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28 March, 21:22

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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  1. 28 March, 21:37
    0
    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
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