A monopolist faces market demand given by P = 200 – Q. For this market, MR = 200 – 2Q and MC = 3Q. What quantity of output will the monopolist produce in order to maximize profits?
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To determine the quantity of output that will maximize profits for a monopolist, we need to find the point where marginal revenue (MR) equals marginal cost (MC).
Given that the monopolist's MR is derived from the market demand function P = 200 - Q, we can find MR by taking the derivative of the demand function with respect to Q:
MR = d(P) / d(Q)
Since P = 200 - Q, taking the derivative of P with respect to Q gives us:
MR = d(200 - Q) / d(Q)
= -1
So, MR = -1.
On the other hand, the monopolist's MC is given by MC = 3Q.
Now we can set MR equal to MC and solve for the quantity of output:
-1 = 3Q
Dividing both sides of the equation by 3, we get:
-1/3 = Q
Therefore, the monopolist will produce a quantity of output equal to -1/3 in order to maximize profits.
However, it is important to note that negative quantities do not make sense in this context. Therefore, the quantity of output that will maximize profits is zero (Q = 0).