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19 July, 11:15

At $ 0.49 per bushel, the daily supply for wheat is 409 bushels, and the daily demand is 589 bushels. When the price is raised to $ 0.85 per bushel, the daily supply increases to 529 bushels, and the daily demand decreases to 229 bushels. Assume that the price-supply and price-demand equations are linear.

(A) Find the supply equation.

(B) Find the demand equation.

(C) Find the equilibrium price and quantity

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  1. 19 July, 11:17
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    (A) Find the supply equation.

    Qs = 245.67 + 333.33Ps

    (B) Find the demand equation.

    Qd = 1079 - 1000Pd

    (C) Find the equilibrium price and quantity

    Price P = $0.625

    Quantity Q = 454 bushels

    Step-by-step explanation:

    The demand equation is of the form;

    Q = a - bP

    The supply equation is of the form;

    Q = c + eP

    We need to determine the values of a, b, c, d;

    At $ 0.49 per bushel, the daily supply for wheat is 409 bushels, and the daily demand is 589 bushels

    589 = a - b (0.49) ... 1

    409 = c + e (0.49) ... 2

    When the price is raised to $ 0.85 per bushel, the daily supply increases to 529 bushels, and the daily demand decreases to 229 bushels;

    229 = a - b (0.85) ... 3

    529 = c + e (0.85) ... 4

    Subtract equation 3 from 1

    589-229 = b (0.85) - b (0.49)

    360 = b (0.36)

    b = 360:0.36

    b = 1000

    Using equation 1

    589 = a - 1000 (0.49)

    a = 589+490 = 1079

    Subtract equation 2 from 4

    529-409 = e (0.85) - e (0.49)

    120 = 0.36e

    e = 120/0.36

    e = 333.33

    Using equation 2

    409 = c + 333.33 (0.49)

    c = 409 - 333.33 (0.49)

    c = 245.67

    Therefore the demand equation is;

    Qd = 1079 - 1000Pd

    The supply equation is;

    Qs = 245.67 + 333.33Ps

    The equilibrium price is at Qs = Qd and Ps = Pd

    1079-1000P = 245.67 + 333.33P

    P = (1079-245.67) / (1000+333.33)

    P = $0.625

    Qd = 1079 - 1000 (0.625)

    Qs = Qd = 454
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