Answer to Question #301771 in Economics of Enterprise for Leonidos

Question

9. Thompson Steel is a major producer of steel. Management estimates that the demand for the company’s steel is given by the equation QS = 5,000 – 1,000PS + 0.1I + 100 Pa Where, QS is steel demanded in thousands of tons per year, PS is the price of steel in dollars per pound, I is the 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? 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 prices will be necessary to compensate for $0.20 reduction in the price of aluminum?

Answer 1

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

$Q_{s}=5000-1000\times1+0.1\times20000+1000\times0.80=6080$

Thus, the steel demand is 6080 tons

b. What is the point income elasticity at the initial values?

Point income elasticity =$\frac{dQ_{d}}{dI}\times \frac{I}{Q_{d}}$

=$0.1\times20000/6080=0.33$

The point elasticity is 0.33

c. What is the point cross elasticity between steel and aluminum? Are steel and aluminum substitutes or complements? 

point cross elasticity = $\frac{dQ_{s}}{dP_{a}}\times \frac{P_{a}}{Q_{s}}$

=$100\times 0.80/6080 = 0.01$

The cross elasticity is 0.01

Because the cross price elasticity is positive, therefore, the two goods (steel and aluminum) are substitutes

d. If the objective is to maintain the quantity of steel demanded as computed in part (a), what reduction in steel prices will be necessary to compensate for a $0.20 reduction in the price of aluminum?

$6080 = 5000-1000\times P_{s} + 0.1\times20000+100\times 0.6$

$1000P_{s}=980$

$P_{s} = 0.98$

Required reduction = $\frac{(1-0.98)}{1}\times 100 = 2\%$

Therefore, the required price reduction is 2%.