Question.3040 - 1. XYZ Corporation is a manufacturer of widgets. Over the past several months, it has been selling its widgets for $100 each and unit sales have averaged 5,000 units per month. This month its competitor, ABC, Inc. raised the price of its widgets from $100 to $110. XYZ noted that its unit sales increased by 200 units. a. What is the cross price elasticity of demand between XYZ’s and AB C’s widgets? b. If XYZ knows that the price elasticity of demand for its widgets is -2.0, what price would XYZ be able to charge and still sell 5,000 widgets, assuming ABC keeps its price at $110? 2. The demand function for bicycles in Mapleville is estimated to be Qd = 2,500 + 10Y – 6 P Where Y denotes income in thousands, Qd is the quantity demanded in units, and P is the price of bicycles. When P = $120, Y = 12, a. What is the price elasticity of demand? b. What is the income elasticity of demand? 3. A local realtor estimated the long-term income elasticity of demand for rental properties to be 0.9 and the long-run income elasticity for owner-occupied housing to be 1.10. Recent estimates indicate that income is forecast to rise at 5% per year over the next 2 years. What is the expected effect on the quantity demanded for rental housing and owner-occupied housing (assuming rental rates and the price of housing remain constant). If housing prices rise during the same period, how would the quantity demanded of each type of housing be affected? 4. Your market research group estimated the following demand curve for gadgets, the product your company produces and sells. Qd = 4,000 – 40P If this relationship between quantity demanded and prices continues to hold true in the future, a. How many gadgets will be demanded at $10, $20, and $30? b. What is the arc price elasticity between $10 and $20; between $20 and $30? c. What is the point price elasticity at each of the three prices? d. If your company sold 3,000 gadgets last year, what is the price it charged?
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1. XYZ Corporation is a manufacturer of widgets. Over the past several months, it has been selling its widgets for $100 each and unit sales have averaged 5,000 units per month. This month its competitor, ABC, Inc. raised the price of its widgets from $100 to $110. XYZ noted that its unit sales increased by 200 units. a. What is the cross price elasticity of demand between XYZ’s and AB C’s widgets? b. If XYZ knows that the price elasticity of demand for its widgets is -2.0, what price would XYZ be able to charge and still sell 5,000 widgets, assuming ABC keeps its price at $110? Solution: a) Cross price elasticity of demand between XYZs and ABCs widgets: = Percentage change in quantity demanded of good XYZ / percentage change in price of good ABC = ((5200-5000)/5000)/ ((110-100)/100) = 0.0400 / 0.100 = 0.4 b) Price elasticity of demand: = Percentage change in quantity demanded / percentage change in price 2. The demand function for bicycles in Mapleville is estimated to be Qd = 2,500 + 10Y – 6 P Where Y denotes income in thousands, Qd is the quantity demanded in units, and P is the price of bicycles. When P = $120, Y = 12, a. What is the price elasticity of demand? b. What is the income elasticity of demand? Solution: a) Solving the equation, Qd = 2500+10Y-6P = 2500+10*12-6*120 = 2500+120-720 = 1900 Changing the price by 10%, new price = 120+120*10% = 132 New demand = 2500+10*12-6*132 = 1828 % change in quantity demanded = (1828-1900)/1900 = -0.03789 Price elasticity = % change in quantity demanded / % change in price Price elasticity = -0.03789/0.10 = -0.3789 b) Solving the equation, Qd = 2500+10Y-6P = 2500+10*12-6*120 = 2500+120-720 = 1900 Changing the income by 10%, new income = 12+10%*12=13.2 New demand = 2500+10*13.2-6*120 = 1912 % change in quantity demanded = (1912-1900)/1900 = 0.0063 Income elasticity = % change in quantity demanded / % change in income Income elasticity = 0.0063/0.1 = 0.0631 3. A local realtor estimated the long-term income elasticity of demand for rental properties to be 0.9 and the long-run income elasticity for owner-occupied housing to be 1.10. Recent estimates indicate that income is forecast to rise at 5% per year over the next 2 years. What is the expected effect on the quantity demanded for rental housing and owner-occupied housing (assuming rental rates and the price of housing remain constant). If housing prices rise during the same period, how would the quantity demanded of each type of housing be affected? Solution: Long term income elasticity of demand for rental properties = 0.9 Long term income elasticity for owner occupied housing = 1.10 Income rise = 5% Expected effect on the quantity demanded for rental housing: Income elasticity of demand = % change in quantity demanded / % change in income % change in quantity demanded = 0.9 * 0.05 = 0.045 Expected effect on the quantity demanded for owner occupied housing: Income elasticity of demand = % change in quantity demanded / % change in income % change in quantity demanded = 1.10 * 0.05 = 0.055 If the housing price rises during the same period, the quantity demanded would be the same as the income rise is offset by the price rise. However, the net impact would depend upon the % rise in the price. 4. Your market research group estimated the following demand curve for gadgets, the product your company produces and sells. Qd = 4,000 – 40P If this relationship between quantity demanded and prices continues to hold true in the future, a. How many gadgets will be demanded at $10, $20, and $30? b. What is the arc price elasticity between $10 and $20; between $20 and $30? c. What is the point price elasticity at each of the three prices? d. If your company sold 3,000 gadgets last year, what is the price it charged? Solution: a) Gadgets demanded at $10 = 4000-40*10 => 3600 Gadgets demanded at $20 = 4000-40*20 => 3200 Gadgets demanded at $30 = 4000-40*30 => 2800 b) Arc price elasticity between $10 and $20 = = [((3200-3600)/(3200+3600))*2] / [((20-10)/(20+10))*2] = -0.1176/0.6667 = -0.1764 Arc price elasticity between $20 and $30 = = [((2800-3200)/(2800+3200))*2] / [((30-20)/(30+20))*2] = -0.1333/0.4000 = -0.3333 c) Point price elasticity of demand at 20 Quantity decrease from 3600 to 3200 = -400/3600 = -0.1111 Price increase from 10 to 20 = 10/10 = 1 PED = -0.1111/1 = -0.1111 Point price elasticity of demand at 30 Quantity decrease from 3200 to 2800 = -400/3200 = -0.125 Price increase from 10 to 20 = 10/20 = 0.5 PED = -0.1111/1 = -0.25 d) 3000 = 4000-40P P = 1000/40 = 25More Articles From Economics
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