In my Microeconomics course, we are handling the 4 imperfect competition models.
Currently we are discussing the Cournot Model, however I am unsure about a certain example. This is given as a lecture example (all information provided).
Let us first assume that we start with a single firm (monopoly).
This monopoly is the owner of a costless spring (and sells the water).
I.e., MC = 0
Start with our demand function:
Q = 120 – P Now, determine the profit maximizing price/output combination. MR = MC MC = 0 Q = 120 – P (Demand function) P = -Q + 120 Thus, MR = -2Q + 120 Thus -2Q + 120 = 0 Thus Q = 60 P = 60 Profits = 3600
I am familiar with the concept of calculating each firm's demand function, what confuses me is, in this example, we have a a single firm (monopoly) and when deriving its mariginal revenue function, one should end up with the following:
P = -Q + 120
d/dQ = P' = -1 (using chainrule for -Q => -1 and dQ of constant = 0)
MR = P' = -1
but in the example given, we arrive at:
MR = -2Q + 120
What am I missing or is this example incomplete (not all information given)?