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Here are the solutions to questions 6 to 13 in English: Question 6: a) Find the quantity demanded of the commodity before the change in price. Step 1: Identify the given values. Change in price ( P) = Rs. -2 Change in quantity demanded ( Q) = 10 units Price elasticity of demand (E_d) = -1 Original price (P) = Rs. 10 We need to find the original quantity (Q). Step 2: Use the formula for price elasticity of demand: E_d = ( Q)/( P) × (P)/(Q) Substitute the given values: -1 = (10)/(-2) × (10)/(Q) Step 3: Solve for Q. -1 = -5 × (10)/(Q) -1 = (-50)/(Q) Q = (-50)/(-1) Q = 50 The quantity demanded before the change in price was 50 units. b) By what percentage does the demand for the commodity fall? Step 1: Identify the given values. Price elasticity of demand (E_d) = -0.2 Percentage increase in price (\% P) = 5\% We need to find the percentage change in quantity demanded (\% Q). Step 2: Use the formula for price elasticity of demand: E_d = (\% Q)/(\% P) Substitute the given values: -0.2 = (\% Q)/(5\%) Step 3: Solve for \% Q. \% Q = -0.2 × 5\% \% Q = -1\% The demand for the commodity falls by 1%. Question 7: If the price of a commodity falls from Rs. 10 to Rs. 8 and its demand rises from 20 units to 30 units, calculate the price elasticity of demand. Step 1: Identify the initial and final values. Initial Price (P_1) = Rs. 10 Final Price (P_2) = Rs. 8 Initial Quantity (Q_1) = 20 units Final Quantity (Q_2) = 30 units Step 2: Calculate the change in price ( P) and change in quantity ( Q). P = P_2 - P_1 = 8 - 10 = -2 Q = Q_2 - Q_1 = 30 - 20 = 10 Step 3: Apply the price elasticity of demand formula. E_d = ( Q)/( P) × (P_1)/(Q_1) E_d = (10)/(-2) × (10)/(20) E_d = -5 × 0.5 E_d = -2.5 The price elasticity of demand is -2.5. Question 8: When the price of a commodity is Rs. 5 per unit, its demand is 100 units. When the price falls to Rs. 4 per unit, demand expands to 150 units. Calculate the price elasticity of demand. Step 1: Identify the initial and final values. Initial Price (P_1) = Rs. 5 Final Price (P_2) = Rs. 4 Initial Quantity (Q_1) = 100 units Final Quantity (Q_2) = 150 units Step 2: Calculate the change in price ( P) and change in quantity ( Q). P = P_2 - P_1 = 4 - 5 = -1 Q = Q_2 - Q_1 = 150 - 100 = 50 Step 3: Apply the price elasticity of demand formula. E_d = ( Q)/( P) × (P_1)/(Q_1) E_d = (50)/(-1) × (5)/(100) E_d = -50 × 0.05 E_d = -2.5 The price elasticity of demand is -2.5. Question 9: When the price of a commodity is Rs. 10 per unit, its demand is 100 units. When the price falls to Rs. 8 per unit, demand expands to 120 units. Calculate the price elasticity of demand. Step 1: Identify the initial and final values. Initial Price (P_1) = Rs. 10 Final Price (P_2) = Rs. 8 Initial Quantity (Q_1) = 100 units Final Quantity (Q_2) = 120 units Step 2: Calculate the change in price ( P) and change in quantity ( Q). P = P_2 - P_1 = 8 - 10 = -2 Q = Q_2 - Q_1 = 120 - 100 = 20 Step 3: Apply the price elasticity of demand formula. E_d = ( Q)/( P) × (P_1)/(Q_1) E_d = (20)/(-2) × (10)/(100) E_d = -10 × 0.1 E_d = -1 The price elasticity of demand is -1. Question 10: When the price of a commodity is Rs. 10 per unit, its demand is 100 units. When the price rises to Rs. 12 per unit, demand contracts to 80 units. Calculate the price elasticity of demand. Step 1: Identify the initial and final values. Initial Price (P_1) = Rs. 10 Final Price (P_2) = Rs. 12 Initial Quantity (Q_1) = 100 units Final Quantity (Q_2) = 80 units Step 2: Calculate the change in price ( P) and change in quantity ( Q). P = P_2 - P_1 = 12 - 10 = 2 Q = Q_2 - Q_1 = 80 - 100 = -20 Step 3: Apply the price elasticity of demand formula. E_d = ( Q)/( P) × (P_1)/(Q_1) E_d = (-20)/(2) × (10)/(100) E_d = -10 × 0.1 E_d = -1 The price elasticity of demand is -1. Question 11: When the price of a commodity is Rs. 10 per unit, its demand is 100 units. When the price falls to Rs. 8 per unit, demand expands to 150 units. Calculate the price elasticity of demand. Step 1: Identify the initial and final values. Initial Price (P_1) = Rs. 10 Final Price (P_2) = Rs. 8 Initial Quantity (Q_1) = 100 units Final Quantity (Q_2) = 150 units Step 2: Calculate the change in price ( P) and change in quantity ( Q). P = P_2 - P_1 = 8 - 10 = -2 Q = Q_2 - Q_1 = 150 - 100 = 50 Step 3: Apply the price elasticity of demand formula. E_d = ( Q)/( P) × (P_1)/(Q_1) E_d = (50)/(-2) × (10)/(100) E_d = -25 × 0.1 E_d = -2.5 The price elasticity of demand is -2.5. Question 12: When the price of a commodity is Rs. 10 per unit, its demand is 100 units. When the price falls to Rs. 8 per unit, demand expands to 120 units. Calculate the price elasticity of demand. Step 1: Identify the initial and final values. Initial Price (P_1) = Rs. 10 Final Price (P_2) = Rs. 8 Initial Quantity (Q_1) = 100 units Final Quantity (Q_2) = 120 units Step 2: Calculate the change in price ( P) and change in quantity ( Q). P = P_2 - P_1 = 8 - 10 = -2 Q = Q_2 - Q_1 = 120 - 100 = 20 Step 3: Apply the price elasticity of demand formula. E_d = ( Q)/( P) × (P_1)/(Q_1) E_d = (20)/(-2) × (10)/(100) E_d = -10 × 0.1 E_d = -1 The price elasticity of demand is -1. Question 13: When the price of a commodity is Rs. 10 per unit, its demand is 100 units. When the price rises to Rs. 12 per unit, demand contracts to 80 units. Calculate the price elasticity of demand. Step 1: Identify the initial and final values. Initial Price (P_1) = Rs. 10 Final Price (P_2) = Rs. 12 Initial Quantity (Q_1) = 100 units Final Quantity (Q_2) = 80 units Step 2: Calculate the change in price ( P) and change in quantity ( Q). P = P_2 - P_1 = 12 - 10 = 2 Q = Q_2 - Q_1 = 80 - 100 = -20 Step 3: Apply the price elasticity of demand formula. E_d = ( Q)/( P) × (P_1)/(Q_1) E_d = (-20)/(2) × (10)/(100) E_d = -10 × 0.1 E_d = -1 The price elasticity of demand is -1. 3 done, 2 left today. You're making progress.