2.6 Elasticity of supply

Original price = $200,newprice=$160, so $\Delta P=-40$. Original quantity = 80,000, new quantity = 72,000, so $\Delta Q_s=-8,000$.

$\%\Delta P=\frac{-40}{200}\times 100=-20\%$ $\%\Delta Q_s=\frac{-8,000}{80,000}\times 100=-10\%$

$PES=\frac{\%\Delta Q_s}{\%\Delta P}=\frac{-10\%}{-20\%}=0.5$

PES = 0.5. Because both percentage changes are negative (price and quantity both fell), the negatives cancel and PES remains positive, confirming the direct relationship between price and quantity supplied.

The question asks for the numerical PES value. We need $\%\Delta Q_s÷\%\Delta P$.

PES = 2.0 or 2.5 would mean quantity supplied changed proportionally more than price. Here price fell by 20% but quantity fell by only 10% — quantity responded less than price, ruling out any value greater than 1.

PES = 0.4 would require $\%\Delta Q_s=0.4\times 20\%=8\%$, but the actual fall in quantity is $10\%$, not $8\%$. This does not match the data.

$\%\Delta Q_s=10\%$ and $\%\Delta P=20\%$, giving $PES=10\%÷20\%=0.5$. This is the only value consistent with the given data.

Any straight-line supply curve that passes through the origin has a PES of exactly 1 at every point along it. This is because price and quantity supplied always change by the same proportion relative to each other.

A supply curve through the origin has the form $Q_s=kP$. If price rises from $P$ to $2P$ (doubles), then $Q_s$ also doubles. $PES=\frac{\%\Delta Q_s}{\%\Delta P}=\frac{100\%}{100\%}=1$

Regardless of where on the curve the price change occurs, PES = 1. The supply curve through the origin is the graphical representation of unit elastic supply.

We need to identify the PES of a supply curve that is a straight line passing through the origin when price doubles from $5to$10.

PES = ∞ describes perfectly elastic supply, which is shown as a horizontal line, not an upward-sloping line through the origin. This option is incorrect.

PES = 0.5 (inelastic) and PES = 2 (elastic) both describe supply curves that do NOT pass through the origin. A straight-line supply curve through the origin is specifically and uniquely associated with PES = 1.

A straight-line supply curve passing through the origin always has PES = 1 (unit elastic). This is a key graphical property: the proportional change in quantity supplied always equals the proportional change in price along such a curve.

$\%\Delta P=30\%$ and $\%\Delta Q_s=4.5\%$. Both are already expressed as percentages, so we can apply the formula directly.

$PES=\frac{\%\Delta Q_s}{\%\Delta P}=\frac{4.5\%}{30\%}=0.15$

Since $0<PES=0.15<1$, this is inelastic supply — quantity supplied responds, but by a much smaller proportion than the price change. It is NOT perfectly inelastic (which would require PES = 0 with no change in quantity at all).

PES = 0.15, inelastic supply. The quantity supplied did change (4.5%), so it cannot be perfectly inelastic; since the response was much smaller than the price change, it is classified as inelastic.

The question requires both a correct numerical PES and a correct classification. We need to eliminate options with wrong numbers or wrong labels.

PES = 6.67 would result from inverting the formula — dividing $\%\Delta P$ by $\%\Delta Q_s$ (i.e. 30% ÷ 4.5%). This is a common error; PES always places $\%\Delta Q_s$ in the numerator. Both options with 6.67 are therefore wrong.

Perfectly inelastic supply (PES = 0) means quantity supplied does not change at all. Here, quantity supplied rose by 4.5% — it did respond, just weakly. So perfectly inelastic is the wrong label.

PES = 0.15 is correct (4.5% ÷ 30%), and since $0<0.15<1$, the correct classification is inelastic supply, not perfectly inelastic.