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    Regression Equation and Elasticity

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    The following question refers to this regression equation.
    QD= 15,000 - 10 P + 1500 A+ 4 PX + 2 I

    Q = Quantity demanded
    P= Price = 7,000
    A = Advertising expense,in thousands = 54
    PX = price of competitor's product = 8,000
    I = average monthly income = 4,000
    Calculate the elasticity for each variable (own price elasticity, cross price elasticity, income elasticity, and elasticity of demand for Advertising) and briefly comment on what that information gives you in each case.

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    Solution Preview

    Please see the attached file.

    The regression equation is given by:

    Q = Quantity Demanded
    P = 7000
    A = 54
    Px = 8000
    I = 4000

    The demand elasticity corresponding to a variable X is calculated as:

    It shows the expected percent change in quantity given a one percent increase in the corresponding variable. So let's see each case:

    - Elasticity corresponding to P (called "own-price elasticity")
    We calculate this as:

    As you can see, we must first calculate Q. We do this by plugging the values of the variables into the regression equation:

    Now, we know that P = ...

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