Calculate the price elasticity of demand at points A and B given the demand schedule. Explain the concept of…

Question

Calculate the price elasticity of demand at points A and B given the demand schedule. Explain the concept of price elasticity of demand.

ScanSolve AI Tutor · Accepted Answer

The Price Elasticity of demand refers to the responsiveness of quantity demanded due to a percentage change in the commodity price. Given the demand schedule: Point A: Price (P_A) = 60, Quantity (Q_A) = 20; Point B: Price (P_B) = 15, Quantity (Q_B) = 40 i. The price elasticity of demand at point A (Point Elasticity) Step 1: Calculate the slope of the demand curve ((Δ Q)/(Δ P)) using the two given points. (Δ Q)/(Δ P) = (Q_B − Q_A)/(P_B − P_A) = (40 − 20)/(15 − 60) = (20)/(−45) = −4/9; Step 2: Apply the point elasticity formula E_p = (Δ Q)/(Δ P) × P_A/Q_A using the values at Point A. E_p = (−4/9) × 60/20; E_p = (−4/9) × 3; E_p = −12/9 = −4/3 E_p ≈ −1.33 The price elasticity of demand at point A is −4/3. ii. The price elasticity of demand at point B (Point Elasticity) Step 1: Use the same slope of the demand curve calculated in part (i). (Δ Q)/(Δ P) = −4/9; Step 2: Apply the point elasticity formula E_p = (Δ Q)/(Δ P) × P_B/Q_B using the values at Point B. E_p = (−4/9) × 15/40; E_p = (−4/9) × 3/8; E_p = −12/72 = −1/6 E_p ≈ −0.167 The price elasticity of demand at point B is −1/6. iii. The price elasticity of demand Between Point A and B (Arc Elasticity) Step 1: Identify the initial and final points for the movement from A to B. P₁ = P_A = 60, Q₁ = Q_A = 20; P₂ = P_B = 15, Q₂ = Q_B = 40; Step 2: Apply the arc elasticity formula E_p = (Q₂ − Q₁)/(P₂ − P₁) × (P₁ + P₂)/(Q₁ + Q₂). E_p = (40 − 20)/(15 − 60) × (60 + 15)/(20 + 40); E_p = (20)/(−45) × 75/60; E_p = (−4/9) × 5/4; E_p = −20/36 = −5/9 E_p ≈ −0.556 The price elasticity of demand between Point A and B is −5/9. iv. The price elasticity of demand Between Point B and A (Arc Elasticity) Step 1: Identify the initial and final points for the movement from B to A. P₁ = P_B = 15, Q₁ = Q_B = 40; P₂ = P_A = 60, Q₂ = Q_A = 20; Step 2: Apply the arc elasticity formula E_p = (Q₂ − Q₁)/(P₂ − P₁) × (P₁ + P₂)/(Q₁ + Q₂). E_p = (20 − 40)/(60 − 15) × (15 + 60)/(40 + 20); E_p = (−20)/(45) × 75/60; E_p = (−4/9) × 5/4; E_p = −20/36 = −5/9 E_p ≈ −0.556 The price elasticity of demand between Point B and A is −5/9.

Calculate the price elasticity of demand at points A and B given the demand schedule. Explain the concept of price elasticity of demand.

Answers

Step-by-step solution

Part i· 2 steps

Calculate the slope of the demand curve ( $\frac{\Delta Q}{\Delta P}$ ) using the two given points.

Apply the point elasticity formula $E_p = \frac{\Delta Q}{\Delta P} \times \frac{P_A}{Q_A}$ using the values at Point A.

Part ii· 2 steps
$-\frac{1}{6}$

Use the same slope of the demand curve calculated in part (i).

Apply the point elasticity formula $E_p = \frac{\Delta Q}{\Delta P} \times \frac{P_B}{Q_B}$ using the values at Point B.

Part iii· 2 steps
$-\frac{5}{9}$

Identify the initial and final points for the movement from A to B.

Apply the arc elasticity formula $E_p = \frac{Q_2 - Q_1}{P_2 - P_1} \times \frac{P_1 + P_2}{Q_1 + Q_2}$ .

Part iv· 2 steps
$-\frac{5}{9}$

Identify the initial and final points for the movement from B to A.

Apply the arc elasticity formula $E_p = \frac{Q_2 - Q_1}{P_2 - P_1} \times \frac{P_1 + P_2}{Q_1 + Q_2}$ .

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More Economics Questions

Calculate the price elasticity of demand at points A and B given the demand schedule. Explain the concept of price elasticity of demand.

Answers

Step-by-step solution

Part i· 2 steps

Calculate the slope of the demand curve (ΔQΔP\frac{\Delta Q}{\Delta P}ΔPΔQ​) using the two given points.

Apply the point elasticity formula Ep=ΔQΔP×PAQAE_p = \frac{\Delta Q}{\Delta P} \times \frac{P_A}{Q_A}Ep​=ΔPΔQ​×QA​PA​​ using the values at Point A.

Part ii· 2 steps−16-\frac{1}{6}−61​

Use the same slope of the demand curve calculated in part (i).

Apply the point elasticity formula Ep=ΔQΔP×PBQBE_p = \frac{\Delta Q}{\Delta P} \times \frac{P_B}{Q_B}Ep​=ΔPΔQ​×QB​PB​​ using the values at Point B.

Part iii· 2 steps−59-\frac{5}{9}−95​

Identify the initial and final points for the movement from A to B.

Apply the arc elasticity formula Ep=Q2−Q1P2−P1×P1+P2Q1+Q2E_p = \frac{Q_2 - Q_1}{P_2 - P_1} \times \frac{P_1 + P_2}{Q_1 + Q_2}Ep​=P2​−P1​Q2​−Q1​​×Q1​+Q2​P1​+P2​​.

Part iv· 2 steps−59-\frac{5}{9}−95​

Identify the initial and final points for the movement from B to A.

Apply the arc elasticity formula Ep=Q2−Q1P2−P1×P1+P2Q1+Q2E_p = \frac{Q_2 - Q_1}{P_2 - P_1} \times \frac{P_1 + P_2}{Q_1 + Q_2}Ep​=P2​−P1​Q2​−Q1​​×Q1​+Q2​P1​+P2​​.

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More Economics Questions

Calculate the slope of the demand curve ( $\frac{\Delta Q}{\Delta P}$ ) using the two given points.

Apply the point elasticity formula $E_p = \frac{\Delta Q}{\Delta P} \times \frac{P_A}{Q_A}$ using the values at Point A.

Part ii· 2 steps
$-\frac{1}{6}$

Apply the point elasticity formula $E_p = \frac{\Delta Q}{\Delta P} \times \frac{P_B}{Q_B}$ using the values at Point B.

Part iii· 2 steps
$-\frac{5}{9}$

Apply the arc elasticity formula $E_p = \frac{Q_2 - Q_1}{P_2 - P_1} \times \frac{P_1 + P_2}{Q_1 + Q_2}$ .

Part iv· 2 steps
$-\frac{5}{9}$

Apply the arc elasticity formula $E_p = \frac{Q_2 - Q_1}{P_2 - P_1} \times \frac{P_1 + P_2}{Q_1 + Q_2}$ .