Final answer:
The equilibrium price for dog clothing is 35, and the equilibrium quantity is 150 units. This is found by setting the demand function equal to the supply function, solving for the price, and then finding the quantity using the determined price.
Step-by-step explanation:
To find the equilibrium price and quantity for dog clothing, we set the demand function Qd equal to the supply function Qs. Given the equations Qd = 500 - 10P and Qs = 5P - 25, we solve for the price P where the quantity demanded equals the quantity supplied.
Solving for P, we have:
Set Qd equal to Qs: 500 - 10P = 5P - 25.
Combine like terms: 10P + 5P = 500 + 25.
Sum the P terms: 15P = 525.
Divide both sides by 15 to find P: P = 525 / 15.
Calculate the value of P: P = 35.
Now that we have the equilibrium price, P, we can find the equilibrium quantity by substituting P back into either the demand or supply equation. If we use the demand equation:
Substitute P = 35 into Qd: Qd = 500 - 10(35)
Calculate Qd: Qd = 500 - 350
Find the quantity: Qd = 150
Thus, the equilibrium price is 35 and the equilibrium quantity is 150 units of dog clothing.