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Consider a demand function: Qd = 10−3P a) Determine and interpret the price elasticity for a price change from 5.00 to 3.00. b) To boost revenue should this firm increase or decrease its price. Explain.

Economics

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Answer

a
-4

Step-by-step solution

4 steps

here are the solutions for questions 10 and 11.

10. Consider a demand function: Qd=10−3PQ_d = 10 - 3P

Part a· 4 steps

Determine and interpret the price elasticity for a price change from \5.00toto$3.00$.

  1. Calculate the initial and new quantities demanded.

    • Initial Price (P1P_1) = \5.00$ Q1=10−3(5)=10−15=−5Q_1 = 10 - 3(5) = 10 - 15 = -5 Since quantity demanded cannot be negative, at a price of \5.00,thequantitydemandedis, the quantity demanded is Q_1 = 0$.
    • New Price (P2P_2) = \3.00$ Q2=10−3(3)=10−9=1Q_2 = 10 - 3(3) = 10 - 9 = 1

  2. Use the midpoint formula for price elasticity of demand (PED).

    PED=Q2−Q1(Q1+Q2)/2P2−P1(P1+P2)/2\text{PED} = \frac{\frac{Q_2 - Q_1}{(Q_1 + Q_2)/2}}{\frac{P_2 - P_1}{(P_1 + P_2)/2}}

  3. Substitute the values into the formula.

    PED=1−0(0+1)/23−5(5+3)/2\text{PED} = \frac{\frac{1 - 0}{(0 + 1)/2}}{\frac{3 - 5}{(5 + 3)/2}} PED=10.5−24\text{PED} = \frac{\frac{1}{0.5}}{\frac{-2}{4}} PED=2−0.5\text{PED} = \frac{2}{-0.5} PED=−4\text{PED} = -4

  4. Interpret the elasticity value.

    The absolute value of the price elasticity of demand is ∣−4∣=4|-4| = 4. Since 4>14 > 1, the demand is elastic. This means that a 1% change in price leads to a 4% change in quantity demanded in the opposite direction.

    The price elasticity of demand is −4\boxed{-4}. Demand is elastic.

Part b

To boost revenue should this firm increase or decrease its price. Explain.

To boost revenue, the firm should decrease its price.
Since the demand is elastic (PED > 1 in absolute terms), a decrease in price will lead to a proportionally larger increase in the quantity demanded, which will result in an overall increase in total revenue.

11. Distinguish between: Total utility, Marginal utility and The law of Diminishing Marginal utility.

  • Total Utility: The overall satisfaction or happiness a consumer receives from consuming a specific quantity of a good or service. It represents the sum of all marginal utilities from each unit consumed.
  • Marginal Utility: The additional satisfaction or benefit a consumer gains from consuming one more unit of a good or service. It is the change in total utility resulting from a one-unit change in consumption.
  • Law of Diminishing Marginal Utility: This economic principle states that as a consumer consumes more and more units of a specific good or service, the additional satisfaction (marginal utility) derived from each successive unit tends to decrease.
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