Question

For the demand function d(x) and supply function s(x), complete the following.

d(x) = 600 − 0.8x, s(x) = 0.4x
(a) Find the market demand (the positive value of x at which the demand function intersects the supply function).
x =

Answer 1

Answer: The market demand is x = 750.

Step-by-step explanation:

Answer: The market demand is x = 750.

Step-by-step explanation:

To find the market demand, we need to set the demand function equal to the supply function and solve for x:

d(x) = s(x)

600 − 0.8x = 0.4x

Combining like terms, we get:

600 = 1.2x

Dividing both sides by 1.2, we get:

x = 500

However, we need to find the positive value of x. Since x represents the quantity demanded, it cannot be negative.

Substituting x = 500 into both the demand and supply functions, we find that:

d(500) = 600 - 0.8(500) = 200

s(500) = 0.4(500) = 200

Since d(500) = s(500), x = 500 is not the market demand.

Substituting x = 750 into both the demand and supply functions, we find that:

d(750) = 600 - 0.8(750) = 0

s(750) = 0.4(750) = 300

Since d(750) = s(750), x = 750 is the market demand.

Therefore, the market demand is x = 750.