Cutting Edge Pharmaceuticals Pty Ltd (a monopoly firm) has the following demand (average revenue) function: AR = 65 – Q The marginal cost of production is constant and equal to $5. a) What is the equation for the MR function? (Hint: MR falls twice as fast (at twice the rate) as AR) (1/2 mark) Determine the profit maximizing level of output (Qm) for the Monopoly firm (1/2 mark)
Question
Cutting Edge Pharmaceuticals Pty Ltd (a monopoly firm) has the following demand (average revenue) function: AR = 65 – Q The marginal cost of production is constant and equal to $5.
a) What is the equation for the MR function? (Hint: MR falls twice as fast (at twice the rate) as AR) (1/2 mark) Determine the profit maximizing level of output (Qm) for the Monopoly firm (1/2 mark)
Solution
a) The Marginal Revenue (MR) function is derived from the Average Revenue (AR) function. Given that MR falls twice as fast as AR, the slope of the MR function will be twice that of the AR function. The AR function is AR = 65 - Q. Therefore, the MR function will be MR = 65 - 2Q.
b) To find the profit maximizing level of output (Qm) for the monopoly firm, we set MR equal to MC and solve for Q.
So, 65 - 2Q = 5 => 2Q = 65 - 5 => 2Q = 60 => Q = 60/2 => Q = 30
Therefore, the profit maximizing level of output (Qm) for the monopoly firm is 30 units.
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