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Given numbers and equations,

d) (8 points) Using a single graph, draw the reaction functions for each firm and identify the Nash Equilibrium. Make sure your graph is accurate and properly and completely labeled. With q1 on the horizontal axis and q2 on the vertical axis: Firm 1's Reaction Function has vertical intercept = 12 and horizontal intercept = 6. Firm 2's Reaction Function has vertical intercept = 6 and horizontal intercept = 12. The Cournot-Nash Equilibrium is at the intersection of the reaction functions where q1 = q2 = 4. (Note: If the axes are labeled with qu on the vertical axis and q2 on the horizontal axis, then the graph will look the same except that Firm 1's Reaction Function has vertical intercept = 6 and horizontal intercept = 12. Firm 2's Reaction Function has vertical intercept = 12 and horizontal intercept = 6.) Each Reaction Function: 2 points (4 points total) CNE: 2 points . Labeling: 2 points. If the graph is not labeled and you can not tell which reaction function is which, then both reaction functions and the labeling are wrong. 12 Firm 1's BR Function Cournot- 6 Nash Equilibrium Firm 2's BR Function 6 127. (20 Total Points) Suppose there are two firms operating in a market. The firms produce identical products, and the total cost for each firm is given by C = 8q;, i = 1,2, where qi is the quantity of output produced by firm i. Therefore the marginal cost for each firm is constant at MC = 10. Also, the market demand is given by P = 100-5Q, where Q= qi + q2 is the total industry output. The following formulas will be useful: If market demand is given by P = a -bQ, then MR, = a - 2bq1 - bq2 MRz = a - bqi - 2bq2 Assume the firms choose their quantities simultaneously. a) (6 points) Determine the Nash equilibrium in quantities; that is, how much output will each firm produce in equilibrium? q1 = 6 42 = 6d) (8 points) Using a single graph, draw the reaction functions for each firm and identify the Nash Equilibrium. Make sure your graph is accurate and properly and completely labeled. With qi on the horizontal axis and qz on the vertical axis: Firm 1's Reaction Function has vertical intercept = 18 and horizontal intercept = 9. Firm 2's Reaction Function has vertical intercept = 9 and horizontal intercept = 18. The Cournot-Nash Equilibrium is at the intersection of the reaction functions where qi = q2 = 6. (Note: If the axes are labeled with qi on the vertical axis and q2 on the horizontal axis, then the graph will look the same except that Firm 1's Reaction Function has vertical intercept = 9 and horizontal intercept = 18. Firm 2's Reaction Function has vertical intercept = 18 and horizontal intercept = 9.) Each Reaction Function: 2 points (4 points total) CNE: 2 points . . Labeling: 2 points. If the graph is not labeled and you can not tell which reaction function is which, then both reaction functions and the labeling are wrong. 18 Firm 1's BR Function Cournot-Nash Equilibrium Firm 2's BR Function 9 187. (20 Total Points) ) Suppose there are two firms operating in a market. The firms produce identical products, and the total cost for each firm is given by C = 8q:, i = 1,2, where q; is the quantity of output produced by firm i. Therefore the marginal cost for each firm is constant at MC = 8. Also, the market demand is given by P = 56-4Q, where Q= q1 + q2 is the total industry output. The following formulas will be useful: If market demand is given by P = a -bQ, then MR1 = a - 2bq1 - bqz MR2 = a -bq1 - 2bq2 Assume the firms choose their quantities simultaneously