As we move down a linear demand curve, the price elasticity goes on decreasing'. Comment.

A linear demand curve is a straight line that represents the relationship between price (P) and quantity demanded (Q). It has the general equation of Q = a - bP, where 'a' and 'b' are constants. Price elasticity of demand (PED) is a measure of how much the quantity demanded of a product changes when there is a change in its price. It is calculated as the percentage change in quantity demanded divided by the percentage change in price, or: PED = \(\frac{\% \Delta Q}{\% \Delta P}\)

We can find the PED on a linear demand curve using calculus. Now let's differentiate the linear demand function Q = a - bP with respect to price P: \(\frac{dQ}{dP} = -b\) Now we substitute this value into the PED formula: PED = \(\frac{\% \Delta Q}{\% \Delta P} = \frac{dQ}{dP} \times \frac{P}{Q}\) Substitute the value of \(\frac{dQ}{dP}\) from above and plug in Q = a - bP: PED = \(-b \times \frac{P}{a - bP}\)

As we move down the linear demand curve (i.e., as the price decreases), the value of P in the PED formula on a linear demand curve also decreases. Since the denominator of the fraction (a - bP) will increase, the absolute value of PED will decrease. To put it more clearly, as we move down the demand curve (from left to right), quantity demanded increases and price decreases: 1. If the price is very high, the PED will be high (elastic) because consumers can significantly reduce their consumption due to the high price. 2. As the price decreases, the PED will decrease (become less elastic) because consumers will be less sensitive to small price changes. So, as we move down a linear demand curve, the price elasticity does indeed go on decreasing.