Question

Susan is a stay-at-home parent who lives in San Francisco and does some consulting work for extra cash. At a wage of $40 per hour, she is willing to work 6 hours per week. At $60 per hour, she is willing to work 16 hours per week.

Using the midpoint method, the elasticity of Susan’s labor supply between the wages of $40 and $60 per hour is approximately (0.04 ; 0,44 ; 2.27 ; 22) , which means that Susan’s supply of labor over this wage range is (Elastic/ Inelastic)   .

Answer 1

Elasticity of labor Supply measures the degree of responsiveness of the quantity of labor Supplied to a change in the wage rate. It is calculated as-

Elasticity of labor Supply= % change in quantity of labor Supplied / % change in wage rate

According to the midpoint method-

% change in quantity of labor Supplied= change in quantity/ Average quantity x 100

And

% change in wage rate= change in wage rate/ Average wage rate x 100

Given that at a wage rate of $40, quantity of labor Supplied is 6 hours per week and at a price of $60, quantity of labor Supplied is 16 hours per week.

Initial wage = $40, new wage = $60

Change in wage rate= New wage - Initial wage

Change in wage rate= $60-$40= $20

Average wage rate=( Initial wage + new wage )/2

Average wage rate= ( $40+$60)/2

Average wage rate= $100/2= $50

So,

% change in wage rate= change in wage rate / Average wage rate x 100

% change in wage rate= $20/$50 x 100

% change in wage rate= 0.4 x 100

% change in wage rate= 40%

Initial quantity Supplied=6 hours per week, new quantity supplied= 16 hours per week

Change in quantity of labor Supplied= new quantity - Initial quantity

Change in quantity of labor Supplied= 16 hours per week-6 hours per week= 10 hours per week

Average quantity=( new quantity+ Initial quantity)/2

Average quantity= ( 16+6)/2= 22/2

Average quantity= 11 hours per week

So,

% change in quantity of labor Supplied= change in quantity / Average quantity x 100

% change in quantity of labor Supplied= 10/11 x 100

% change in quantity of labor Supplied= 0.91 x 100

% change in quantity of labor Supplied= 91%

So,

Elasticity of labor Supply= % change in quantity of labor Supplied / % change in wage rate

Elasticity of labor Supply= 91% / 40%

Elasticity of labor Supply= 2.27

Hence, Elasticity of Susan's labor supply is 2.27 ( ANSWER)

Which means that Susan's Supply of labor over this wage range is ELASTIC ( ANSWER)

Elasticity of labor Supply is said to be ELASTIC when percentage change in quantity of labor Supplied is more than percentage change in wage rate. As such, Elasticity of labor Supply is greater than 1. Here, we can see that percentage change in quantity of labor Supplied (91%) is more than percentage change in wage rate ( 40%) and hence Elasticity of labor Supply is greater than 1. As such, Susan's Elasticity of labor Supply is ELASTIC

Option Inelastic is Incorrect because Elasticity of labor supply is said to be inelastic when percentage change in quantity of labor Supplied is less than percentage change in wage rate and Elasticity of labor supply is less than 1. Here, as Elasticity of supply of labor (2.27) is greater than 1 indicating that Elasticity of supply of labor is Elastic and not Inelastic