Asked by Natasha Rodriguez on Jul 12, 2024
Verified
Suppose that the inverse demand for bean sprouts is given by P(Y) 370 4Y and the total cost of producing Y units for any firm is TC(Y) 10Y.If the industry consists of two Cournot duopolists, then in equilibrium each firm's production is
A) 45 units.
B) 22.50 units.
C) 15 units.
D) 30 units.
E) 23.13 units.
Cournot Duopolists
Firms in a duopoly market structure who decide on their output level assuming the output of the competitor is fixed, leading to a strategic interdependence.
Total Cost
The sum of fixed and variable costs incurred in the production of goods or services.
Inverse Demand
A representation of demand that shows the price as a function of quantity demanded, contrary to the typical demand curve.
- Utilize the framework of Cournot equilibrium to estimate the production outputs of entities in duopoly settings.
Verified Answer
CB
Courtney BlackburnJul 18, 2024
Final Answer :
D
Explanation :
To find the equilibrium production levels of the two Cournot duopolists, we need to use the following steps:
1. First, we need to find the industry demand function by adding the individual demand functions of the two firms:
P(Y) = 370 - 4Y
2. We can then find the inverse supply function for each firm by using the first-order condition for profit maximization:
MR = MC
where MR is the marginal revenue (equal to the derivative of the industry demand function) and MC is the marginal cost (equal to the derivative of the cost function):
MR = 370 - 8Y
MC = 10
Setting MR = MC, we get:
370 - 8Y = 10
Y = 45
So each firm produces 45/2 = 22.5 units.
Therefore, the answer is D, each firm's production level is 30 units.
1. First, we need to find the industry demand function by adding the individual demand functions of the two firms:
P(Y) = 370 - 4Y
2. We can then find the inverse supply function for each firm by using the first-order condition for profit maximization:
MR = MC
where MR is the marginal revenue (equal to the derivative of the industry demand function) and MC is the marginal cost (equal to the derivative of the cost function):
MR = 370 - 8Y
MC = 10
Setting MR = MC, we get:
370 - 8Y = 10
Y = 45
So each firm produces 45/2 = 22.5 units.
Therefore, the answer is D, each firm's production level is 30 units.
Learning Objectives
- Utilize the framework of Cournot equilibrium to estimate the production outputs of entities in duopoly settings.