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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. What is the equilibrium monopoly price (Pm) set by the firm (1/2 mark) and what will be the monopoly profit earned? (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.

What is the equilibrium monopoly price (Pm) set by the firm (1/2 mark) and what will be the monopoly profit earned? (1/2 mark)

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Solution

To find the equilibrium monopoly price (Pm), we first need to find the quantity where Marginal Revenue (MR) equals Marginal Cost (MC).

  1. First, we need to find the MR. Since the Average Revenue (AR) is given by AR = 65 - Q, we know that this is also the demand function (P = 65 - Q), because in a monopoly, AR = Price (P).

  2. The MR in a linear demand curve like this one is given by MR = 65 - 2Q.

  3. We set MR = MC to find the equilibrium quantity. So, 65 - 2Q = 5. Solving for Q gives Q = 30.

  4. Substituting Q = 30 into the demand function gives P = 65 - 30 = 35.So,theequilibriummonopolyprice(Pm)is35. So, the equilibrium monopoly price (Pm) is 35.

To find the monopoly profit:

  1. We need to find total revenue (TR) and total cost (TC).

  2. TR is given by PQ, so TR = 3530 = $1050.

  3. Since MC is constant at 5,TC=MC∗Q=5∗30=5, TC = MC*Q = 5*30 = 150.

  4. Therefore, the monopoly profit is TR - TC = 1050−1050 - 150 = $900.

This problem has been solved

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