Management for a major producer of steel estimates that the demand for the compa
ID: 1140981 • Letter: M
Question
Management for a major producer of steel estimates that the demand for the company's steel is given by the equation Q5,000 1,000P+0.1M+100Pa where Qs is steel demand in thousands of tons per year, P, is the price of steel in dollars per pound, M is income per capita, and Pa is the price of aluminum in dollars per pound. Initially, the price of steel is S1 per pound, income per capita is $20,000, and the price of aluminum is $0.80 per pound. a. How much steel will be demanded at the initial prices and income? Show your calculations! b. What is the point income elasticity at the initial values? Formula used: Items given and their values: Your work: c. What type of good is steel? How do you knowl? d. What is the point cross-price elasticity between steel and aluminum? Formula used: Items given and their values: Your work: Answer e. Are steel and aluminum substitutes or complements? How do you know?Explanation / Answer
Qs = 5000 – 1000Ps + 0.1M + 100 Pa, now we are given that Ps = 1, M = 20000 and Pa = 0.80
We substitute these values and get
Qs =5000-1000*1+0.1*20000+100*0.80 = 6080 (The demand for steel at Ps = 1, M = 20000 and Pa = 0.80)
Point Elasticity = (dQs/dPs)*(Ps/Qs) = -1000*(1/6080) = -0.16447
Income Ed = (dQs/dM)*(M/Qs) = 0.1*20000/6080 = 0.328947 positive value showing a positive relation between demand for steel and income of the buyer. It indicates that with a rise in income consumer buys more of steel. Thus it is a normal good.
Cross Price Elasticity = (dQs/dPa)*(Pa/Qs) = 100*0.80/6080 = 0.013 (The two goods can be said substitutes as there is a positive relation between the demand for steel and price of aluminimum. If price of aluminium rises, the demand or steel go up. The cross elasticity however is very low showing that they are somewhat substitutes if this cross ed = 0, then there would have been no relation between the two.
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