Question

homework: calculate ped when $p_0 = 2$, $p_1 = 3$ and $q_0 = 10$, $q_1 = 8$ and what does your ped mean?
figure
elasticity along a linear demand curve
the slope of a linear demand curve is constant, but its elasticity is not. the price elasticity of demand is calculated using the demand schedule in the table and the mid - point method. at points with a low price and high quantity, the demand curve is inelastic. at points with a high price and low quantity, the demand curve is elastic.

price	quantity	total revenue (price × quantity)	percentage change in price	percentage change in quantity	elasticity	description
6	2	12	18	67	3.7	elastic
5	4	20	22	40	1.8	elastic
4	6	24	29	29	1.0	unit elastic
3	8	24	40	22	0.6	inelastic
2	10	20	67	18	0.3	inelastic
1	12	12	200	15	0.1	inelastic
0	14	0

Explanation:

Step1: Calculate the percentage change in quantity demanded

The formula for the percentage change in quantity demanded using the mid - point method is $\%\Delta Q=\frac{Q_1 - Q_0}{\frac{Q_1+Q_0}{2}}\times100$. Here, $Q_0 = 10$ and $Q_1=8$.
$\%\Delta Q=\frac{8 - 10}{\frac{8 + 10}{2}}\times100=\frac{- 2}{9}\times100\approx - 22.22\%$

Step2: Calculate the percentage change in price

The formula for the percentage change in price using the mid - point method is $\%\Delta P=\frac{P_1 - P_0}{\frac{P_1+P_0}{2}}\times100$. Here, $P_0 = 2$ and $P_1 = 3$.
$\%\Delta P=\frac{3 - 2}{\frac{3+2}{2}}\times100=\frac{1}{2.5}\times100 = 40\%$

Step3: Calculate the price elasticity of demand (PED)

The formula for PED is $PED=\frac{\%\Delta Q}{\%\Delta P}$.
$PED=\frac{-22.22\%}{40\%}\approx - 0.56$

The meaning of a PED of approximately $- 0.56$: Since $|PED|=0.56<1$, the demand is inelastic. This means that a change in price leads to a proportionately smaller change in the quantity demanded. For example, a 1% increase in price will lead to a $0.56\%$ decrease in the quantity demanded.

Answer:

The price elasticity of demand (PED) is approximately $-0.56$, and the demand is inelastic.