A homogenous product is produced by two rival firms. They have the same costs. The market demand is: P = 80 – Q P = 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 MR, = MC¡ to derive the equation of Firm 1's reaction curve, Q,*(Q). Also write the symmetric reaction curve equation for Firm 2. Q1*(Q? : Q2*(Q1) : c. Solve for the profit-maximizing price. Find the output, revenue, cost, and profit of each firm. Add the firms' revenue (TR = TR1 + TR2), cost (TC = TC, + TC2), and profit (N = Ni + N2). Qi* Qz* = p* = %3D TR1 = TC = TR = TC = %3D 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

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For this question I cannot completely understand how to solve given it is a cournot model based question. Could I have help
A homogenous product is produced by two rival firms. They have the same costs.
The market demand is:
P = 80 – Q
P = 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.
TR =
MR1 =
b. Set MR1 = MC, to derive the equation of Firm l's reaction curve, Q1*(Q2). Also write the
symmetric reaction curve equation for Firm 2.
Q1*(Q?) =
%3D
Qz*(Q!) =
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 (M = N1 + N2).
Q1*
Q2*
p* =
%3D
TR1 =
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 (ETN), 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).
Transcribed Image Text:A homogenous product is produced by two rival firms. They have the same costs. The market demand is: P = 80 – Q P = 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. TR = MR1 = b. Set MR1 = MC, to derive the equation of Firm l's reaction curve, Q1*(Q2). Also write the symmetric reaction curve equation for Firm 2. Q1*(Q?) = %3D Qz*(Q!) = 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 (M = N1 + N2). Q1* Q2* p* = %3D TR1 = 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 (ETN), 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).
Cournot Duopoly Model
e. Generalize your result using parameters a and c:
Demand and cost are: P = a – Q1
TC1 = cQ1
TC2 = cQ2
Q1*(Q?)
Q2*(Q1)
P1* =
P2
TR1 =
TC1 =
N1 =
TR =
TC =
Transcribed Image Text:Cournot Duopoly Model e. Generalize your result using parameters a and c: Demand and cost are: P = a – Q1 TC1 = cQ1 TC2 = cQ2 Q1*(Q?) Q2*(Q1) P1* = P2 TR1 = TC1 = N1 = TR = TC =
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