Question

1. calculating the price elasticity of supply

shen is a mechanic living in houston who does home renovation projects to supplement his normal income. at an hourly wage rate of $27, he is willing to renovate 9 hours per week. upping the wage to $42 per hour, he is willing to renovate 17 hours per week.
using the midpoint method, the elasticity of shens labor supply between the wages of $27 and $42 per hour is approximately ____ , which means that shens supply of labor over this wage range is ____ .

Explanation:

Step1: Define midpoint elasticity formula

The midpoint formula for price (wage) elasticity of supply is:
$$E_s = \frac{\frac{Q_2 - Q_1}{\frac{Q_2 + Q_1}{2}}}{\frac{W_2 - W_1}{\frac{W_2 + W_1}{2}}}$$
Where $Q_1=9$, $Q_2=17$, $W_1=27$, $W_2=42$

Step2: Calculate quantity change ratio

Compute the percentage change in labor hours:
$$\frac{Q_2 - Q_1}{\frac{Q_2 + Q_1}{2}} = \frac{17 - 9}{\frac{17 + 9}{2}} = \frac{8}{13} \approx 0.6154$$

Step3: Calculate wage change ratio

Compute the percentage change in wage:
$$\frac{W_2 - W_1}{\frac{W_2 + W_1}{2}} = \frac{42 - 27}{\frac{42 + 27}{2}} = \frac{15}{34.5} \approx 0.4348$$

Step4: Compute elasticity value

Divide the quantity ratio by the wage ratio:
$$E_s = \frac{0.6154}{0.4348} \approx 1.415$$

Step5: Interpret elasticity

Since $E_s > 1$, the supply is elastic.

Answer:

1.42 (rounded to two decimal places); elastic