ANSWER
The price elasticity of demand will decrease down the demand curve. When moving from left to right, down the demand curve, the price elasticity of demand changes from being elastic to inelastic.
Explanation
Price elasticity of demand varies between different pairs of points down along a linear demand curve; it diminishes in absolute value down the curve. This is because, as the consumer moves down the curve, equal changes in quantity demanded represent smaller and smaller percentage changes, yet equal changes in price will represent larger and larger percentage changes. As a result, the absute value of the price elasticity of demand falls.
Thus, at the upper portion of the demand curve (leftwards), demand is price elastic. This is because the higher the price and the lower the quantity demanded, the larger the absolute value of the price elasticity of demand since the percentage change in quantity demanded exceeds the percentage change in price. On the middle portion of the demand curve, elasticity becomes unitary. On the lower portion of the curve (rightwards), price is lower and quantity demanded larger and the absolute value of demand elasticity is relatively smaller (inelastic) for the percentage change in quantity demanded is smaller than the percentage in price.
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