Final answer:
The equilibrium price is $1.50 per dozen eggs, and the equilibrium quantity is 500 dozen eggs, determined by setting the demand function equal to the supply function and solving for the price and quantity. These values can then be represented on a graph where the demand and supply curves intersect.
Step-by-step explanation:
To find the free-market equilibrium price and quantity of eggs using the demand function Qd = 650 - 100P and the supply function Qs = 50 + 300P, we start by setting Qd equal to Qs:
- 650 - 100P = 50 + 300P
- 600 = 400P
- P = 600/400 = 1.5
At the equilibrium price P = 1.5, we can solve for the equilibrium quantity:
- Qd = 650 - 100(1.5) = 500
- Qs = 50 + 300(1.5) = 500
Therefore, the equilibrium price is $1.50 per dozen eggs, and the equilibrium quantity is 500 dozen eggs.
Next, we draw a graph with price on the vertical axis and quantity on the horizontal axis. The demand curve will start at a price intercept of 6.5 (when Qd is 0) and slope downwards, while the supply curve will start at a price intercept of 0.1667 (when Qs is 0) and slope upwards. The point where these two curves intersect represents the equilibrium price and quantity.