The market for plywood is characterized by the following demand and supply equations: QD = 800 – 10P and QS = 50P – 1,000, where P is the pr

The market for plywood is characterized by the following demand and supply equations: QD = 800 – 10P and QS = 50P – 1,000, where P is the price per sheet of plywood and Q measures the quantity of plywood. What is the size of the deadweight loss if the government imposes a price ceiling of $25 per sheet of plywood?

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  1. Answer: Dead weight loss-= $3750

    Explanation:

    QD = 800 – 10P

     QS = 50P – 1,000,

    At equilibrium, quantity demanded is equal to quantity supplied , so we have that, equating the two equations becomes

    800 – 10p = 50p – 1000.

    800 + 1000 = 50p + 10p

    1800 = 60p

    p = $30.

    QD= QS= 800 – 10*30 = 500 units

    QD= QS= 50×30 -1000= 500 units

    Qd = Qs = 500 units.

     When P = $25 by government putting a price ceiling, which is below the equilibrium price,it will  lead to more demand than supply in the market

    QD = 800 – 10P

    QD= 800-10X25

    QD=800-250= 550units

    QS = 50P – 1,000,

    Qs = 50 X25  – 1000

    = 1,250-1000

    QS = 250 units.

    When quantity demanded =250units as a result of  Quantity supplied  at 250units. we will  have our new price to be

    QD = 800 – 10P

    250 = 800 – 10p

    10p = 800 -250

    10p = 550

    p = $55.

    To calculate  Dead weight Loss, we use the formulae,

    0.5 x  (P2 – P1)  x (Q1 – Q2) where P1 and P2 are old and new prices and Q1 AND Q2 are old and new quantities

    DWL = 0.5 x (55-25) X (500-250)

    = 0.5 x 30x 250

    Dead weight loss = $3750.

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