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What is the price elasticity of demand as price increases from 2 per unit to 4 per unit? Use the point formula in your calculation.

Economics

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Answer

A

1/3\boxed{1/3}

Step-by-step solution

13 steps

Here are the solutions to the questions:

1. What is the price elasticity of demand as price increases from $2 per unit to $4 per unit? Use the point formula in your calculation.

  1. Determine the equation of the demand curve from the diagram.

    The demand curve is a straight line passing through (Q=0,P=8)(Q=0, P=8) and (Q=16,P=0)(Q=16, P=0).
    The slope of the demand curve (ΔPΔQ\frac{\Delta P}{\Delta Q}) is 8−00−16=8−16=−12\frac{8-0}{0-16} = \frac{8}{-16} = -\frac{1}{2}.
    So, the inverse slope (ΔQΔP\frac{\Delta Q}{\Delta P}) is −2-2.
    The demand function can be written as Q=−2P+16Q = -2P + 16.

  2. Identify the initial price and quantity.

    As price increases from 2perunit,weusetheinitialpointforthepointelasticityformula.When2 per unit, we use the initial point for the point elasticity formula. When P = $2,, Q = -2(2) + 16 = -4 + 16 = 12.So,theinitialpointis. So, the initial point is (P=2, Q=12)$.

  3. Calculate the price elasticity of demand using the point formula.

    The point elasticity of demand formula is Ed=dQdP×PQE_d = \frac{dQ}{dP} \times \frac{P}{Q}.
    From Step 1, dQdP=−2\frac{dQ}{dP} = -2.

    Ed=−2×212=−2×16=−13E_d = -2 \times \frac{2}{12} = -2 \times \frac{1}{6} = -\frac{1}{3}

    The absolute value of the elasticity is 13\frac{1}{3}.

  4. Select the correct option.

    The calculated elasticity is −13-\frac{1}{3}, and its absolute value is 13\frac{1}{3}.
    The correct option is a) 1/3\boxed{1/3}.

    2. Suppose that a 2% increase in price results in a 6% decrease in quantity demanded. Own-price elasticity of demand is equal to:

  5. Use the formula for price elasticity of demand.

    The formula for price elasticity of demand is Ed=%ΔQ%ΔPE_d = \frac{\% \Delta Q}{\% \Delta P}.

  6. Substitute the given percentage changes.

    A 6% decrease in quantity demanded means %ΔQ=−6%\% \Delta Q = -6\%.
    A 2% increase in price means %ΔP=2%\% \Delta P = 2\%.

    Ed=−6%2%=−3E_d = \frac{-6\%}{2\%} = -3
  7. Select the correct option.

    The absolute value of the elasticity is ∣−3∣=3|-3| = 3.
    The correct option is d) 3\boxed{3}.

    3. If goods X and Y are SUBSTITUTES, then which of the following could be the value of the cross price elasticity of demand for good Y?

  8. Understand the relationship between substitutes and cross-price elasticity.

    For substitute goods, an increase in the price of one good (e.g., good Y) leads to an increase in the quantity demanded of the other good (good X).
    The cross-price elasticity of demand (ExyE_{xy}) is calculated as Exy=%ΔQx%ΔPyE_{xy} = \frac{\% \Delta Q_x}{\% \Delta P_y}.

  9. Determine the sign of the cross-price elasticity for substitutes.

    If PyP_y increases (positive change), QxQ_x increases (positive change). Therefore, the ratio of two positive changes will be positive.
    So, for substitutes, the cross-price elasticity of demand must be positive (Exy>0E_{xy} > 0).

  10. Evaluate the given options.

    a) -1 (negative)

    b) -2 (negative)

    c) Neither a) nor b).

    d) Both a) and b).
    Since the cross-price elasticity for substitutes must be positive, neither -1 nor -2 are possible values.
    The correct option is c) Neither a) nor b)\boxed{\text{Neither a) nor b)}}.

    4. If pizza is a normal good, then which of the following could be the value of income elasticity of demand?

  11. Understand the definition of a normal good in relation to income elasticity.

    A normal good is a good for which demand increases as consumer income increases.
    The income elasticity of demand (EIE_I) is calculated as EI=%ΔQ%ΔIE_I = \frac{\% \Delta Q}{\% \Delta I}.

  12. Determine the sign of the income elasticity for a normal good.

    If income (II) increases (positive change), the quantity demanded (QQ) also increases (positive change). Therefore, the ratio of two positive changes will be positive.
    So, for a normal good, the income elasticity of demand must be positive (EI>0E_I > 0).

  13. Evaluate the given options.

    a) 0.2 (positive)

    b) 0.8 (positive)

    c) 1.4 (positive)

    d) All of the above.
    All the values 0.2, 0.8, and 1.4 are positive, which is consistent with pizza being a normal good. (0.2 and 0.8 would indicate a necessity, while 1.4 would indicate a luxury, both of which are types of normal goods).
    The correct option is d) All of the above\boxed{\text{All of the above}}.

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