Answer to Question #198666 in Math for Sarah

Question

The supply and demand functions for a product are 𝑞𝑠 = 𝑝 2 − 300 𝑎𝑛𝑑 𝑞𝑑 = 𝑝 2 − 30𝑝 + 2200 . Determine the market equilibrium price and quantity.

Answer 1

In equilibrium $q_s=q_d$

$$p^2-300=p^2-30p+2200$$

$$30p=2500$$

$$p=\dfrac{250}{3}\approx83.33$$

$$q_s=(\dfrac{250}{3})^2-300\approx6644$$

$$q_d\approx6644$$