This economics question tests your understanding of economic models and analysis. The step-by-step answer below applies the relevant framework and explains the reasoning.
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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 (( Q)/( P)) using the two given points. ( Q)/( 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 = ( Q)/( 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). ( Q)/( P) = -(4)/(9) Step 2: Apply the point elasticity formula E_p = ( Q)/( 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. P_1 = P_A = 60, Q_1 = Q_A = 20 P_2 = P_B = 15, Q_2 = Q_B = 40 Step 2: Apply the arc elasticity formula E_p = (Q_2 - Q_1)/(P_2 - P_1) × (P_1 + P_2)/(Q_1 + Q_2). 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. P_1 = P_B = 15, Q_1 = Q_B = 40 P_2 = P_A = 60, Q_2 = Q_A = 20 Step 2: Apply the arc elasticity formula E_p = (Q_2 - Q_1)/(P_2 - P_1) × (P_1 + P_2)/(Q_1 + Q_2). 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). 3 done, 2 left today. You're making progress.