There's a market with n = 4 oligopolistic firms. The industry-wide output of is Q = 60 metric kilotons and a market price of (when expressed per metric kiloton) p = 30 mio. €. The marginal cost parameters are c1=6, c2=7, c3=8 and c4=9 (total cost per firm: ci * qi). The firms in this market can be best thought of as choosing outputs (not prices). Assume that the inverse market demand function can be described by the following functional form: Price = A - bQ. How can we find the NE if we have two unknown? Being A and b if we have the input of A = 30 + 60b?
I don't really understand how. I must use the Nash equilibrium analysis to determine estimates for the demand function parameters A and b, so I could eventually draw a conclusion on how much market share each firm has. A = 30 + 60b and b = (A - 30) / 60, now if I plug each in, I just get A=A and b=b, which is not getting me very far, I tried using the profit function πi = (p - ci) * Qi and derivate but I still get mixed conclusions.. Would appreciate some help if it seems evident, I am just confused.. Thank you! @@naomiutgoff
situation is two firms compete in same market and situation are, suppose; (1) (current condition of market) firm A has 60% market share and firm B has 20 % under the competition policy (2) Firm A has 40% and Firm B also has 40% (3) Firm A has 30 % and Firm B has 60 market share. So how we proof it Nash equilibrium through game theory ? Please help me in this matter. Thank You Professor
You will obtain different market shares in Nash equilibrium if you start with firms with different costs. Try P = 11 - q1 - q2, c1 = 3, c2 =4. The Nash equilibrium quantities are q1 = 3, q2 = 2. Firm 1 (the low cost firm) has more of the market than firm 2 (the high cost firm). In this example, firm 1 has 60% of the market and firm 2 has 40% of the market. In real life, differences in market share are often due to factors beyond cost of production. One natural weakness of the Cournot model is that firms produce perfect substitutes, i.e. completely identical goods. Firms in real life produce partial substitutes, i.e. similar but not the same goods (think Coke vs. Pepsi).
Can anyone help me in understanding what are the possible values of q(1) from the graph drawn between q(1) and q(2) drawn in the video if q1 is rational and he knows that q2 is rational too . I have been trying for many days but my answer seems to be incorrect. q1 ~ q(a)
I'm not sure I entirely understand your question. Are you asking what happens if we restrict q1 and q2 to the rational numbers? Or are you asking what happens if players 1 and 2 are rational? Either way, the Nash equilbrium and analysis don't change. In the first case, nothing changes because the Nash equilibrium quantities are rational. In the second case, we have already assumed rationality on the part of both players. I hope this helps!
@@naomiutgoff This is the coursera question he seems to be asking. Posting here verbatim. Please don't provide direct answers but if you can give some helpful pointers that'd be great ma'am! Q) Now let’s think about the case where N=2 (there are two firms: A and B), a=5, b=1 and c=2. The firm A decides its amount of production - q(A) According to the following conditions: 1) The firm A is rational. 2) The firm A knows that the firm B is rational. From the options below, identify q (a) that the firm A never chooses. Select all that apply. a) 0 b) 0.25 c)0.5 d) 0.75 e) 1 f)1.25 g)1.5 h)1.75 i) 2
@@naomiutgoff Hello ma'am, this has been solved now. Thanks for your video. Let me know if you are interested in solution to this question. I can reply here with the solution.😊
This is the coursera question he seems to be asking. Posting here verbatim. Please don't provide direct answers but if you can give some helpful pointers that'd be great ma'am! Q) Now let’s think about the case where N=2 (there are two firms: A and B), a=5, b=1 and c=2. The firm A decides its amount of production - q(A) According to the following conditions: 1) The firm A is rational. 2) The firm A knows that the firm B is rational. From the options below, identify q (a) that the firm A never chooses. Select all that apply. a) 0 b) 0.25 c)0.5 d) 0.75 e) 1 f)1.25 g)1.5 h)1.75 i) 2
Great video Ma'am. Please keep on making video of mathematical economics. Thank You so much Ma'am.
Very thorough explanation, thank you for posting the video!
Thankyou so much ma’am for explaining each n every thing thoroughly 🙏
My pleasure 😊
thanks a lot professor. it was so helpfull
thanks so much madam this is really awesome and helpful.
How can you mathematically evaluate the symmetry in step 4?
I'm not sure I understand this question. We know the game is symmetric because the firms have identical cost functions.
