A product has the demand function
p = 100 - 0.5q
where p is in dollars and q is the number of units.
(a) Find the elasticity (q) as a function of q, and graph the function
f (q) = η (q)
(b) Find where f (q) = 1, which gives the quantity for which the product has unitary elasticity.
(c) The revenue function for this product is
R(q) = pq = (100 - 0.5q)q
Graph R(q) and find the q-value for which the maximum revenue occurs.
(d) What is the relationship between elasticity and maximum revenue?