Question

Suppose that the quantity supplied S and quantity demanded D of T-shirts at a concert are given by the following functions: S(p) = - 200 + 50p D(p) = 1,000 - 25p where p is the price of a T-shirt. Find the equilibrium price for T-shirts at this concert. What is the equilibrium quantity?

Answer 1

The equilibrium price for T-shirts at the concert is $16, while the equilibrium quantity is 600 T-shirts.

Step-by-step explanation:

The equilibrium price for T-shirts at the concert can be found by setting the quantity demanded equal to the quantity supplied.

To find the equilibrium price, we need to solve the equation D(p) = S(p).

Substituting the given equations for D(p) and S(p), we have 1000 - 25p = -200 + 50p.

Combining like terms and simplifying, we get 75p = 1200.

Dividing both sides by 75, we find p = 16.

Therefore, the equilibrium price for T-shirts at this concert is $16.

To find the equilibrium quantity, we can substitute the equilibrium price into either the D(p) or S(p) equation.

Using D(p), we have D(16) = 1000 - 25(16) = 1000 - 400 = 600.

Therefore, the equilibrium quantity is 600 T-shirts.