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Calculate the market demand function.

Economics

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2 parts
a

QMD=3900−150PQ_{MD} = 3900 - 150P

QMS=150+100PQ_{MS} = 150 + 100P

c(ii)

15 FCFA\text{15 FCFA}

1650 units\text{1650 units}

Step-by-step solution

9 steps

Part a· 2 steps

Determine the market demand and supply functions for fairly used Mercedes cars.

  1. Calculate the market demand function.

    The individual demand function is Qd=52−2PQ_d = 52 - 2P, and there are 75 buyers.

    QMD=75×(52−2P)Q_{MD} = 75 \times (52 - 2P) QMD=3900−150PQ_{MD} = 3900 - 150P
  2. Calculate the market supply function.

    The individual supply function is Qs=15+10PQ_s = 15 + 10P, and there are 10 sellers.

    QMS=10×(15+10P)Q_{MS} = 10 \times (15 + 10P) QMS=150+100PQ_{MS} = 150 + 100P

    The market demand function is QMD=3900−150P\boxed{Q_{MD} = 3900 - 150P} and the market supply function is QMS=150+100P\boxed{Q_{MS} = 150 + 100P}.

Part b· 2 steps

Complete the market demand and supply schedule of fairly used Mercedes cars below.

  1. Calculate Quantity Demanded (QMDQ_{MD}) and Quantity Supplied (QMSQ_{MS}) for each price using the functions from part (a).

    • For P=5P = 5: QMD=3900−150(5)=3900−750=3150Q_{MD} = 3900 - 150(5) = 3900 - 750 = 3150 units QMS=150+100(5)=150+500=650Q_{MS} = 150 + 100(5) = 150 + 500 = 650 units
    • For P=10P = 10: QMD=3900−150(10)=3900−1500=2400Q_{MD} = 3900 - 150(10) = 3900 - 1500 = 2400 units QMS=150+100(10)=150+1000=1150Q_{MS} = 150 + 100(10) = 150 + 1000 = 1150 units
    • For P=15P = 15: QMD=3900−150(15)=3900−2250=1650Q_{MD} = 3900 - 150(15) = 3900 - 2250 = 1650 units QMS=150+100(15)=150+1500=1650Q_{MS} = 150 + 100(15) = 150 + 1500 = 1650 units
    • For P=20P = 20: QMD=3900−150(20)=3900−3000=900Q_{MD} = 3900 - 150(20) = 3900 - 3000 = 900 units QMS=150+100(20)=150+2000=2150Q_{MS} = 150 + 100(20) = 150 + 2000 = 2150 units
  2. Complete the schedule.

    Price (FCFA)5101520
    Quantity demanded(units)315024001650900
    Quantity supplied(units)650115016502150

Part c(i)

The equilibrium price

Using the market demand and supply functions obtained in a) above, determine

Part c(ii)

15 FCFA\text{15 FCFA}

The equilibrium quantity

  1. Set market demand equal to market supply to find the equilibrium price.

    QMD=QMSQ_{MD} = Q_{MS} 3900−150P=150+100P3900 - 150P = 150 + 100P 3900−150=100P+150P3900 - 150 = 100P + 150P 3750=250P3750 = 250P P=3750250P = \frac{3750}{250} P=15P = 15

    The equilibrium price is 15 FCFA\boxed{\text{15 FCFA}}.

  2. Substitute the equilibrium price into either the market demand or market supply function to find the equilibrium quantity.

    Using QMDQ_{MD}:

    Q=3900−150(15)Q = 3900 - 150(15) Q=3900−2250Q = 3900 - 2250 Q=1650Q = 1650

    The equilibrium quantity is 1650 units\boxed{\text{1650 units}}.

Part d· 3 steps

If the government fixes a minimum price of 20 FCFA for these cars, how much will it cost her to maintain the Price?

  1. Calculate the quantity demanded and quantity supplied at the minimum price of 20 FCFA.

    At P=20P = 20 FCFA:
    QMD=3900−150(20)=3900−3000=900Q_{MD} = 3900 - 150(20) = 3900 - 3000 = 900 units
    QMS=150+100(20)=150+2000=2150Q_{MS} = 150 + 100(20) = 150 + 2000 = 2150 units

  2. Determine the surplus quantity.

    Surplus = QMS−QMD=2150−900=1250Q_{MS} - Q_{MD} = 2150 - 900 = 1250 units.

  3. Calculate the cost to the government to maintain the price.

    Cost = Surplus quantity ×\times Minimum price
    Cost = 1250 units×20 FCFA/unit=25000 FCFA1250 \text{ units} \times 20 \text{ FCFA/unit} = 25000 \text{ FCFA}
    The cost to

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