In the field of industrial organization, economists study the strategic behavior of firms under alternative market...
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In the field of industrial organization, economists study the strategic behavior of firms under alternative market structures and regulatory policies. One such market structure is known as an oligopoly where a few dominant firms strategically interact with each other to maximize their own profits. To an economist, the term "strategic interaction" implies that a firm takes into account his competitor's production decisions when making its own production decision. TC= The Cournot duopoly model analyzes such strategic interaction between two firms that choose output to maximize profit. 1. The Cournot duopoly model applies to the market for warm nuclear waste-water. Let q and qz denote the number of water bottles produces by duopolists 1 and 2, respectively. The inverse market demand curve may be written as a. P(91,92) =200 - 2(q1 + 92). Suppose the total cost function for each firm is given as TC(q)=100 + 15q1 TC(92) = 100 + 10qz Write the profit function for firm 1. Denote it as (q1,q2). b. Firm 1's objective is to maximize its own profit by choosing its own quantity. This is equivalent to finding an(91.92)/091, setting it equal to zero and solving for q as a function of q2. This is known as firm 1's best response function. It tells us how firm 1 would optimally respond to any level of its competitor's output. Specify firm 1's best response function: 2 92 + 292 c. Graph firm 1's best response function below. Put q2 on the vertical axis and q on the horizontal axis. 1009 90. 80 20 60 So 40 30 20 = 185+2q2=0 81= 19 10 20 30 40 So 60 70 8690 100 4 (20 185 +292 = -185 7185 222-185 2 92=92.5-29. d. Write the profit function for firm 2. Denote it as 2 2 (91, 92). e. Firm 2's objective is to maximize its own profit by choosing its own quantity. This is equivalent to finding d2 (91,92)/0q2, setting it equal to zero, and solving for q2 as a function of q1. This is known as firm 2's best response function. It tells us how firm 2 would lo optimall respond to any level of its competitor's output. Specify firm 2's best response function: f. Graph firm 2's best response function on the same graph from part (c). (Remember that q is on the vertical axis and q is on the horizontal axis.) g. The Nash equilibrium represents the equilibrium levels of output that maximize both firm 1 and firm 2's profits simultaneously. It occurs where the two best response functions cross. Solve for the Nash equilibrium by solving this system of two equations. Call the solution (992) and illustrate it on the graph. In the field of industrial organization, economists study the strategic behavior of firms under alternative market structures and regulatory policies. One such market structure is known as an oligopoly where a few dominant firms strategically interact with each other to maximize their own profits. To an economist, the term "strategic interaction" implies that a firm takes into account his competitor's production decisions when making its own production decision. TC= The Cournot duopoly model analyzes such strategic interaction between two firms that choose output to maximize profit. 1. The Cournot duopoly model applies to the market for warm nuclear waste-water. Let q and qz denote the number of water bottles produces by duopolists 1 and 2, respectively. The inverse market demand curve may be written as a. P(91,92) =200 - 2(q1 + 92). Suppose the total cost function for each firm is given as TC(q)=100 + 15q1 TC(92) = 100 + 10qz Write the profit function for firm 1. Denote it as (q1,q2). b. Firm 1's objective is to maximize its own profit by choosing its own quantity. This is equivalent to finding an(91.92)/091, setting it equal to zero and solving for q as a function of q2. This is known as firm 1's best response function. It tells us how firm 1 would optimally respond to any level of its competitor's output. Specify firm 1's best response function: 2 92 + 292 c. Graph firm 1's best response function below. Put q2 on the vertical axis and q on the horizontal axis. 1009 90. 80 20 60 So 40 30 20 = 185+2q2=0 81= 19 10 20 30 40 So 60 70 8690 100 4 (20 185 +292 = -185 7185 222-185 2 92=92.5-29. d. Write the profit function for firm 2. Denote it as 2 2 (91, 92). e. Firm 2's objective is to maximize its own profit by choosing its own quantity. This is equivalent to finding d2 (91,92)/0q2, setting it equal to zero, and solving for q2 as a function of q1. This is known as firm 2's best response function. It tells us how firm 2 would lo optimall respond to any level of its competitor's output. Specify firm 2's best response function: f. Graph firm 2's best response function on the same graph from part (c). (Remember that q is on the vertical axis and q is on the horizontal axis.) g. The Nash equilibrium represents the equilibrium levels of output that maximize both firm 1 and firm 2's profits simultaneously. It occurs where the two best response functions cross. Solve for the Nash equilibrium by solving this system of two equations. Call the solution (992) and illustrate it on the graph.
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Related Book For
Introduction to Real Analysis
ISBN: 978-0471433316
4th edition
Authors: Robert G. Bartle, Donald R. Sherbert
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