Question

From the data in Table 5.6 about the supply of alarm clocks, calculate the price elasticity of supply from point J to point K, point L to point M, and point N to point P. Classify the elasticity at each point as elastic, inelastic, or unit elastic.

Short answer

J-k: 2.83 --Highly Elastic
L-M: 1.00-- Perfectly elastic
N-P: 0.64 -Inelastic

Step-by-step solution

Definition

The elasticity of demand :

The elasticity of demand is the degree to which demand fluctuates in reaction to changes in another economic component, such as price or income. If demand for an item or service remains constant regardless of price changes, it is said to be inelastic.

Calculation

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

$$\begin{gathered} \%changeinquantity \\ =70–50/\left(\right(70+50)÷2)\times 100 \\ =(20/60)\times 100 \\ =33.33 \\ \%changeinprice \\ =\$9–\$8/((\$9+\$8)÷2)\times 100 \\ =(1/8.5)\times 100 \\ =11.76 \\ ElasticityofSupply \\ =33.33\%/11.76\% \\ =2.83 \end{gathered}$$

Calculation

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:

$$\begin{gathered} \%changeinquantity \\ =88–80/\left(\right(88+80)÷2)\times 100 \\ =(8/84)\times 100 \\ =9.52 \\ \%changeinprice \\ =\$11–\$10/((\$11+\$10)÷2)\times 100 \\ =110.5\times 100 \\ =9.52 \\ ElasticityofDemand \\ =9.52\%/9.52\% \\ =1.0 \end{gathered}$$

Step 4:Calculation

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:

$$\begin{gathered} \%changeinquantity \\ =100–95/\left(\right(100+95)÷2)\times 100 \\ =5/97.5\times 100 \\ =5.13 \\ \%changeinprice \\ =\$13–\$12/((\$13+\$12)÷2)\times 100 \\ =1/12.5\times 100 \\ =8.0 \\ ElasticityofSupply \\ =5.13\%/8.0\% \\ =0.64 \end{gathered}$$

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