2.5 Elasticities of demand

Original price P_1 = \120$,newprice$P_2 = $150$.Originalquantity$Q_1 = 80$,newquantity$Q_2 = 56$.

$\%\Delta Q_d=\frac{56-80}{80}\times 100=\frac{-24}{80}\times 100=-30\%$

$\%\Delta P=\frac{150-120}{120}\times 100=\frac{30}{120}\times 100=+25\%$

$PED=\frac{-30\%}{+25\%}=-1.4$ Report as a positive value: PED = 1.4.

Since $1.4>1$, demand is elastic — the percentage fall in quantity demanded (30%) is proportionally larger than the percentage rise in price (25%).

We need to calculate PED using the basic formula and classify the result as elastic or inelastic. The key is whether the final value is greater than or less than 1.

A value of 0.71 would require the % change in quantity to be smaller than the % change in price. Here %ΔQd = 30% and %ΔP = 25%, so quantity changed proportionally more — the value cannot be less than 1. Eliminated.

A value of 1.75 would require either a smaller price change or a larger quantity change than what is given. Using the correct figures, $30\%÷25\%=1.2$… wait — rechecking: $-24/80=30\%$ and $30/120=25\%$, giving PED = 1.4, not 1.75. Eliminated.

0.57 is far too low. This might arise from inverting the formula (dividing %ΔP by %ΔQd: $25/30\approx 0.57$), which is a common error. The correct formula places %ΔQd in the numerator. Eliminated.

PED = 1.4; elastic demand is correct. The percentage fall in quantity (30%) divided by the percentage rise in price (25%) equals 1.4, which is greater than 1, confirming elastic demand.

The basic PED formula uses the original price and quantity as the denominator. The 'original' value differs depending on the direction of change, so the same two points on a demand curve yield different PED values depending on which point is treated as the starting point.

The midpoint formula uses the average of the two prices, $\bar{P}=(P_1+P_2)/2$, and the average of the two quantities, $\bar{Q}=(Q_1+Q_2)/2$, as the base for percentage changes. These averages are the same regardless of which point is labelled 'original'.

Whether you calculate the change from $P_1$ to $P_2$ or from $P_2$ to $P_1$, the numerator changes sign but so does the denominator in the same proportion, and since PED is reported as a positive magnitude, the result is identical.

The correct answer is that the midpoint formula uses the average of the two prices and quantities as denominators, making it directionally symmetric. This is the specific feature that eliminates the inconsistency present in the basic formula.

The question asks for the correct explanation of why the midpoint formula produces one consistent PED value regardless of direction of the price change.

Using the original price as the base is precisely what the basic formula does, and this is what causes directional inconsistency. The midpoint formula was designed to replace this with an average. Eliminated.

Both the basic and midpoint formulas still use percentage changes, not absolute changes. Converting to absolute changes would make PED unit-dependent and would not eliminate directional inconsistency. Eliminated.

This is the opposite of reality. The midpoint formula is specifically recommended when price changes are large because that is when the basic formula's directional problem is most serious. For small changes, both formulas give similar results. Eliminated.

Because it averages the two prices and the two quantities as the denominator is correct. Using the average as the base means the denominator is unchanged regardless of which direction the price change runs, producing one consistent PED value.