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Economics

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Step-by-step solution

4 steps

Here's a breakdown of the problem, assuming the demand function is Qd=23−32PQ_d = 23 - \frac{3}{2}P.

  1. Calculate the quantity demanded (QdQ_d) for various prices.

    The demand function is given as Qd=23−32PQ_d = 23 - \frac{3}{2}P.
    We will calculate QdQ_d for the prices P=20P=20, P=22P=22, and P=28P=28. Note that quantity demanded cannot be negative in a real-world scenario, so if a calculation yields a negative QdQ_d, we will consider it to be 0.

    • For P=20P = 20:

      Qd=23−32(20)=23−3×10=23−30=−7Q_d = 23 - \frac{3}{2}(20) = 23 - 3 \times 10 = 23 - 30 = -7

      Since quantity demanded cannot be negative, Qd=0Q_d = \boxed{0}.

    • For P=22P = 22:

      Qd=23−32(22)=23−3×11=23−33=−10Q_d = 23 - \frac{3}{2}(22) = 23 - 3 \times 11 = 23 - 33 = -10

      Since quantity demanded cannot be negative, Qd=0Q_d = \boxed{0}.

    • For P=28P = 28:

      Qd=23−32(28)=23−3×14=23−42=−19Q_d = 23 - \frac{3}{2}(28) = 23 - 3 \times 14 = 23 - 42 = -19

      Since quantity demanded cannot be negative, Qd=0Q_d = \boxed{0}.

  2. Determine points for drawing the demand curve.

    To draw the demand curve, we typically plot Price (P) on the vertical axis and Quantity Demanded (QdQ_d) on the horizontal axis. We find the intercepts:

    • QdQ_d-intercept (when P=0P=0):

      Qd=23−32(0)=23Q_d = 23 - \frac{3}{2}(0) = 23

      This gives the point (Qd,P)=(23,0)(Q_d, P) = (23, 0).

    • P-intercept (when Qd=0Q_d=0):

      0=23−32P0 = 23 - \frac{3}{2}P 32P=23\frac{3}{2}P = 23 P=23×23=463≈15.33P = 23 \times \frac{2}{3} = \frac{46}{3} \approx 15.33

      This gives the point (Qd,P)=(0,15.33)(Q_d, P) = (0, 15.33).

  3. Describe how to draw the demand curve.

    The demand curve is a straight line connecting the points (23,0)(23, 0) and (0,15.33)(0, 15.33). For any price above P≈15.33P \approx 15.33, the quantity demanded is 0. The calculated points from Step 1 (for P=20,22,28P=20, 22, 28) all result in Qd=0Q_d=0, meaning they lie on the vertical axis (where Qd=0Q_d=0) above the P-intercept.

  4. State factors that cause a change in demand.

    A change in demand (a shift of the entire demand curve) is caused by factors other than the price of the good itself. These factors include:

    • Consumer income: An increase in income generally increases demand for normal goods and decreases demand for inferior goods.
    • Tastes and preferences: Changes in consumer preferences can increase or decrease demand.
    • Price of related goods:
      • Substitutes: An increase in the price of a substitute good increases demand for the original good.
      • Complements: An increase in the price of a complementary good decreases demand for the original good.
    • Consumer expectations: Expectations about future prices or income can influence current demand.
    • Number of buyers: An increase in the number of consumers in the market will increase overall demand.
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