Question

The demand function for a product is modeled by p = 400 − 4x, 0 ≤ x ≤ 100, where p is the price per unit (in dollars) and x is the number of units. (a) Determine when the demand is elastic and inelastic. (Enter your answer using interval notation. If an answer does not exist, enter DNE.)

Answer 1

Demand is Elastic when Price > 200 ; Demand is inelastic when Price < 200

Explanation:

p = 400 - 4x

4x = 400 - p

x = (400 - p) / 4 → x = 100 - p/4

Elasticity of demand [ P ed ] = (Δx / Δp) x (p / x)

Δx / Δp [Differentiating x w.r.t p] = 0 - 1/4 → = -1/4

P ed = -1 x p

4 (400 - p)/4

= -1 x 4p = -p / (400-p)

4 (400 - p)

Price Elasticity of demand : only magnitude is considered, negative sign is ignored (due to negative price demand relationship as per law of demand).

So, Ped = p / (400 - p)

Demand is Elastic when P.ed > 1

p / (400-p) > 1

p > 400 - p

p + p > 400 → 2p > 400

p > 400 / 2 → p > 200

Demand is inelastic when P.ed < 1

p / (400-p) < 1

p < 400 - p

p + p < 400 → 2p < 400

p < 400 / 2 → p < 200