity demanded is infinite at any price. This means that the elasticity of demand is infinite at all points on a horizontal demand curve.
In conclusion, the only type of demand curve that does not have a uniform elasticity of demand at all points is a vertical demand curve.