Question

calculate the price elasticity of demand (in absolute value) at points a, b, c, d, and e on the demand curve below. demand price quantity point elasticity a (click to select) b (click to select) c (click to select) d (click to select) e (click to select)

Explanation:

Step1: Recall the formula for point - price elasticity of demand

The formula for point - price elasticity of demand $\epsilon_p=-\frac{\text{d}Q}{\text{d}P}\times\frac{P}{Q}$. For a linear demand curve $P = a - bQ$, $\frac{\text{d}P}{\text{d}Q}=-b$, so $\frac{\text{d}Q}{\text{d}P}=-\frac{1}{b}$. The equation of the linear demand curve in the form $P = a - bQ$. Using two - point form, if the demand curve passes through $(Q_1,P_1)=(0,100)$ and $(Q_2,P_2)=(100,0)$, the slope $b = 1$ (since $b=\frac{\Delta P}{\Delta Q}=\frac{0 - 100}{100-0}=- 1$), and the demand function is $P = 100 - Q$, so $\frac{\text{d}Q}{\text{d}P}=-1$.

Step2: Calculate elasticity at point A

At point $A$, $P = 100$ and $Q = 0$. Using the formula $\epsilon_p=-\frac{\text{d}Q}{\text{d}P}\times\frac{P}{Q}$, substituting $\frac{\text{d}Q}{\text{d}P}=- 1$, $P = 100$ and $Q = 0$, we get $\epsilon_p=\infty$ (since $\frac{100}{0}$ is undefined in the context of elasticity calculation and represents perfectly elastic demand at the vertical - intercept of the demand curve).

Step3: Calculate elasticity at point B

At point $B$, $P = 75$ and $Q = 25$. Using the formula $\epsilon_p=-\frac{\text{d}Q}{\text{d}P}\times\frac{P}{Q}$, with $\frac{\text{d}Q}{\text{d}P}=-1$, we have $\epsilon_p=(-(-1))\times\frac{75}{25}=3$.

Step4: Calculate elasticity at point C

At point $C$, $P = 50$ and $Q = 50$. Using the formula $\epsilon_p=-\frac{\text{d}Q}{\text{d}P}\times\frac{P}{Q}$, with $\frac{\text{d}Q}{\text{d}P}=-1$, we get $\epsilon_p=(-(-1))\times\frac{50}{50}=1$.

Step5: Calculate elasticity at point D

At point $D$, $P = 25$ and $Q = 75$. Using the formula $\epsilon_p=-\frac{\text{d}Q}{\text{d}P}\times\frac{P}{Q}$, with $\frac{\text{d}Q}{\text{d}P}=-1$, we have $\epsilon_p=(-(-1))\times\frac{25}{75}=\frac{1}{3}$.

Step6: Calculate elasticity at point E

At point $E$, $P = 0$ and $Q = 100$. Using the formula $\epsilon_p=-\frac{\text{d}Q}{\text{d}P}\times\frac{P}{Q}$, substituting $\frac{\text{d}Q}{\text{d}P}=-1$, $P = 0$ and $Q = 100$, we get $\epsilon_p = 0$ (perfectly inelastic demand at the horizontal - intercept of the demand curve).

Answer:

Point	Elasticity
B	3
C	1
D	$\frac{1}{3}$
E	0