S(p)= -200+50p
D(p)=1000-25p
Find the equilibrium price for t shirts at this concert. What is the equilibrium quantity?
To find the equilibrium price and quantity for t-shirts at this concert, we need to set the supply (S) equal to the demand (D).
We have the supply function S(p) = -200 + 50p and the demand function D(p) = 1000 - 25p.
Setting S(p) equal to D(p), we get -200 + 50p = 1000 - 25p.
Now, let's solve the equation to find the equilibrium price.
-200 + 50p + 25p = 1000
75p = 1200
p = 1200/75
p = 16
So the equilibrium price for t-shirts at this concert is $16.
To find the equilibrium quantity, we can substitute this equilibrium price (p = 16) into the supply or demand equation.
Using the demand function D(p) = 1000 - 25p, we substitute p = 16 into the equation:
D(p) = 1000 - 25(16)
D(p) = 1000 - 400
D(p) = 600
Therefore, the equilibrium quantity for t-shirts at this concert is 600.