Question:

(a) (5 points) The demand for a certain commodity is \(p=-0.01q+1000\). Find the elasticity of demand \(\eta \). Here p is “price” and q is “quantity”.

(b) (5 points) Assume a demand of \(p=-0.01q+1000\). Find the exact values of p and q that maximize the revenue R. (We know two methods for this. Use the method of your choice, but show your work).

(c) (10 points) Assume the demand is \(p=-0.01q+1000\), and assume the price is set to maximize revenue, what is the consumers’ surplus? If you did not do the previous part, use p = $550.