Question: A steel industry trade group estimates that the demand for steel in a particular market is given as

Q_s = 2,000 - 160P_s + 8I + 140P_a,

where Q_s is the demand for steel (in pounds) per year, P_s is the price of steel in cents per pound, I is income per capita in dollars, and P_a is the price of aluminum in cents per pound. Currently the price of steel is 160¢ per pound, income per capita is $20,000, and the price of aluminum is 300¢ per pound.

a. How much steel will be demanded at the current prices and income?

b. What is the own price elasticity of demand for steel? Interpret the elasticity in a mathematic and economic context -- what does this number tell you? Is the own price elasticity consistent with economic principles? Explain.

c. What is the income elasticity? Interpret the elasticity in a mathematic and economic context -- what does this number tell you? Is the income elasticity consistent with economic principles? Explain.

d. What is the practical interpretation of your answers to b. and c. when looked at together? What kinds of conclusions can you make about the demand for steel?

e. If management's objective is to maintain the quantity of steel demanded at current levels (as computed in a. above), what change in the price of steel would be necessary to compensate for a 10¢ decrease in the price of aluminum?