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amanda2517
30.03.2020 •
Mathematics
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.)
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Ответ:
Demand is Elastic when Price > 200 ; Demand is inelastic when Price < 200
Step-by-step 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
Ответ:
£32
Step-by-step explanation:
12 + 4(5) = 32
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