Question

An increase in the market price of men's haircuts, from $\backslash (15$per haircut to $\backslash )25$per haircut, initially causes a local barbershop to have its employees work overtime to increase the number of daily haircuts provided from $35$to$45$. When the $\$25$ market price remains unchanged for several weeks and all other things remain equal as well, the barbershop hires additional employees and provides $65$ haircuts per day. What is the short-run price elasticity of supply? What is the long-run price elasticity of supply?

Short answer

The price elasticity of supply for daily haircut in long is equal to $1.2.$

Step-by-step solution

Given data:

Increase in men's haircuts, from $\$15$to $\$25$per haircut, causes local barbershop to make employees to work overtime to increase daily haircuts from $35$to $45$.In case of unchanged for several weeks, all other things also remain equal as well, the barber provides $65$haircuts per day by hire additional employees.

To find short-run price elasticity of supply and long -run price elasticity of supply.

Calculation of elasticity of supply :

Supply elasticity measures the price responsiveness of a supply. Supply elasticity indicates the rate of change in supply due to percentage price changes. This is calculated as

$e_v=\frac{Q_2-Q_1}{\left(\frac{Q_2+Q_1}{2}\right)}÷\frac{P_2-P_1}{\left(\frac{P_2+P_1}{2}\right)}$

Here,

$P_1-$initial price

role="math" localid="1651937712468" $P_2-$final price

$Q_1-$initial quantity supplied

$Q_2-$ final quantity supplied after the price change

Long run and Short run:

The elasticity ofthe supply often depends onhow long it is measured.This means that the elasticity of the supply of the same goodcan be different in the shortand long term. This is becausecompanies cannot change their inputs in the shortterm. Therefore, to change the supply,you need to change thestrength ofthe existinginput. In the long run,companies can change all inputsaccordingly, with a moreprice-elastic supply.

To calculate the elasticity of supply in short run:

In this case, the price will rise from $\$15$to $\$25$ in the short term. This allows the company to increase its supply to only $35$to $45$haircuts per day. next,

localid="1651938728835" $P_1=\$15$$,P_2=\$25,$localid="1651938843275" $Q_1=35$and $Q_2=45$.

Calculate the elasticity of supply in short run is:

$e_s=\frac{Q_2-Q_1}{\left(\frac{Q_2+Q_1}{2}\right)}÷\frac{P_2-P_1}{\left(\frac{P_2+P_1}{2}\right)}$

$=\frac{45-35}{\left(\frac{45+35}{2}\right)}÷\frac{25-15}{\left(\frac{25+15}{2}\right)}$

$$\begin{gathered} =\frac{10}{40}÷\frac{10}{20} \\ =0.5 \end{gathered}$$

Therefore, the short-run elasticity of supply is$0.5.$

To calculate the elasticity of supply in long run :

In this case, the price will rise from $\$15$to $\$25$ in the long run. This allows the company to increase offers only for 35 to 65 haircuts per day. next,

$P_1=\$15,P_2=\$25,Q_1=35$and $Q_2=65.$

Calculate the elasticity of supply in long-run is:

$e_s=\frac{Q_2-Q_1}{\left(\frac{Q_2+Q_1}{2}\right)}÷\frac{P_2-P_1}{\left(\frac{P_2+P_1}{2}\right)}$

$=\frac{65-35}{\left(\frac{65+35}{2}\right)÷\frac{25-15}{\left(\frac{25+15}{2}\right)}}$

$=\frac{30}{50}÷\frac{10}{20}$

localid="1651939733281" $=1.2.$

Therefore, the price elasticity of supply for daily haircut equal to$1.2$in the long run.