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?

Question

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Respuesta :

Tundexi Tundexi · Answer 1 · 2020-09-18T04:02:33+02:00

Answer:

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