2.7 Suppose that the U.S. demand for maple syrup, in thousands of gallons per year, is Qd = 6000 - 30P, where is the price per gallon. What is the elasticity of P demand at a price of $75 per gallon? Answer: The elasticity of demand is -0.60. Explanation: At price denoted equals the percentage change in the amount demanded for each 1 P, Ed percent increase in the price. Demand for maple syrup is given by: = 6,000 30P Qd – The elasticity of demand for a linear demand curve starting at price and quantity is: P Q . For a linear demand curve of the form = the first term in parentheses equals QD A BP, – Therefore: –B. Specifically: = x 75/ (6,000 (30 x 75)) Ed –30 – = Ed –0.6 2.8 Consider again Problem 7. At what price is the expenditure on maple syrup by U.S. consumers highest? Answer: The expenditure on syrup by U.S. consumers is highest at $100. Explanation: The largest expenditure and maximum revenue occur when price elasticity of demand equals A small increase in price causes total expenditure to increase if –1. demand is inelastic and decrease if demand is elastic. Total expenditure is largest at a price for which the elasticity equals –1. Specifically, = x (P/ (6,000 (30P)) –1 –30 – 6,000 30P 30P – = 6,000 = 60P 100 P = 2.9 Suppose the demand function for jelly beans in Cincinnati is linear. Two years ago, the price of jelly beans was $1 per pound, and consumers purchased 100,000
2.7 Suppose that the U.S. demand for maple syrup, in thousands of gallons per year, is Qd = 6000 - 30P, where P is the price per gallon. What is the elasticity of demand at a price of $75 per gallon? Answer: The elasticity of demand is -0.60. Explanation: At price P, denoted Ed equals the percentage change in the amount demanded for each 1 percent increase in the price. Demand for maple syrup is given by: Qd = 6,000 – 30P The elasticity of demand for a linear demand curve starting at price P and quantity Q is: . For a linear demand curve of the form QD = A – BP, the first term in parentheses equals –B. Therefore: Specifically: Ed = –30 x 75/ (6,000 – (30 x 75)) Ed = –0.6 2.8 Consider again Problem 7. At what price is the expenditure on maple syrup by U.S. consumers highest? Answer: The expenditure on syrup by U.S. consumers is highest at $100. Explanation: The largest expenditure and maximum revenue occur when price elasticity of demand equals –1. A small increase in price causes total expenditure to increase if demand is inelastic and decrease if demand is elastic. Total expenditure is largest at a price for which the elasticity equals –1. Specifically, –1 = –30 x (P/ (6,000 – (30P)) 6,000 – 30P = 30P 6,000 = 60P P = 100 2.9 Suppose the demand function for jelly beans in Cincinnati is linear. Two years ago, the price of jelly beans was $1 per pound, and consumers purchased 100,000
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