Answer Key Chapter 5 - Principles of Microeconomics 2e | OpenStax (2024)

From point B to point C, price rises from $70 to $80, and Qd decreases from 2,800 to 2,600. So:

$$\begin{array}{rcl}\text{\%changeinquantity}& =& \frac{2600–2800}{\left(2600+2800\right)÷2}\mathrm{\times \; 100}\\ & =& \frac{\mathrm{–200}}{2700}\mathrm{\times \; 100}\\ & =& \mathrm{–7.41}\\ \text{\% changeinprice}& =& \frac{80–70}{\left(80+70\right)÷2}\mathrm{\times \; 100}\\ & =& \frac{10}{75}\mathrm{\times \; 100}\\ & =& 13.33\\ \text{ElasticityofDemand}& =& \frac{\mathrm{–7.41\%}}{\mathrm{13.33\%}}\\ & =& 0.56\end{array}$$

The demand curve is inelastic in this area; that is, its elasticity value is less than one.

Answer from Point D to point E:

$$\begin{array}{rcl}\text{\%changeinquantity}& =& \frac{2200–2400}{\left(2200+2400\right)÷2}\mathrm{\times \; 100}\\ & =& \frac{\mathrm{–200}}{2300}\mathrm{\times \; 100}\\ & =& \mathrm{–8.7}\\ \%\text{changeinprice}& =& \frac{100–90}{\left(100+90\right)÷2}\mathrm{\times \; 100}\\ & =& \frac{10}{95}\mathrm{\times \; 100}\\ & =& 10.53\\ \text{ElasticityofDemand}& =& \frac{\mathrm{–8.7\%}}{\mathrm{10.53\%}}\\ & =& 0.83\end{array}$$

The demand curve is inelastic in this area; that is, its elasticity value is less than one.

Answer from Point G to point H:

$$\begin{array}{rcl}\text{\%changeinquantity}& =& \frac{1600–1800}{1700}\mathrm{\times \; 100}\\ & =& \frac{\mathrm{–200}}{1700}\mathrm{\times \; 100}\\ & =& \mathrm{–11.76}\\ \text{\% changeinprice}& =& \frac{130–120}{125}\mathrm{\times \; 100}\\ & =& \frac{10}{125}\mathrm{\times \; 100}\\ & =& 8.00\\ \text{ElasticityofDemand}& =& \frac{\mathrm{–11.76\%}}{\mathrm{8.00\%}}\\ & =& \mathrm{–1.47}\end{array}$$

The demand curve is elastic in this interval.

From point J to point K, price rises from $8 to $9, and quantity rises from 50 to 70. So:

$$\begin{array}{rcl}\text{\%changeinquantity}& =& \frac{70–50}{\left(70+50\right)÷2}\mathrm{\times \; 100}\\ & =& \frac{20}{60}\mathrm{\times \; 100}\\ & =& 33.33\\ \text{\% changeinprice}& =& \frac{\mathrm{\$9}–\mathrm{\$8}}{\left(\mathrm{\$9}+\mathrm{\$8}\right)÷2}\mathrm{\times \; 100}\\ & =& \frac{1}{8.5}\mathrm{\times \; 100}\\ & =& 11.76\\ \text{ElasticityofSupply}& =& \frac{\mathrm{33.33\%}}{\mathrm{11.76\%}}\\ & =& 2.83\end{array}$$

The supply curve is elastic in this area; that is, its elasticity value is greater than one.

From point L to point M, the price rises from $10 to $11, while the Qs rises from 80 to 88:

$$\begin{array}{rcl}\text{\%changeinquantity}& =& \frac{88–80}{\left(88+80\right)÷2}\mathrm{\times \; 100}\\ & =& \frac{8}{84}\mathrm{\times \; 100}\\ & =& 9.52\\ \text{\%changeinprice}& =& \frac{\mathrm{\$11}–\mathrm{\$10}}{\left(\mathrm{\$11}+\mathrm{\$10}\right)÷2}\mathrm{\times \; 100}\\ & =& \frac{1}{10.5}\mathrm{\times \; 100}\\ & =& 9.52\\ \text{ElasticityofDemand}& =& \frac{\mathrm{9.52\%}}{\mathrm{9.52\%}}\\ & =& 1.0\end{array}$$

The supply curve has unitary elasticity in this area.

From point N to point P, the price rises from $12 to $13, and Qs rises from 95 to 100:

$$\begin{array}{rcl}\text{\%changeinquantity}& =& \frac{100–95}{\left(100+95\right)÷2}\times 100\\ & =& \frac{5}{97.5}\times 100\\ & =& 5.13\\ \text{\% changeinprice}& =& \frac{\mathrm{\$13}–\mathrm{\$12}}{\left(\mathrm{\$13}+\mathrm{\$12}\right)÷2}\mathrm{\times \; 100}\\ & =& \frac{1}{12.5}\mathrm{\times \; 100}\\ & =& 8.0\\ \text{ElasticityofSupply}& =& \frac{\mathrm{5.13\%}}{\mathrm{8.0\%}}\\ & =& 0.64\end{array}$$

The supply curve is inelastic in this region of the supply curve.

$$\begin{array}{rcl}\text{Percentagechangeinquantitydemanded}& =& \text{[(changeinquantity)/(originalquantity)]×100}\\ & =& \text{[22 – 30]/[(22 + 30)/2]×100}\\ & =& \text{–8/26×100}\\ & =& \text{–30.77}\\ \text{Percentagechangeinincome}& =& \text{[(changeinincome)/(originalincome)]×100}\\ & =& \text{[38,000 – 25,000]/[(38,000 + 25,000)/2]×100}\\ & =& \text{13/31.5×100}\\ & =& \text{41.27}\end{array}$$

In this example, bread is an inferior good because its consumption falls as income rises.

The formula for cross-price elasticity is % change in Qd for apples / % change in P of oranges. Multiplying both sides by % change in P of oranges yields:

% change in Qd for apples = cross-price elasticity X% change in P of oranges

= 0.4 × (–3%) = –1.2%, or a 1.2 % decrease in demand for apples.