p q2 89 16 and the demand function is p 1592 1024 288 fi

p = q2 + 89 16 and the demand function is p =-1592 + 1024 + 288, find the equilibrium quantity and equilibrium price. If the supply function for a commodity is (q, p) = (

Solution

1) p = q^2 +8q + 16 ; p = -15q^2 +102q + 288

Equilibrium quantity and price : q^2 +8q + 16 = -15q^2 +102q + 288

16q^2 - 94q - 272 =0

solve the quadratic: q = 8, -2.125 >neglect -ve value

So,q = 8 .Plug q=8 to find p:

p = 8^2 + 8*8 +16 = 64 +64 +16 = 144

(q, p ) = ( 8 , 144)

3) Revenue, R(x) = 100x

C(x) = x^2 +40x + 500

At equilibrium: R(x) = C(x)

100x = x^2 +40x +500

x^2 -60x +500 =0

x^2 -50x - 10x +500 =0

x(x-50) -10(x -50) =0

(x -10)(x -50)=0

x = 10, 50 units

4) C(x) = 4500 +4360x ; R(x) = 4500x - x^2

At equilibrium: R(x) = C(x)

4500 +4360x = 4500x - x^2

-x^2 + 140x -4500 =0

On solving for x we get :

x = 50, 90 , units