Question

James teaches basketball lessons for extra cash at a wage of $75.00 per hour. she is willing to teach 18 hours per week. At $100.00 per hour she teaches 20 kids per week. The Elasticity of Jame's labor supply between the wages of $75.00 and $100.00 per hour is (fill in the blank), whick means that Jame's supply of labor over the range is (fill in the blank).

** the choices to pick from are:

1

0.4

2.71

0.37

and

unit elastic, inelastic, elastic

Answer 1

Elasticity of labour supply gives the sensitivity of supply of labour to changes in the wage rate. It is defined as the ratio of percentage change in labour supply (S) upon percentage change in wage rate (W).

es = %change in labour supply / % change in wage rate

es = (dS/S * 100) / (dW/W * 100) = (W/S) * (dS/dW)

where dS = S2- S1 and dW = W2 - W1

When the wage rae is $75 per hour, the no. of hours taught is 18 hours per week.

So let W1 = 75 and S1= 18

And when wage rate increases to $100 per hour, the no. of hours taught is 20 hours per week.

So let W2 = 100 and S2 = 20

Now,

es  = (W/S) * (dS/dW) = (W1/S1) * (S2-S1/W2-W1)

= (75/18) * (20-18/100-75)

= (75/18) * (2/25)

= 4.2 * 0.08 = 0.336 = 0.34 ~ 0.37 (closest option given)

So, es  = 0.37 < 1

Since elasticity of labour supply is less than one, it is inelastic. This means that there is a low responsiveness of labour supply to changes in wage rate .

Thus, the elasticity of Jame's labor supply between the wages of $75.00 and $100.00 per hour is (0.37), which means that Jame's supply of labor over the range is (inelastic).