Question

From the data in Table 5.6 about 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.

Point	Price	Quantity supplied
J	\(8	50
K	\)9	70
L	\(10	80
M	\)11	88
N	\(12	95
P	\)13	100

Short answer

Supply curve from point J to K is elastic; from point L to M is unitary elastic; and from point N to P is inelastic.

Step-by-step solution

Step 1. Formula:

The elasticity of supply curve is computed through the Midpoint Method. To compute the elasticity of supply, the equations are used:

$$\begin{gathered} \%\mathrm{change}\mathrm{in}\mathrm{quantity}=\frac{{\mathrm{Q}}_2-{\mathrm{Q}}_1}{\left({\mathrm{Q}}_2+{\mathrm{Q}}_1\right)/2}\times 100 \\ \%\mathrm{change}\mathrm{in}\mathrm{price}=\frac{{\mathrm{P}}_2-{\mathrm{P}}_1}{\left({\mathrm{P}}_2+{\mathrm{P}}_1\right)/2}\times 100 \\ \mathrm{Price}\mathrm{elasticity}\mathrm{of}\mathrm{supply}=\frac{\%\mathrm{change}\mathrm{in}\mathrm{quantity}}{\%\mathrm{change}\mathrm{in}\mathrm{price}} \end{gathered}$$

Step 2. Supply curve price elasticity from point J to K:

$\begin{array}{rcl}\%\mathrm{change}\mathrm{in}\mathrm{quantity}& =& \frac{70-50}{\left(70+50\right)/2}\times 100\\ & =& \frac{20}{120/2}\times 100\\ & =& \frac{20}{60}\times 100\\ & =& 33.33\%\end{array}$

$\begin{array}{rcl}\%\mathrm{change}\mathrm{in}\mathrm{price}& =& \frac{9-8}{\left(9+8\right)/2}\times 100\\ & =& \frac{1}{17/2}\times 100\\ & =& \frac{1}{8.5}\times 100\\ & =& 11.76\%\end{array}$

$\begin{array}{rcl}\mathrm{Price}\mathrm{elasticity}\mathrm{of}\mathrm{supply}& =& \frac{33.33}{11.76}\\ & =& 2.83\end{array}$

As the price elasticity value of supply curve is greater than 1, the supply curve is elastic in this part.

Step 3. Supply curve price elasticity from point L to M:

$\begin{array}{rcl}\%\mathrm{change}\mathrm{in}\mathrm{quantity}& =& \frac{88-80}{\left(88+80\right)/2}\times 100\\ & =& \frac{8}{168/2}\times 100\\ & =& \frac{8}{84}\times 100\\ & =& 9.52\%\end{array}$

$\begin{array}{rcl}\%\mathrm{change}\mathrm{in}\mathrm{price}& =& \frac{11-10}{\left(11+10\right)/2}\times 100\\ & =& \frac{1}{21/2}\times 100\\ & =& \frac{1}{10.5}\times 100\\ & =& 9.52\%\end{array}$

$\begin{array}{rcl}\mathrm{Price}\mathrm{elasticity}\mathrm{of}\mathrm{supply}& =& \frac{9.52}{9.52}\\ & =& 1\end{array}$

As the price elasticity value of supply curve is equal to 1, the supply curve is unitary elastic in this part.

Step 4. Supply curve price elasticity from point N to P:

$\begin{array}{rcl}\%\mathrm{change}\mathrm{in}\mathrm{quantity}& =& \frac{100-95}{\left(100+95\right)/2}\times 100\\ & =& \frac{5}{195/2}\times 100\\ & =& \frac{5}{97.5}\times 100\\ & =& 5.13\%\end{array}$

$\begin{array}{rcl}\%\mathrm{change}\mathrm{in}\mathrm{price}& =& \frac{13-12}{\left(13+12\right)/2}\times 100\\ & =& \frac{1}{25/2}\times 100\\ & =& \frac{1}{12.5}\times 100\\ & =& 8\%\end{array}$

$\begin{array}{rcl}\mathrm{Price}\mathrm{elasticity}\mathrm{of}\mathrm{supply}& =& \frac{5.13}{8}\\ & =& 0.64\end{array}$

As the price elasticity value of supply curve is less than 1, the supply curve is inelastic in this part.