Question

for each of the regions, use the midpoint method to identify whether the supply of this good is elastic or inelastic.
region elastic inelastic
between v and w
between x and y
true or false: as firms reach near maximum capacity at high levels of quantity supplied, supply becomes more elastic because firms may need to invest in additional capital in order to further increase production.
true
false

Explanation:

Step1: Define midpoint elasticity formula

The midpoint formula for price elasticity of supply is:
$$E_s = \frac{\frac{Q_2 - Q_1}{\frac{Q_1 + Q_2}{2}}}{\frac{P_2 - P_1}{\frac{P_1 + P_2}{2}}}$$
If $|E_s| > 1$, supply is elastic; if $|E_s| < 1$, supply is inelastic.

Step2: Calculate elasticity for V-W

From the graph: $Q_V=10, P_V=20$; $Q_W=20, P_W=22$
$$\%ΔQ = \frac{20-10}{\frac{10+20}{2}} = \frac{10}{15} = \frac{2}{3}$$
$$\%ΔP = \frac{22-20}{\frac{20+22}{2}} = \frac{2}{21} = \frac{2}{21}$$
$$E_s = \frac{\frac{2}{3}}{\frac{2}{21}} = 7$$
Since $7>1$, supply is elastic.

Step3: Calculate elasticity for X-Y

From the graph: $Q_X=64, P_X=120$; $Q_Y=72, P_Y=270$
$$\%ΔQ = \frac{72-64}{\frac{64+72}{2}} = \frac{8}{68} = \frac{2}{17}$$
$$\%ΔP = \frac{270-120}{\frac{120+270}{2}} = \frac{150}{195} = \frac{10}{13}$$
$$E_s = \frac{\frac{2}{17}}{\frac{10}{13}} = \frac{26}{170} ≈ 0.15$$
Since $0.15<1$, supply is inelastic.

Step4: Analyze true/false statement

Near maximum capacity, firms cannot easily increase output (even with higher prices), so supply becomes more inelastic, not elastic. The statement is false.

Answer:

1. Region between V and W: Elastic
2. Region between X and Y: Inelastic
3. True or False: False