I was hoping I could have some help on parts c-e of this problem I’m getting a little stuck on making sure my values are correct given this this is a cournot duopoly model. A homogenous product is produced by two rival firms. They have the same costs.The market demand is:P = 80 –-QР%3D 80— Q1 — Q2orThe firms' total cost equations are:C1 = 50Q1C2 = 50Q2a. Both firms choose their output level at the same time. In estimating its marginal revenue,each firm takes its rival's output as given and maximizes profit subject to that assumption.Write Firm 1's total revenue (= PQ1) and marginal revenue equations.TR1 =MR1 =b. Set MR1 = MC1 to derive the equation of Firm 1's reaction curve, Q1*(Q2). Also write thesymmetric reaction curve equation for Firm 2.Qi*(Q2 :%3DQz*(Q1) =c. Solve for the profit-maximizing price. Find the output, revenue, cost, and profit of each firm.Add the firms' revenue (TR = TRỊ + TR2), cost (TC = TC1 + TC2), and profit (N = N1 + N2).Qz*p* =TRỊ =TC1 =TR =TC =d. GRAPH the Cournot reaction curves. Label the Cournot equilibrium point (EcouRN). Label thepoint that shows what the firms' outputs would be if, instead, they behaved like perfectcompetitors (EPTN), and happened to each supply the same output. Finally, label the pointthat represents the firms' outputs if, instead, they colluded-behaved like a singlemonopolist-and split the profit equally (EcoLLu).II Cournot Duopoly Modele. Generalize your result using parameters a and c:Demand and cost are: P = a – Q1 – Q2TC =cQ1TC2 =CQ2Qi*(Q2) =Q2*(Q1) =Q1*Qz*P1* =P2* =TRỊ =TC =TR =TC ==

Introduction We have given a cournot duopoly market. Here are two firms in the market. Both will…

e. Generalize your result using parameters a and c: Demand and cost are: P = a - Q1 - Q2 TC1 = cQ1 TC2 = cQ2 Qi*(Q?) = Q2*(Qi) = . Q1* = Q²* P1* = P2* = TRỊ = TC1 = П TR = TC = II II

e. Generalize your result using parameters a and c: Demand and cost are: P = a - Q1 - Q2 TC1 = cQ1 TC2 = cQ2 Qi(Q?) = Q2(Qi) = . Q1* = Q²* P1* = P2* = TRỊ = TC1 = П TR = TC = II II

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Chapter1: Making Economics Decisions

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Question

I was hoping I could have some help on parts c-e of this problem I’m getting a little stuck on making sure my values are correct given this this is a cournot duopoly model.

A homogenous product is produced by two rival firms. They have the same costs.
The market demand is:
P = 80 –
-Q
Р%3D 80— Q1 — Q2
or
The firms' total cost equations are:
C1 = 50Q1
C2 = 50Q2
a. Both firms choose their output level at the same time. In estimating its marginal revenue,
each firm takes its rival's output as given and maximizes profit subject to that assumption.
Write Firm 1's total revenue (= PQ1) and marginal revenue equations.
TR1 =
MR1 =
b. Set MR1 = MC1 to derive the equation of Firm 1's reaction curve, Q1*(Q2). Also write the
symmetric reaction curve equation for Firm 2.
Qi*(Q2 :
%3D
Qz*(Q1) =
c. Solve for the profit-maximizing price. Find the output, revenue, cost, and profit of each firm.
Add the firms' revenue (TR = TRỊ + TR2), cost (TC = TC1 + TC2), and profit (N = N1 + N2).
Qz*
p* =
TRỊ =
TC1 =
TR =
TC =
d. GRAPH the Cournot reaction curves. Label the Cournot equilibrium point (EcouRN). Label the
point that shows what the firms' outputs would be if, instead, they behaved like perfect
competitors (EPTN), and happened to each supply the same output. Finally, label the point
that represents the firms' outputs if, instead, they colluded-behaved like a single
monopolist-and split the profit equally (EcoLLu).
II

Cournot Duopoly Model
e. Generalize your result using parameters a and c:
Demand and cost are: P = a – Q1 – Q2
TC =
cQ1
TC2 =
CQ2
Qi*(Q2) =
Q2*(Q1) =
Q1*
Qz*
P1* =
P2* =
TRỊ =
TC =
TR =
TC =
=

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Chapter 14: Oligopoly 1 23.Explain how the outcome of the Cournot model is achieved. 24.An essential assumption of the Cournot model is that each firm aims to maximize profits, based on the expectation that its own output decision will not have an effect on the decisions of its rivals. Critically evaluate this assumption. 25.In choosing the optimal output, the monopolist had only to consider its own costs and the demand curve that it faced. How do things change under duopoly and what does the Cournot model argue about how firms will behave? 26.What is the output level predicted by the Cournot model? Discuss this in terms of the different market models that have been surveyed so far. 27.Evaluate the following statement. The Cournot model basically assumes that the sole decision of each firm in a duopoly is one of determining how much to produce not which price to set. 28.What is price leadership?
Can you help me solve this please?
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