Calculate the price elasticity of demand for a change in price from $10.00 to $15.00.

Price

Quantity

$10.00

20

$15.00

15

Question

Calculate the price elasticity of demand for a change in price from $10.00 to $15.00.

Price

Quantity

$10.00

20

$15.00

15

BlackTom AI · Accepted Answer

To approach this problem, I will compute the price elasticity of demand using the available price and quantity data:

Prices: P1 = 10, P2 = 15
Quantities: Q1 = 20, Q2 = 15

First, determine the changes in quantity and price:
- Change in quantity, ΔQ = Q2 - Q1 = 15 - 20 = -5
- Change in price, ΔP = P2 - P1 = 15 - 10 = 5

Next, decide on a method for elasticity. The most common approach for a discrete change is the arc (midpoint) elasticity formula, which reduces bias when the change is sizable. The midpoint method uses average quantities and prices:
- Average quantity, Q̄ = (Q1 + Q2) / 2 = (20 + 15) / 2 = 17.5
- Average price, P̄ = (P1 + P2) / 2 = (10 + 15) / 2 = 12.5

The arc elasticity of demand is given by:
E = (ΔQ / ΔP) × (P̄ / Q̄)
Plugging in the numbers:
- ΔQ / ΔP = (-5) / 5 = -1
- P̄ / Q̄ = 12.5 / 17.5 ≈ 0.7143
Therefore, E ≈ (-1) × 0.7143 ≈ -0.7143

So, the elasticity of demand for this price change, using the midpoint method, is approximately -0.71 (rounded to two decimals).

If you instead used other common methods (for example, elasticity relative to the initial values), you would get a different number: using the initial base, E = (ΔQ / Q1) / (ΔP / P1) = (-5 / 20) / (5 / 10) = (-0.25) / 0.5 = -0.50. If you used the final base, E = (ΔQ / Q2) / (ΔP / P2) = (-5 / 15) / (5 / 15) = (-0.333…) / (0.333…) = -1.0. These illustrate how the chosen method/base affects the numerical result.

In summary, with the standard arc/midpoint method, the elasticity is about -0.71, indicating inelastic demand over this price range. The alternative methods yield different numbers such as -0.50 or -1.00 depending on the base used; the midpoint approach is generally preferred for sizable discrete changes because it minimizes base-based bias.

Calculate the price elasticity of demand for a change in price from $10.00 to $15.00. Price Quantity $10.00 20 $15.00 15 数值题

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