Chapter 3 Quantitative Demand Analysis EX1: Suppose a 10 percent price decrease causes consumers to increase their purchases by 30%. What s the price elasticity? EX2: Suppose the 10 percent decrease in price causes a 5 percent increase in sales. What s price elasticity? EX3: Suppose a manager knows the demand elasticity for a company s product is equal to 2.5 over the range of prices currently being considered by the firm s marketing department. The manager is considering decreasing price by 8 percent and wishes to predict the percentage by which quantity demanded will increase. EX4: Suppose a manager of a different firm faces the demand elasticity equal to 0.5 over the range of the prices it would consider charging for its product. The manager wishes to stimulate sales by 15 percent. The manager is willing to lower price to accomplish the increase in sales buy needs to know the percentage amount by which price must be lowered to obtain the 15 percent increase in sales. Note: If the inverse demand function is P=a bq, then EE QQXX dd,pp XX = 1 bb. PP QQ EX5: P=40 0.5Q what are the elasticities at each point below: Point A: Q=20 Point B: P=20 Point C: Q=6 1
EX6: Relation between MR and Demand: when demand is linear, P=a bq, marginal revenue is also linear, intersects the vertical (price) axis at the same point demand does, and is twice a steep as demand. The equation of the linear marginal revenue curve is MR= EX7: Relation between MR and Elasticity: for any demand curve, when demand is elastic, marginal revenue is. When demand is inelastic, marginal revenue is. When demand is unitary elastic, marginal revenue is. EX8: Relation between MR and TR: Marginal revenue is price at every level of output after the first unit. When MR is positive (negative), total revenue increases (decreases) as quantity increases, and demand is elastic (inelastic). When MR is, the elasticity of demand is unitary. EX9: Suppose it is estimated that the cross price elasticity of demand between clothing and food is 0.18. If the price of food is projected to increase by 10 percent, by how much will demand for clothing change? Are the two goods substitutes or complements? EX10: Suppose that the income elasticity of demand for transportation is estimated to be 1.80. If income is projected to decrease by 15 percent, what is the impact on the demand for transportation? is transportation a normal or inferior good? 2
EX11: The daily demand for Invigorated PED shoes is estimated to be QQ XX dd = 100 3PP XX + 4PP YY 0.01MM + 2AA XX Suppose good X sells at $25 a pair, good Y sells at $35, the company utilizes 50 units of advertising, and average consumer income is $20,000. Calculate the own price, cross price and income elasticities of demand. EX12: An analyst for a major apparel company estimates that the demand for its raincoats is given by ln Q xd =10-1.2lnP x +3lnR-2lnA y where R denotes the daily amount of rainfall and A Y the level of advertising on good Y. What would be the impact on demand of a 10 percent increase in the daily amount of rainfall? EX13: Assume that the price elasticity of demand is -2 for a certain firm's product. If the firm raises price, the firm's managers can expect total revenue to: A. decrease. B. increase. C. remain constant. D. either increase or remain constant, depending upon the size of the price increase. EX14: A price elasticity of zero corresponds to a demand curve that is: A. horizontal. B. downward sloping with a slope always equal to 1. C. vertical. D. either vertical or horizontal. 3
EX15: As we move down along a linear demand curve, the price elasticity of demand becomes more: A. elastic. B. inelastic. C. log-linear. D. variable. EX16: The quantity consumed of a good is relatively unresponsive to changes in price whenever demand is: A. elastic. B. unitary. C. falling. D. inelastic. EX17: If the absolute value of the own price elasticity of steak is 0.4, a decrease in price will lead to: A. a reduction in total revenue. B. an increase in total revenue. C. no change in total revenue. D. None of the statements is correct. EX18: Demand is perfectly elastic when the absolute value of the own price elasticity of demand is: A. zero. B. one. C. infinite. D. unknown. EX19: Which of the following factors would NOT affect the own price elasticity of a good? A. Time B. Price of an input C. Available substitutes D. Expenditure share EX20: Demand is more inelastic in the short term because consumers: A. are impatient. B. have no time to find available substitutes. C. are present-oriented. D. None of the statements is correct 4
ECO 3320 Chapter 2 Instructor: Lanlan Chu 5