demand and supply curve

Question

Answer 1

a).

30p + x - 90 = 0

30p = -x + 90

p = (-1/30) x+ 3    ---------------> Demand function

The function (-1/30) x+ 3 is a linear function .There are no rational or radical expressions, so there is nothing that will restrict the domain. Any real number can be used for x to get a meaningful output.

The domain of the above function is (- ∞, ∞). 

66p - x - 40 = 0

66p = x + 40

p = (1/66) x+ 40/66    ---------------> Supply function

The function (1/66) x+ 40/66 is a linear function .There are no rational or radical expressions, so there is nothing that will restrict the domain. Any real number can be used for x to get a meaningful output.

The domain of the above function is (- ∞, ∞).

Answer 2

b)

30p + x - 90 = 0                ---------------- (1)

Demand function

Qd = -30p+90

66p - x - 40 = 0

Supply function.

Qs = 66p-40

For equilibrium:

-30p+90 = 66p-40

96p = 130

p = 130/96 =1.354

Substitute p = 1.354 in equation (1).

30(1.354) + x - 90 = 0  

x = 49.375

Answer 3

Find the demand function:

30p + x - 90 = 0

30p = -x + 90

p = (-1/30) x+ 3

Find the revenue function:

R(x) =p*x

        =((-1/30) x+ 3)*x

        =(-1/30) x^2 + 3x

d)

Revenue at equilibrium:

At equilibrium x = 49.375

R(x) = (-1/30) x^2 + 3x

         = (-1/30) (49.375)^2 + 3(49.375)

          = 66.86