Answer the following questions for the price-demand equation. p + 0.005x = 30 A. Express the demand x as a function of the price p.
B. Find the elasticity of demand, E(p).
C. What is the elasticity of demand when p = 15 AND what does that mean?
D. If the price is increased by 20%, what is the approximate change in demand?

a. x = 6000 - 200p

b. E(p) = p / (p - 30)

c. E(15) = -1

d. %change in Δ  = -20p/30-p

Step-by-step explanation:

P + 0.005x = 30

a. P + 0.005x = 30

  -P                   -P

         0.005x = 30 - p

We divide both side by 0.005

0.005x = 30 - p

0.005      0.005

x = 30 - p / 0.005    > x = 6000 - 200p

b. E (b) = b/x * dx/dp

x = 6000 - 200p

dx/dp = -200

E(p) = p/x (-200)

E(p) = p / 6000 - 200p * (-200)

E(p) = p / 200(30-p) * (-200)

Cross through by the 200

E(p) = p / (30 - p)

E(p) = p / (p - 30)

c. E(p) = p / (p - 30)

E(15) = 15 / (15-30)

E(15) = 15 / -15

E(15) = -1

This implies that if price increases 1 units, then demand goes down by 1 unit.

d. dx/dp = -200

Δx = dy/dp Δp = (-200) 20p/100

Δx/x = -40/x = -40P / 6000 - 200p

%change in Δ = Δx/x * 100 = -40p/60 - 2p

%change in Δ  = -20p/30-p

the expected value of the random variable : 0, 1 and 2

step-by-step explanation: