"Assume your company sells unique cell phone cases, and that demand is Q1 = 20 - 0.5P1.
a. Use calculus to find the level of output that maximizes total revenue. What price would you have to sell the cases to reach this level of output? How much total revenue would be earned?
b. Calculate the point elasticity of demand at this TR-maximizing price and quantity. Does the elasticity have the expected value? Explain.
c. Now assume that demand conditions have changed such that Q2 = 25 - (1/1.2)P2. How much revenue would you earn if you continued selling the same quantity as you did in part a? Calculate the point elasticity when using your part a Q; should your company raise or lower its current selling price to maximize total revenue as a result of the new demand conditions?
d. Use calculus to determine the TR-max level of output, price, and TR (as you did in part a).
e. Using the two equations for demand, determine equations for MR as a function of Q. Make two graphs, one of P and MR for the Q1 = 20 - 0.5P1 demand, and one of P and MR for the Q2 = 25 - (1/1.2)P2 demand. Do the graphs confirm your earlier answers? Why or why not?