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25 September, 20:33

The inverse demand curve for product X is givenby: PX = 25 - 0.005Q + 0.15PY, where PX represents price in dollars per unit, Qrepresents rate of sales in pounds per week, andPY represents selling price of another product Y indollars per unit. The inverse supply curve ofproduct X is given by: PX = 5 + 0.004Q.

a. Determine the equilibrium price and sales of X. Let PY = $10.

b. Determine whether X and Y are substitutes or complements.

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  1. 26 September, 00:28
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    (a) $14.56; 2,388.88

    (b) Substitute goods

    Explanation:

    Given that,

    Inverse demand curve: PX = 25 - 0.005Q + 0.15PY

    Inverse supply curve: PX = 5 + 0.004Q

    (a) Let PY = $10

    For Equilibrium,

    Supply = Demand

    5 + 0.004Q = 25 - 0.005Q + 0.15PY

    5 + 0.004Q = 25 - 0.005Q + 0.15 (10)

    0.004Q + 0.005Q = 20 + 1.5

    0.009Q = 21.5

    Q = 21.5 : 0.009

    = 2,388.88

    PX = 25 - 0.005Q + 0.15PY

    = 25 - 0.005 (2,388.89) + 0.15 (10)

    = 25 - 11.94 + 1.5

    P = 14.56

    (b) PX = 25 - 0.005Q + 0.15PY

    Q = (25 + 0.15PY - PX) : 0.005

    From the above equation, the coefficient of the price good Y is positive which means that the quantity is positively related with the price of good Y.

    Therefore, as the price of good Y increases then as a result demand for good X increases.

    Hence, good X and Good Y are substitute goods.
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