Algebra Chapter 4: Elasticity and Its Applications
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Questions and Answers

What is the formula for the income elasticity of demand?

  • Qb = 100 –30Pb – 20Pc + 0.005I
  • Ec = e X
  • OR = -b (P/Q)
  • Ey = c X (correct)
  • What is the value of Qb in the given example?

  • 50
  • 65
  • 60
  • 55 (correct)
  • What is the value of the income elasticity of demand in the example?

  • +2.2727 (correct)
  • +2.1
  • +2.5
  • +1.5
  • What is the cross-price elasticity of demand for bubblegum with respect to chips?

    <p>-0.3636</p> Signup and view all the answers

    What is the formula for cross-price elasticity of demand?

    <p>Ec = e X</p> Signup and view all the answers

    What is the price of bubblegum per pack in the example?

    <p>R5</p> Signup and view all the answers

    What is the annual household income in the example?

    <p>R25 000</p> Signup and view all the answers

    What is the formula for the demand function in the example?

    <p>Qb = 100 –30Pb – 20Pc + 0.005I</p> Signup and view all the answers

    What is the formula for a straight line demand curve?

    <p>Qd = a - bP</p> Signup and view all the answers

    What does the intercept 'a' represent in the formula for a straight line demand curve?

    <p>The point of intersection on the y-axis</p> Signup and view all the answers

    What is the formula to calculate the point elasticity of demand?

    <p>-b (P/Q)</p> Signup and view all the answers

    What is the value of the equilibrium price of petrol in the given example?

    <p>3</p> Signup and view all the answers

    What is the value of the equilibrium quantity of petrol in the given example?

    <p>50 000</p> Signup and view all the answers

    What is the meaning of the slope of a straight line demand curve?

    <p>The change in quantity with respect to price</p> Signup and view all the answers

    Study Notes

    Algebra for Elasticity

    • Formula for a straight line: y = mx + c
    • Formula for a straight line demand curve: P = -aQ + b or Qd = a - bP
    • Formula for a straight line supply curve: P = aQ + b or Qs = a + bP
    • a = intercept, b = constant slope i.e. the impact of a unit change in x on the level of y
    • Slope of a straight line: Δy / Δx = (y2 - y1) / (x2 - x1)

    Point (Own-Price) Elasticity of Demand

    • Steps to calculate point elasticity of demand:
      • Make sure Q is the subject of the formula
      • Find equilibrium price and quantity
      • Calculate point elasticity of demand: -b (P/Q)
    • Recall: -b = slope, where ΔQ/ΔP is the slope of the curve

    Example of Point Elasticity of Demand

    • Demand function: QD = 65 000 – 5 000P
    • Supply function: QS = 5 000 + 15 000P
    • Equilibrium price and quantity: P = 3, Q = 50 000
    • Elasticity of demand at market equilibrium: -b (P/Q)

    Income Elasticity of Demand

    • Formula: Ey = CX (I/Y), where Ey is income elasticity of demand, C is the numerical value, I is income, and Y is quantity demanded
    • Example: Qb = 100 – 30Pb – 20Pc + 0.005I, where Qb is quantity demanded of bubblegum
    • Calculate Qb, then Ey = CX (I/Y) = +0.005 (25000/55) = +2.2727

    Cross-Price Elasticity of Demand

    • Formula: Ec = eX (Pc/Q), where Ec is cross-price elasticity of demand, e is the numerical value, Pc is price of related good, and Q is quantity demanded
    • Example: Qb = 100 – 30Pb – 20Pc + 0.005I, where Qb is quantity demanded of bubblegum
    • Calculate Qb, then Ec = eX (Pc/Q) = -20 (1/55) = -0.3636

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    Description

    Quiz on algebra formulas and concepts, focusing on elasticity and its applications, including straight line demand and supply curves.

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