The supply of agricultural labour in a village is given by the equation $L_s=0.5W^{0.4}$, where $L_s$ is labour supplied (in thousands) and $W$ is the daily wage rate (in rupees). If the wage rate rises from Rs. 80 to Rs. 100, calculate the price elasticity of supply of agricultural labour over this interval.

Step-by-step solution

1. Calculate labour supplied at $W=80$: $L_1=0.5\times 80^{0.4}$. Using a calculator, $80^{0.4}\approx 4.03$, so $L_1\approx 2.015$ thousand workers.
2. Calculate labour supplied at $W=100$: $L_2=0.5\times 100^{0.4}$. $100^{0.4}\approx 4.64$, so $L_2\approx 2.32$ thousand workers.
3. Find the percentage change in quantity supplied using the midpoint formula: $\Delta Q\%=\frac{L_2-L_1}{(L_1+L_2)/2}\times 100=\frac{2.32-2.015}{(2.015+2.32)/2}\times 100\approx 13.2\%$.
4. Find the percentage change in wage rate using the midpoint formula: $\Delta W\%=\frac{100-80}{(100+80)/2}\times 100=\frac{20}{90}\times 100\approx 22.22\%$.
5. Elasticity $\epsilon =\frac{\Delta Q\%}{\Delta W\%}=\frac{13.2}{22.22}\approx 0.59$.
6. Since the question asks for elasticity over the interval (not midpoint), use the simple change method: $\epsilon =\frac{(L_2-L_1)/L_1}{(W_2-W_1)/W_1}=\frac{(2.32-2.015)/2.015}{(100-80)/80}=\frac{0.151}{0.25}=0.60$.
7. Rounded to two decimal places, elasticity is about $0.60$, indicating inelastic supply. (If using midpoint method, value is $0.32$; both show inelasticity).

Concept tested: Elasticity of labour supply

Published 4 October 2026 · How this solution was prepared and checked