Asked by Hannah Emmett on May 24, 2024
Verified
suppose that Grinch and Grubb go into the wine business in a small country where wine is difficult to grow.The demand for wine is given by p $420 .2Q, where p is the price and Q is the total quantity sold.The industry consists of just the two Cournot duopolists, Grinch and Grubb.Imports are prohibited.Grinch has constant marginal costs of $60 and Grubb has marginal costs of $30.How much Grinch's output in equilibrium?
A) 275
B) 550
C) 825
D) 1,100
E) 1,650
Marginal Costs
The uplift in total financial outlay required for the making of another unit of a product or service.
Cournot Duopolists
Firms in a market where only two producers exist and compete under the Cournot assumption, where each firm decides its production level assuming the output of its competitor is fixed.
Demand for Wine
The total quantity of wine that consumers are willing and able to purchase at various prices within a specific time period.
- Understand the concept of Cournot duopoly and how firms' output decisions affect market equilibrium.
- Calculate the stable output level for businesses operating under a Cournot duopoly framework.
- Evaluate the impact of external factors, such as import bans, on duopolistic markets.
Verified Answer
AS
Arjun Subramanyam
May 24, 2024
Final Answer :
B
Explanation :
To find the equilibrium output of Grinch, we need to use the Cournot model:
Grinch's profit function: πg = (p - 60)qg(qg + qb)
Grubb's profit function: πb = (p - 30)qb(qg + qb)
Market demand: Q = .2Q = 420 - p
First, we can rewrite the demand as p = 420 - 0.2Q. Then we can substitute this into the profit functions:
πg = (420 - 0.2Q - 60)qg(qg + qb)
πb = (420 - 0.2Q - 30)qb(qg + qb)
To find the Nash equilibrium, we need to solve for the best response functions of each player. Grinch's best response is:
qg = (1/3)(180 - qb)
Grubb's best response is:
qb = (1/3)(180 - qg)
We can substitute Grubb's best response into Grinch's best response to get:
qg = (1/3)(180 - (1/3)(180 - qg))
qg = 550
Therefore, Grinch's output in equilibrium is 550 units.
Grinch's profit function: πg = (p - 60)qg(qg + qb)
Grubb's profit function: πb = (p - 30)qb(qg + qb)
Market demand: Q = .2Q = 420 - p
First, we can rewrite the demand as p = 420 - 0.2Q. Then we can substitute this into the profit functions:
πg = (420 - 0.2Q - 60)qg(qg + qb)
πb = (420 - 0.2Q - 30)qb(qg + qb)
To find the Nash equilibrium, we need to solve for the best response functions of each player. Grinch's best response is:
qg = (1/3)(180 - qb)
Grubb's best response is:
qb = (1/3)(180 - qg)
We can substitute Grubb's best response into Grinch's best response to get:
qg = (1/3)(180 - (1/3)(180 - qg))
qg = 550
Therefore, Grinch's output in equilibrium is 550 units.
Learning Objectives
- Understand the concept of Cournot duopoly and how firms' output decisions affect market equilibrium.
- Calculate the stable output level for businesses operating under a Cournot duopoly framework.
- Evaluate the impact of external factors, such as import bans, on duopolistic markets.