There's a market with n = 4 oligopolistic firms. The industry-wide output of is Q = 60 metric kilotons and a market price of (when expressed per metric kiloton) p = 30 mio. €. The marginal cost parameters are c1=6, c2=7, c3=8 and c4=9 (total cost per firm: ci * qi). The firms in this market can be best thought of as choosing outputs (not prices). Assume that the inverse market demand function can be described by the following functional form: Price = A - bQ. How can we find the NE if we have two unknown? Being A and b if we have the input of A = 30 + 60b?
A and b are not unknowns - they are parameters. You want to find q1, q2, q3, q4 in terms of A and b.
I don't really understand how. I must use the Nash equilibrium analysis to determine estimates for the demand function parameters A and b, so I could eventually draw a conclusion on how much market share each firm has. A = 30 + 60b and b = (A - 30) / 60, now if I plug each in, I just get A=A and b=b, which is not getting me very far, I tried using the profit function πi = (p - ci) * Qi and derivate but I still get mixed conclusions.. Would appreciate some help if it seems evident, I am just confused.. Thank you! @@naomiutgoff
situation is two firms compete in same market and situation are, suppose; (1) (current condition of market) firm A has 60% market share and firm B has 20 % under the competition policy (2) Firm A has 40% and Firm B also has 40% (3) Firm A has 30 % and Firm B has 60 market share. So how we proof it Nash equilibrium through game theory ? Please help me in this matter. Thank You Professor
You will obtain different market shares in Nash equilibrium if you start with firms with different costs. Try P = 11 - q1 - q2, c1 = 3, c2 =4. The Nash equilibrium quantities are q1 = 3, q2 = 2. Firm 1 (the low cost firm) has more of the market than firm 2 (the high cost firm). In this example, firm 1 has 60% of the market and firm 2 has 40% of the market.
In real life, differences in market share are often due to factors beyond cost of production. One natural weakness of the Cournot model is that firms produce perfect substitutes, i.e. completely identical goods. Firms in real life produce partial substitutes, i.e. similar but not the same goods (think Coke vs. Pepsi).
@@naomiutgoff Professor Please share your email. I want to show you my work
Can anyone help me in understanding what are the possible values of q(1) from the graph drawn between q(1) and q(2) drawn in the video if q1 is rational and he knows that q2 is rational too .
I have been trying for many days but my answer seems to be incorrect.
q1 ~ q(a)
I'm not sure I entirely understand your question. Are you asking what happens if we restrict q1 and q2 to the rational numbers? Or are you asking what happens if players 1 and 2 are rational? Either way, the Nash equilbrium and analysis don't change. In the first case, nothing changes because the Nash equilibrium quantities are rational. In the second case, we have already assumed rationality on the part of both players. I hope this helps!
@@naomiutgoff This is the coursera question he seems to be asking. Posting here verbatim.
Please don't provide direct answers but if you can give some helpful pointers that'd be great ma'am!
Q) Now let’s think about the case where N=2 (there are two firms: A and B), a=5, b=1 and c=2. The firm A decides its amount of production - q(A)
According to the following conditions:
1) The firm A is rational.
2) The firm A knows that the firm B is rational.
From the options below, identify q (a)
that the firm A never chooses. Select all that apply.
a) 0 b) 0.25 c)0.5 d) 0.75 e) 1 f)1.25 g)1.5 h)1.75 i) 2
@@shivaprasad098765432 You really need to consult with whoever is running the Coursera course.
@@naomiutgoff Hello ma'am, this has been solved now. Thanks for your video.
Let me know if you are interested in solution to this question. I can reply here with the solution.😊
@@shivaprasad098765432 Hello Shivaprasad, can u help me solve the problem? I don't understand the 13×13 matrix term ! Help me brother
thanks
This is the coursera question he seems to be asking. Posting here verbatim.
Please don't provide direct answers but if you can give some helpful pointers that'd be great ma'am!
Q) Now let’s think about the case where N=2 (there are two firms: A and B), a=5, b=1 and c=2. The firm A decides its amount of production - q(A)
According to the following conditions:
1) The firm A is rational.
2) The firm A knows that the firm B is rational.
From the options below, identify q (a)
that the firm A never chooses. Select all that apply.
a) 0 b) 0.25 c)0.5 d) 0.75 e) 1 f)1.25 g)1.5 h)1.75 i) 2