Question

The demand product is P=400-10Qd and the supply is P=200+10Qs. What is the price elasticity I’d demand for this product when the market is in equilibrium?

Answer 1

Market equilibrium occurs when $P_d=P_s$:

$$400-10Q_E=200+10Q_E,$$ $$200=20Q_E,$$ $$Q_E=10.$$

Then we can find equilibrium price:

$$P_E=400-10\cdot10=\$300.$$

We can find the elasticity of the demand when the market is in equilibrium as follows:

$$E_d=-(\dfrac{1}{slope})\dfrac{P}{Q_d},$$ $$E_d=-(\dfrac{1}{-10})\dfrac{300}{10}=-3.0.$$