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Question

Answer 1

a).

p = √(x+74)

Square on both sides

p² = (x+74)

x+74 = p²

x = p² - 74                 ---------------> supply function

p = √(142 - x)

Square on both sides

p² = (142 - x)

142 - x = p²

x = - p² + 142                 ---------------> Demand function

Find the domain of the demand function :

p = √(142 - x)

Let the function f(x) = √(142 - x)

The domain of a function is all values of x, those makes the function mathematically correct.

Since there shouldn't be any negative numbers in the square root.

The expression (142 - x) should be zero or positive.

142 - x ≥ 0

142 ≥ x

x ≤ 142.

The domain of the above function is (-∞, 142].

Find the domain of the supply function :

p = √(x+74)

Let the function f(x) = √(x+74)

The domain of a function is all values of x, those makes the function mathematically correct.

Since there shouldn't be any negative numbers in the square root.

The expression (x+74) should be zero or positive.

x+74 ≥ 0

x ≥ -74

The domain of the above function is [-74, ∞).
 

 

Answer 2

b)

Supply function.

x = p² - 74                 ---------------- (1)

Demand function.

x = - p² + 142             --------------- (2)

For equilibrium:

p² - 74  = - p² + 142

2p² = 216

p = √216 =14.7

Substitute p = 14.7 in equation (1).

x = p² - 74

x = 14.7² - 74

x = 142

Answer 3

c)

Demand function:

p = √(142 - x)  

Find the revenue function:

R(x) =p*x

        =(√(142 - x))*x

        =x√(142 - x).

Answer 4

d)

Revenue at equilibrium:

At equilibrium x = 142

R(x) = (√(142 - x))*x

         = (√(142 - 142))*142

         = 0