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# Point Income Elasticity/Point Cross Elasticity

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5. The McNight company is a major producer of steel. Management estimates that the demand for the company's steel is given by the equation:
Qs=5,000-1000Ps + 0.1I + 100 Pa
Where Qs is steel demand in thousands of tons per year, Ps is the price of steel in dollars per pound, I 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 he initial prices and income?
b. What is the point income elasticity at the initial values?
c. What is the point cross elasticity between steel and aluminum? Are steel and aluminum substitutes or complements?
d. If the objective is to maintain the quantity of steel demanded as computed in part (A), what reduction in steel price will be necessary to compensate for a \$0.20 reduction in the price of aluminum?

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#### Solution Preview

Answer (a):
Qs=5,000-1000Ps + 0.1I + 100 Pa
Ps = 1
I= 20,000
Pa = 0.80

Putting these values in the demand curve above we get:
Qs = 5000 - 1000x1 + 0.1x20000 + 100x0.80
= 5000 - 1000 + 2000 + 80
= 6080

Answer ...

#### Solution Summary

The solution explains the price elasticity of demand concept using the scenario provided.

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## 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? Explain 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? Explain.

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