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13 January, 09:19

Revenue

Repeat Exercise 45 given that when p = $5, x = 300 units, and when p = $4, x = 400 units.

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Answers (1)
  1. 13 January, 09:23
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    i. C = 9.76, k = - 0.00223

    ii. the demand model can be written as;

    p = 9.76e^ (-0.00223x)

    Question:

    i. Find th values of C and k.

    ii. Write the demand.

    Step-by-step explanation:

    The provided demand model is p = Ce^ (kx) the values of p and x are;

    p = $5, x = 300 units and when p = $4, x=400 units.

    We need to find the values of C and k

    First case; Substituting the first case p = $5, x = 300

    5 = Ce^300k ... 1

    Second case: substituting p = $4, x = 400

    4 = Ce^400k ... 2

    Dividing eqn1 by 2

    5/4 = (Ce^300k) / (Ce^400k)

    5/4 = e^ (300k-400k)

    5/4 = e^ (-100k)

    -100k = ln (5/4)

    k = ln (5/4) / (-100)

    k = - 0.00223

    At substituting k into eqn1

    5 = Ce^ (300 * - 0.00223)

    C = 5/e^ (300 * - 0.00223)

    C = 9.76

    Therefore the demand model can be written as;

    p = 9.76e^ (-0.00223x)
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