In a village the supply of agricultural labour is given by $L_s=0.4W^{0.6}$, where $L_s$ is in thousands of workers and $W$ is the daily wage rate in rupees. If the wage rises from Rs. 90 to Rs. 120, calculate the price elasticity of supply of agricultural labour over this interval using the arc‑elasticity method.

Step-by-step solution

1. Calculate labour supplied at the initial wage: $L_1=0.4\times 90^{0.6}\approx 5.95$ thousand workers.
2. Calculate labour supplied at the new wage: $L_2=0.4\times 120^{0.6}\approx 7.08$ thousand workers.
3. Find the change in labour supplied: $\Delta L=L_2-L_1=1.13$ thousand.
4. Compute the average labour supplied: $L_{avg}=(L_1+L_2)/2\approx 6.515$ thousand.
5. Find the change in wage: $\Delta W=120-90=30$ rupees.
6. Compute the average wage: $W_{avg}=(90+120)/2=105$ rupees.
7. Apply the arc‑elasticity formula: $\epsilon =(\Delta L/L_{avg})÷(\Delta W/W_{avg})=(1.13/6.515)/(30/105)\approx 0.607$.
8. Round to two decimal places: $\epsilon \approx 0.61$.
9. Interpretation: the supply is inelastic since $\epsilon <1$.

Concept tested: Elasticity of agricultural labour supply

Published 16 October 2026 · How this solution was prepared and checked