Point price, income and cross elasticities
The McNight Company is a major producer of steel. Management estimates that the demand for its steel is given by the equation: Qd = 500 - 1000P + 0.1Y + 300Pa, where Q = steel demand in thousands of tons per year, P = price of steel in dollars per pound, Y is income per capita, and Pa is the price of aluminum in dollars per pound. Initially the price of steel is $1 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 level?
B. Based on the equation, what is the relationship between steel and aluminum? describe briefly how you know.
C. What are the point price, income, and cross elasticities at the present values? Interpret your answers, saying how much a 1% change in each variable impacts demand.
D. If the objective is to increase total revenue, should the price be increased or decreased? What if the objective is to increase total profit? describe.