Asked by Tajmia Muhammad on Jul 05, 2024
Verified
Suppose that the duopolists Carl and Simon face a demand function for pumpkins of Q 16,800 800P, where Q is the total number of pumpkins that reach the market and P is the price of pumpkins.Suppose further that each farmer has a constant marginal cost of $1 for each pumpkin produced.If Carl believes that Simon is going to produce Qs pumpkins this year, then the reaction function tells us how many pumpkins Carl should produce in order to maximize his profits.Carl's reaction function is RC (Qs)
A) 16,800 800Qs.
B) 4,000 Qs/2.
C) 8,000 Qs/2.
D) 16,800 1,600Qs.
E) 12,000 Qs.
Reaction Function
In economics, it represents how one economic agent's decision changes in response to another's action, especially in competitive markets or games.
Demand Function
A mathematical representation showing the relationship between the quantity demanded of a good and its price, along with other determinants.
Marginal Cost
Additional cost incurred by increasing product or service production by one unit, emphasizing the concept of incremental expenditure.
- Pinpoint the balance production level for companies in a Cournot duopoly environment.
- Facilitate the use of the Cournot model in a multitude of market situations and demand function contexts.
- Understand the concept of reaction functions and how they guide firms' production decisions.
Verified Answer
πC = (Q - RC(Qs))P - Q
Taking the derivative of this with respect to Q and setting it to zero, we can solve for RC:
RC = 8,000 - 50Qs
Therefore, the best choice is option C, 8,000 Qs/2.
Learning Objectives
- Pinpoint the balance production level for companies in a Cournot duopoly environment.
- Facilitate the use of the Cournot model in a multitude of market situations and demand function contexts.
- Understand the concept of reaction functions and how they guide firms' production decisions.
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