A demand curve that is unit elastic everywhere is
a. linear and slopes downward
b. linear and slopes upward
c. vertical
d. horizontal
e. nonlinear
I don't know the answer
vertical
A demand curve that is unit elastic everywhere means that the price elasticity of demand is equal to -1 at all points along the curve. This means that a 1% change in price will result in a 1% change in quantity demanded. To determine the characteristics of such a demand curve, we need to understand the relationship between price and quantity demanded.
To find the correct answer, let's examine the options one by one:
a. Linear and slopes downward: A linear downward-sloping demand curve means that as price increases, quantity demanded decreases. However, unit elasticity means that the percentage change in price is equal to the percentage change in quantity demanded. In this case, a 1% increase in price would result in a 1% decrease in quantity demanded, which does not align with the downward-sloping nature of the curve. Therefore, option (a) is incorrect.
b. Linear and slopes upward: A linear upward-sloping demand curve means that as price increases, quantity demanded also increases. Similar to the previous option, a 1% increase in price would lead to a 1% increase in quantity demanded, contradicting a upward-sloping curve. Thus, option (b) is incorrect.
c. Vertical: A vertical demand curve indicates that the quantity demanded remains constant regardless of price changes. This means that any percentage change in price would result in no change in quantity demanded. As a result, a vertical demand curve cannot be unit elastic everywhere since it implies a fixed quantity demanded. Thus, option (c) is incorrect.
d. Horizontal: A horizontal demand curve suggests that the quantity demanded is infinitely responsive to any price changes. In other words, any percentage change in price would cause an infinitely large percentage change in quantity demanded. A horizontal demand curve is, by definition, perfectly elastic, rather than unit elastic. Therefore, option (d) is incorrect.
e. Nonlinear: A nonlinear demand curve can take various shapes, such as concave or convex curves. While the nonlinearity allows for a possibility of being unit elastic at some points along the curve, it is not guaranteed. A nonlinear demand curve may have different elasticities at different price points. Therefore, option (e) is incorrect.
In conclusion, none of the provided options correctly describe a demand curve that is unit elastic everywhere.