You have the following data. A monopolist produces 1000 units of output per month, and
sells it at the price of 10 each. You know that the monopolist does not do any price discrimination,
and you also know that the price-cost margin of this firm (P-MC)/P is evaluated at 0.2. Estimate the
dead-weight loss associated with this monopoly. Estimate what the perfectly competitive market
price would be in this case (Hint: find MC, represent deadweight loss as a triangle, and solve for
difference in monopoly and competitive output).
*** how do i go about doing this
To estimate the deadweight loss associated with this monopoly and the perfectly competitive market price, you will need to follow these steps:
Step 1: Calculate the monopolist's marginal cost (MC) using the price-cost margin (P-MC)/P.
Given that the price-cost margin (P-MC)/P is evaluated at 0.2, we can write:
0.2 = (P - MC)/P
Simplifying this equation, we find:
P - MC = 0.2P
Rearranging the equation, we get:
0.8P = MC
So, the monopolist's marginal cost (MC) is 0.8 times the price (P).
Step 2: Calculate the monopolist's profit maximizing quantity.
Since the monopolist produces and sells 1000 units of output per month, we can deduce that this is the monopolist's profit maximizing quantity.
Step 3: Calculate the monopolist's profit.
The monopolist's profit (π) can be calculated using the formula:
π = (P - MC) × Quantity
Substituting the values, we can calculate the monopolist's profit.
Step 4: Calculate the competitive output.
To estimate the competitive output, we need to find the quantity at which the marginal cost (MC) equals the price (P). In perfect competition, this is the long-run equilibrium condition.
Since the marginal cost (MC) is 0.8P, and the price is given as 10, we can set up the equation:
0.8P = 10
Solving for P, we find:
P = 10 / 0.8 = 12.5
Therefore, the perfectly competitive market price would be 12.5.
Step 5: Calculate the deadweight loss.
Deadweight loss represents the loss in social welfare due to the monopolistic market power. In this case, the deadweight loss can be represented as a triangle.
To calculate the deadweight loss, we need to find the difference in output between the monopoly and the competitive market.
The difference in output is given by:
Difference in output = Monopoly output - Competitive output
Substituting the values, we find:
Difference in output = 1000 - Competitive output
Since the competitive output is unknown, we need to find it.
Equating the monopoly marginal cost (0.8P) to the competitive price (P = 12.5), we have:
0.8P = P
0.8 × 12.5 = P
P = 10
This tells us that the competitive output will be the same as the monopoly output, which is 1000.
Therefore, the deadweight loss is:
Deadweight loss = 1/2 × (Competitive output - Monopoly output) × (Competitive price - Marginal cost)
Substituting the values, we find:
Deadweight loss = 1/2 × (1000 - 1000) × (12.5 - 0.8 × 10)
The equation simplifies to:
Deadweight loss = 0.5 × 0 × 4 = 0
Therefore, the deadweight loss associated with this monopoly is zero.
In summary, the perfectly competitive market price would be 12.5, and there is no deadweight loss associated with this monopoly.