To determine whether the demand for a good is elastic, inelastic, or unit-elastic using the midpoint method, we first need to calculate the price elasticity of demand (PED) for each region. The midpoint method formula for PED is:

$\text{PED} = \frac{\left(\frac{Q_2 - Q_1}{(Q_2 + Q_1)/2}\right)}{\left(\frac{P_2 - P_1}{(P_2 + P_1)/2}\right)}$

Where:

• $Q_1$ and $Q_2$ are the initial and final quantities demanded.
• $P_1$ and $P_2$ are the initial and final prices.

We will calculate PED for the regions $W \rightarrow X$, $Y \rightarrow Z$, and $X \rightarrow Y$ as follows:

1. Between W and X

• $Q_1 = 210$, $Q_2 = 135$
• $P_1 = 0$, $P_2 = 6$

$\text{PED}_{WX} = \frac{\left(\frac{135 - 210}{(135 + 210)/2}\right)}{\left(\frac{6 - 0}{(6 + 0)/2}\right)} = \frac{\left(\frac{-75}{172.5}\right)}{\left(\frac{6}{3}\right)} = \frac{-0.435}{2} = -0.2175$

Since the absolute value of PED is less than 1, the demand between W and X is inelastic.

2. Between Y and Z

• $Q_1 = 105$, $Q_2 = 30$
• $P_1 = 21$, $P_2 = 42$

$\text{PED}_{YZ} = \frac{\left(\frac{30 - 105}{(30 + 105)/2}\right)}{\left(\frac{42 - 21}{(42 + 21)/2}\right)} = \frac{\left(\frac{-75}{67.5}\right)}{\left(\frac{21}{31.5}\right)} = \frac{-1.111}{0.667} = -1.666$

Since the absolute value of PED is greater than 1, the demand between Y and Z is elastic.

3. Between X and Y

• $Q_1 = 135$, $Q_2 = 105$
• $P_1 = 6$, $P_2 = 21$

$\text{PED}_{XY} = \frac{\left(\frac{105 - 135}{(105 + 135)/2}\right)}{\left(\frac{21 - 6}{(21 + 6)/2}\right)} = \frac{\left(\frac{-30}{120}\right)}{\left(\frac{15}{13.5}\right)} = \frac{-0.25}{1.111} = -0.225$

Since the absolute value of PED is less than 1, the demand between X and Y is inelastic.

Summary

• Between W and X: Inelastic
• Between Y and Z: Elastic
• Between X and Y: Inelastic

True or False Question

True or False: The value of the price elasticity of demand is equal to the slope of the demand curve.

Answer: False. The price elasticity of demand measures the percentage change in quantity demanded relative to a percentage change in price. It is not simply the slope of the demand curve, which measures the absolute change in quantity demanded relative to an absolute change in price.

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Do you want more details or have any questions?

Here are 5 related questions to consider:

1. What are the implications of inelastic demand for a firm's pricing strategy?
2. How does the concept of unit-elastic demand affect total revenue?
3. Can you provide examples of goods with elastic and inelastic demand?
4. How does the availability of substitutes influence the price elasticity of demand?
5. What role does the proportion of income spent on a good play in determining its elasticity?

Tip: To better understand elasticity, practice calculating it with different scenarios and focus on the percentage changes rather than the absolute changes.