Question

Calculate equilibrium price and quantity from the given equations.

Hint:

To find equilibrium, set the quantity demanded equal to the quantity supplied and solve for the price. Then substitute the price into either equation to find the equilibrium quantity.

Answer 1

Step 1: Define the equilibrium condition.
At equilibrium, the quantity demanded (\( q_d \)) is equal to the quantity supplied (\( q_s \)). Therefore, we can set the demand equation equal to the supply equation: \[ q_d = q_s \]
Step 2: Substitute the given equations.
We are given the following equations: \[ q_d = 400 - P \] \[ q_s = 200 + P \] At equilibrium, \( q_d = q_s \), so: \[ 400 - P = 200 + P \]
Step 3: Solve for \( P \) (equilibrium price).
Simplifying the equation: \[ 400 - 200 = P + P \] \[ 200 = 2P \] \[ P = \frac{200}{2} = 100 \]
Step 4: Calculate the equilibrium quantity.
Substitute \( P = 100 \) into either the demand or supply equation to find the equilibrium quantity. Using the demand equation: \[ q_d = 400 - 100 = 300 \] So, the equilibrium price is \( P = 100 \) and the equilibrium quantity is \( q = 300 \).