Question

1. The research department of Cardinal Novelties has estimated the demand function facing the firm for price increases and price declines from the prevailing price are, respectively: Q = 220 -10P and Q’ = 145-5P

The marginal and average total cost functions of the firm were also estimated to be, respectively: MC =2.5 + .05Q and ATC = 2.5 + .025Q

Determine the best level of output of the firm, the price at which the firm sells its output, as well as the total profit. (20 points)

• Reference Figure 6, p. 432,  This is a kinked demand problem.  The kinked demand model is an oligopoly model to explain a feature, common to many oligopolies, a reluctant to change the price.  You are attempting to determine whether the firm is maximizing profits at the price and quantity coordinates where it is, currently.  You first determine what those coordinates are and then find whether the marginal cost at the current quantity is between the marginal revenues of the two demand curves at the current quantity.  If it is then the firm is maximizing profits, if not then you fall back on the MR=MC rule (use the higher MR if MC is above the range and the lower MR if MC is below the range).  If you approach this problem by first equating MC to MR, you will get it wrong and will not likely receive any of the 20 points associated with the problem.
• You are trying to determine whether the MC goes through the gap in the MR

1. Find kink price and quantity (where two demand curves intersect)
2. Find the MC by plugging in the Q you found in part a.
3. There two marginal revenues, one associated with each demand
4. You must find MR equations for both -   Find both reverse demand curves, Double slope of each to get MR equation
5. Plug in Q from part a into each MR
6. Is the MC between the two MR’s?  If it is then they maximize profit at the kink (current P and Q).  If not, equate MR and MC (if MC is about the larger MR use that MR, if MC is below the lower MR use that MR).  

Answer 1