A monopolist faces a demand of Q = 14 - P, where P is price. The firm has chosen to produce exactly 4 units of Q. Assume marginal cost (MC) is 6. In this case, the dead weight loss (DWL) in the market is: (be sure to show all work)
a) 4.5
b) 6.5
c) 8
d) 10
THANK YOU!!!
To calculate the deadweight loss in a monopolistic market, we need to compare the efficient level of output (where marginal cost equals marginal revenue) with the monopolist's chosen level of output.
Given the demand function Q = 14 - P, we can derive the monopolist's marginal revenue (MR) function by taking the derivative of the demand function:
MR = d(Q)/dP = d(14 - P)/dP = -1
Since the monopolist is producing 4 units of Q, we can derive the monopolist's price from the demand function:
Q = 14 - P
4 = 14 - P
P = 10
Now we can calculate the monopolist's marginal cost (MC), which is given as 6.
To find the efficient level of output, we set MR equal to MC:
MR = MC
-1 = 6
Since -1 does not equal 6, we know that the monopolist is not producing the efficient level of output.
To calculate the deadweight loss, we need to determine the difference between the efficient level of output and the monopolist's chosen level of output. In this case, the monopolist is producing 4 units of Q, but the efficient level of output is determined by setting MR equal to MC, which results in a quantity of -1.
The deadweight loss can be calculated as follows:
DWL = (1/2) * (P1 - P2) * (Q1 - Q2)
= (1/2) * (10 - (-1)) * (4 - (-1))
= (1/2) * (11) * (5)
= 55/2
= 27.5
Thus, the deadweight loss in this market is 27.5.
Since 27.5 is not one of the options provided, it seems there might be a mistake in the problem or the answer choices. You may want to double-check the question or refer to your course materials to ensure the accuracy of the given information.