question archive A firm with market power has an inverse demand curve of P = 450 - 5Q and marginal cost of MC = 40Q, where Q is measured in thousands
A firm with market power has an inverse demand curve of P = 450 - 5Q and marginal cost of MC = 40Q, where Q is measured in thousands
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A firm with market power has an inverse demand curve of P = 450 - 5Q and marginal cost of MC = 40Q, where Q is measured in thousands. What is the deadweight loss from market power at the firms profit maximizing output level?
a. 15000
b. 280000
c. 22500
d. 9400
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If P = 450 - 5Q and MC = 40Q to determine the deadweight loss (DWL) calculate the perfect competition and monopoly quantities and prices.
In perfect competition set price equal to marginal cost and solve for the equilibrium quantity. Plug the equilibrium quantity into the inverse demand curve and solve for the competitive price.
In perfect competition P=MC
450 - 5Q = 40Q
45Q = 450
Q = 10
P = 450 - 5*10 = 400
Quantity is equal to 10 and price is equal to 400 in perfect competition
Since the demand function is given, multiply the inverse demand by quantity to find the total revenue function. Take the derivative of the total revenue function to find the marginal revenue function. Set the marginal revenue equal to the marginal cost and solve for the profit maximizing quantity. Plug the profit maximizing quantity into the inverse demand curve and solve for price to find the profit maximizing price.
In a monopoly MR=MC
Total Revenue = P * Q = 450Q - 5Q^2
Marginal Revenue = 450 - 10Q
450 - 10Q = 40Q
50Q = 450
Q = 9
P = 450 - 5*9 = 405
Quantity is equal to 9 and price is equal to 405 in profit maximization.
The deadweight loss is equal to the area between the the inverse demand and marginal cost from the profit maximizing quantity to the competitive quantity. Since the profit maximizing price is known solve for the marginal cost at the same quantity. The deadweight loss is equal to 0.5 multiplied by the difference between the profit maximizing price and the marginal cost at the profit maximizing quantity multiplied by the difference between the profit maximizing quantity and the perfectly competitive quantity.
To find DWL solve for MC when Q = 9
MC = 40*9 = 360
DWL = 0.5 * (405 - 360) * (10 - 9) = 22.5
The answer is C. The deadweight loss is 22500
