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?
Answer Below:
XYZ xxxxxxxxxxx is x manufacturer xx widgets xxxx the xxxx several xxxxxx it xxx been xxxxxxx its xxxxxxx for xxxx and xxxx sales xxxx averaged xxxxx per xxxxx This xxxxx its xxxxxxxxxx ABC xxx raised xxx price xx its xxxxxxx from xx XYZ xxxxx that xxx unit xxxxx increased xx units x What xx the xxxxx price xxxxxxxxxx of xxxxxx between xxx rsquo x and xx C xxxxx s xxxxxxx b xx XYZ xxxxx that xxx price xxxxxxxxxx of xxxxxx for xxx widgets xx - xxxx price xxxxx XYZ xx able xx charge xxx still xxxx widgets xxxxxxxx ABC xxxxx its xxxxx at xxxxxxxx a xxxxx price xxxxxxxxxx of xxxxxx between xxxx and xxxx widgets xxxxxxxxxx change xx quantity xxxxxxxx of xxxx XYZ xxxxxxxxxx change xx price xx good xxx - x b xxxxx elasticity xx demand xxxxxxxxxx change xx quantity xxxxxxxx percentage xxxxxx in xxxxx The xxxxxx function xxx bicycles xx Mapleville xx estimated xx be xx Y xxxxx P xxxxx Y xxxxxxx income xx thousands xx is xxx quantity xxxxxxxx in xxxxx and x is xxx price xx bicycles xxxx P x a xxxx is xxx price xxxxxxxxxx of xxxxxx b xxxx is xxx income xxxxxxxxxx of xxxxxx Solution x Solving xxx equation xx Y- x - x Changing xxx price xx new xxxxx New xxxxxx - xxxxxx in xxxxxxxx demanded x - xxxxx elasticity xxxxxx in xxxxxxxx demanded xxxxxx in xxxxx Price xxxxxxxxxx - x b xxxxxxx the xxxxxxxx Qd xx P x - xxxxxxxx the xxxxxx by xxx income xxx demand x change xx quantity xxxxxxxx - xxxxxx elasticity xxxxxx in xxxxxxxx demanded xxxxxx in xxxxxx Income xxxxxxxxxx A xxxxx realtor xxxxxxxxx the xxxxxxxxx income xxxxxxxxxx of xxxxxx for xxxxxx properties xx be xxx the xxxxxxxx income xxxxxxxxxx for xxxxxxxxxxxxxx housing xx be xxxxxx estimates xxxxxxxx that xxxxxx is xxxxxxxx to xxxx at xxx year xxxx the xxxx years xxxx is xxx expected xxxxxx on xxx quantity xxxxxxxx for xxxxxx housing xxx owner-occupied xxxxxxx assuming xxxxxx rates xxx the xxxxx of xxxxxxx remain xxxxxxxx If xxxxxxx prices xxxx during xxx same xxxxxx how xxxxx the xxxxxxxx demanded xx each xxxx of xxxxxxx be xxxxxxxx Solution xxxx term xxxxxx elasticity xx demand xxx rental xxxxxxxxxx Long xxxx income xxxxxxxxxx for xxxxx occupied xxxxxxx Income xxxx Expected xxxxxx on xxx quantity xxxxxxxx for xxxxxx housing xxxxxx elasticity xx demand xxxxxx in xxxxxxxx demanded xxxxxx in xxxxxx change xx quantity xxxxxxxx Expected xxxxxx on xxx quantity xxxxxxxx for xxxxx occupied xxxxxxx Income xxxxxxxxxx of xxxxxx change xx quantity xxxxxxxx change xx income xxxxxx in xxxxxxxx demanded xx the xxxxxxx price xxxxx during xxx same xxxxxx the xxxxxxxx demanded xxxxx be xxx same xx the xxxxxx rise xx offset xx the xxxxx rise xxxxxxx the xxx impact xxxxx depend xxxx the xxxx in xxx price xxxx market xxxxxxxx group xxxxxxxxx the xxxxxxxxx demand xxxxx for xxxxxxx the xxxxxxx your xxxxxxx produces xxx sells xx ndash x If xxxx relationship xxxxxxx quantity xxxxxxxx and xxxxxx continues xx hold xxxx in xxx future x How xxxx gadgets xxxx be xxxxxxxx at xxx b xxxx is xxx arc xxxxx elasticity xxxxxxx and xxxxxxx and x What xx the xxxxx price xxxxxxxxxx at xxxx of xxx three xxxxxx d xx your xxxxxxx sold xxxxxxx last xxxx what xx the xxxxx it xxxxxxx Solution x Gadgets xxxxxxxx at x amp xx Gadgets xxxxxxxx at x amp xx Gadgets xxxxxxxx at x amp xx b xxx price xxxxxxxxxx between xxx - x - x Arc xxxxx elasticity xxxxxxx and x - x - x Point xxxxx elasticity xx demand xx Quantity xxxxxxxx from xx - x Price xxxxxxxx from xx PED x - xxxxx price xxxxxxxxxx of xxxxxx at xxxxxxxx decrease xxxx to x - xxxxx increase xxxx to xxx - x d x P xMore Articles From Economics
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