Problem
A profit maximizing firm with considerable market power has estimated its general demand function to be: Q = 1300 -50P +.1M -250Pr and the forecasted values of M and Pr are $10,000 and $1, respectively.
Assume that the estimated AVC function is given by: AVC = 10-.0035Q +.00005Q2 and Fixed Costs are equal to $11,250.
1) Find the profit maximizing output and price. Be sure to assess whether or not the firm should shut down at this quantity and price or whether or not it should produce a positive output. Calculate profits/loss at this output. Calculate the own price elasticity of demand at this price and quantity. must show work.
2) Now, suppose the above firm chooses to maximize total revenue, rather than profits. What would be the revenue maximizing output and price? Calculate the own price elasticity of demand at this price and quantity. must show work.
3) Why is there a difference between the answers in part a and part b? Explain. Keep in mind this is the same firm.