Question

The demand for apple orchard workers is given by the equation W = 80 - 3 Q and the supply

is given by W = 30 + 2 Q where W is the daily wage rate and Q is the quantity of workers.

Calculate Elasticity of demand and supply at equilibrium price and quantity.

Answer 1

$W=80-3Q$

$W=30+2Q$

At equilibrium, demand=supply;

so, $80-3Q=30+2Q$

like terms, 5Q=50;

$\frac{\cancel5Q}{\cancel5}=\frac{50}{5}$

$Q=\frac{50}{5}=10$

We can find W by substituting Q with 10 in one of the equations.

$W=80-(3\times10)=50$

So, equilibrium point is at 50 for W and 10 for Q.

Elasticity:

$Change in W=50-0=50$

$Average of W=\frac{50+0}{2}=25$

$Percentage change=\frac{50}{25}\times100=200.$

Change in Q$Change in Q=10-0=10$

$Average of Q=\frac{10+0}{2}=5$

$Percentage change=\frac{10}{5}\times100=200.$

$Elasticity=\frac{percentage change in W}{percentage change in Q}=\frac{200}{200}=1$

Elasticity is 1.