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Given the following demand and supply equations, Qd = 50 − 2P and Qs = 30 + 3P, create a demand schedule and a supply schedule for prices ranging from 1 to 5.

Economics

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Step-by-step solution

17 steps

Part 2

Demand and Supply Activity

Part a· 2 steps

Create a demand schedule and a supply schedule for prices ranging from $1 to $5.

The given equations are:
Demand: Qd=50−2PQ_d = 50 - 2P
Supply: Qs=30+3PQ_s = 30 + 3P

  1. Calculate QdQ_d and QsQ_s for each price from P=1P=1 to P=5P=5.

    For P=1P=1:
    Qd=50−2(1)=48Q_d = 50 - 2(1) = 48
    Qs=30+3(1)=33Q_s = 30 + 3(1) = 33

    For P=2P=2:
    Qd=50−2(2)=46Q_d = 50 - 2(2) = 46
    Qs=30+3(2)=36Q_s = 30 + 3(2) = 36

    For P=3P=3:
    Qd=50−2(3)=44Q_d = 50 - 2(3) = 44
    Qs=30+3(3)=39Q_s = 30 + 3(3) = 39

    For P=4P=4:
    Qd=50−2(4)=42Q_d = 50 - 2(4) = 42
    Qs=30+3(4)=42Q_s = 30 + 3(4) = 42

    For P=5P=5:
    Qd=50−2(5)=40Q_d = 50 - 2(5) = 40
    Qs=30+3(5)=45Q_s = 30 + 3(5) = 45

  2. Organize the calculated values into a schedule.

    P ($)QdQ_dQsQ_s
    14833
    24636
    34439
    44242
    54045

Part b· 3 steps

Draw the demand and supply curves on a graph.

  1. Set up a graph with Price (P) on the y-axis and Quantity (Q) on the x-axis.

  2. Plot the points for the demand curve (QdQ_d) from the schedule (e.g., (48, 1), (46, 2), etc.) and connect them to form the demand curve.

  3. Plot the points for the supply curve (QsQ_s) from the schedule (e.g., (33, 1), (36, 2), etc.) and connect them to form the supply curve.

Part c· 4 steps

Identify the equilibrium price and quantity and indicate the points on the diagram.

  1. Find the equilibrium where Qd=QsQ_d = Q_s.

    50−2P=30+3P50 - 2P = 30 + 3P
  2. Solve for P.

    50−30=3P+2P50 - 30 = 3P + 2P 20=5P20 = 5P P=205P = \frac{20}{5} P=4P = 4

    The equilibrium price is \boxed{4}$.

  3. Substitute P=4P=4 into either the demand or supply equation to find the equilibrium quantity.

    Qd=50−2(4)=50−8=42Q_d = 50 - 2(4) = 50 - 8 = 42 Qs=30+3(4)=30+12=42Q_s = 30 + 3(4) = 30 + 12 = 42

    The equilibrium quantity is 42\boxed{42}.

  4. On the diagram, the equilibrium point is where the demand and supply curves intersect, at (Quantity = 42, Price = $4).

Part d· 4 steps

What happens in the market at a price of $2? Indicate this scenario on the diagram.

  1. Calculate QdQ_d and QsQ_s at P=2P=2.

    Qd=50−2(2)=50−4=46Q_d = 50 - 2(2) = 50 - 4 = 46 Qs=30+3(2)=30+6=36Q_s = 30 + 3(2) = 30 + 6 = 36
  2. Compare QdQ_d and QsQ_s.

    At P=2P=2, Qd=46Q_d = 46 and Qs=36Q_s = 36. Since Qd>QsQ_d > Q_s, there is a shortage.

  3. Calculate the magnitude of the shortage.

    Shortage=Qd−Qs=46−36=10\text{Shortage} = Q_d - Q_s = 46 - 36 = \boxed{10}
  4. On the diagram, at a price of $2, draw a horizontal line from $2 on the y-axis to intersect both the supply and demand curves.

    The distance between the supply curve (at Qs=36Q_s=36) and the demand curve (at Qd=46Q_d=46) at this price represents the shortage.

Part e· 4 steps

What happens in the market at a price of $5? Indicate this scenario on the diagram.

  1. Calculate QdQ_d and QsQ_s at P=5P=5.

    Qd=50−2(5)=50−10=40Q_d = 50 - 2(5) = 50 - 10 = 40 Qs=30+3(5)=30+15=45Q_s = 30 + 3(5) = 30 + 15 = 45
  2. Compare QdQ_d and QsQ_s.

    At P=5P=5, Qd=40Q_d = 40 and Qs=45Q_s = 45. Since Qs>QdQ_s > Q_d, there is a surplus.

  3. Calculate the magnitude of the surplus.

    Surplus=Qs−Qd=45−40=5\text{Surplus} = Q_s - Q_d = 45 - 40 = \boxed{5}
  4. On the diagram, at a price of $5, draw a horizontal line from $5 on the y-axis to intersect both the demand and supply curves.

    The distance between the demand curve (at Qd=40Q_d=40) and the supply curve (at Qs=45Q_s=45) at this price represents the surplus.

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