Chapter 14.3, Problem 32E

Elasticity The price along the West Coast of the United States for Japanese spruce logs (in dollars per cubic meter) based on the demand (in thousands of cubic meters per day) has been approximated by

      $p=0.604q^2-20.16q+\mathrm{263.067.}$

Source: Kamiak Econometrics.

(a)    Find the elasticity when the demand is 11 thousand cubic meters a day. (Hint: To find dq/dp when p is expressed in terms of q, you may use the fact that

      $\frac{dq}{dp}=\frac{1}{dp/dq}.$

 Review the explanation of the derivative of the natural logarithm to see why this is true.)

(b)    Is the demand for spruce logs elastic or inelastic?

(c)    What happens to the elasticity as q approaches 16.6887? Discuss the limitations of this model for the price as a function of the demand.