Given the supply and demand functions, determine the equilibrium price and quantity.
P=Qs^2 + 11Qs + 75
P= -Qd + 103
Q=
P=
10pts for correct and detailed answer
P=Qs^2 + 11Qs + 75
P= -Qd + 103
Q=
P=
10pts for correct and detailed answer
-
Not actually a physics question, but I'll give it a go...
P = Qs² + 11Qs + 75 (equation 1)
P = -Qd + 103 (equation 2)
At equilibrium the supply quantity(Qs) = demand quantity (Qd). So equation 2 becomes
P = -Qs + 103 (equation 3)
Equating right hand sides of equations 1 and 3 gives
Qs² + 11Qs + 75 = -Qs + 103
Arranging int to standard quadratic form gives
Qs² + 12Qs - 28 = 0
Factorising
(Qs + 14)(Qs - 2) = 0
So Qs = -14 or 2. Since a negative supply quantity isn't meaningful, we use
Qs = 2, so
Qd = 2
Substituting in equation 2
P = -Qd + 103
= 103 - 2
= 101
Q (=Qs =Qd) = 2
P = Qs² + 11Qs + 75 (equation 1)
P = -Qd + 103 (equation 2)
At equilibrium the supply quantity(Qs) = demand quantity (Qd). So equation 2 becomes
P = -Qs + 103 (equation 3)
Equating right hand sides of equations 1 and 3 gives
Qs² + 11Qs + 75 = -Qs + 103
Arranging int to standard quadratic form gives
Qs² + 12Qs - 28 = 0
Factorising
(Qs + 14)(Qs - 2) = 0
So Qs = -14 or 2. Since a negative supply quantity isn't meaningful, we use
Qs = 2, so
Qd = 2
Substituting in equation 2
P = -Qd + 103
= 103 - 2
= 101
Q (=Qs =Qd) = 2
-
why are asking this question in physics site?