Math Problem Statement

Hitunglah elastisitas antara P = 5 dan P = 3, serta P = 3 dan P = 7 berdasarkan tabel harga dan jumlah permintaan (Qd).

Solution

The image you provided contains a table and formula related to price elasticity of demand. Here's the breakdown of the elements and how to solve it:

Information from the Image:

  1. Table:

    • QdQ_d (Quantity Demanded) and PP (Price):
      Qd (Quantity Demanded)P (Price)
      53
      35
      17
  2. Formula for Elasticity of Price EpE_p: Ep=Q2Q1P2P1×P2+P1Q2+Q1E_p = \frac{Q_2 - Q_1}{P_2 - P_1} \times \frac{P_2 + P_1}{Q_2 + Q_1}

  3. Questions:

    • (a) Calculate the elasticity between P=5P = 5 and P=3P = 3.
    • (b) Calculate the elasticity between P=3P = 3 and P=7P = 7.

Step-by-Step Solutions:

(a) Elasticity between P=5P = 5 and P=3P = 3:

  • From the table:
    • When P=5P = 5, Q=3Q = 3
    • When P=3P = 3, Q=5Q = 5

Plug into the formula: Ep=5335×3+55+3=22×88=1E_p = \frac{5 - 3}{3 - 5} \times \frac{3 + 5}{5 + 3} = \frac{2}{-2} \times \frac{8}{8} = -1 The price elasticity is 1-1, indicating unitary elasticity.

(b) Elasticity between P=3P = 3 and P=7P = 7:

  • From the table:
    • When P=3P = 3, Q=5Q = 5
    • When P=7P = 7, Q=1Q = 1

Plug into the formula: Ep=1573×7+31+5=44×106=1×53=531.67E_p = \frac{1 - 5}{7 - 3} \times \frac{7 + 3}{1 + 5} = \frac{-4}{4} \times \frac{10}{6} = -1 \times \frac{5}{3} = -\frac{5}{3} \approx -1.67 The price elasticity is approximately 1.67-1.67, indicating elastic demand.


Would you like further clarification or more details? Here are some related questions:

  1. What does it mean when elasticity is negative?
  2. How does unitary elasticity affect revenue?
  3. How do we interpret elastic vs inelastic demand?
  4. What other factors might influence the elasticity of a product?
  5. Can elasticity be used to predict consumer behavior?

Tip: The greater the absolute value of elasticity, the more sensitive the quantity demanded is to changes in price.

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Math Problem Analysis

Mathematical Concepts

Price Elasticity of Demand
Algebra

Formulas

Ep = (Q2 - Q1) / (P2 - P1) * (P2 + P1) / (Q2 + Q1)

Theorems

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Suitable Grade Level

University Economics