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In the AFC championship game between the Indianapolis Colts and the New England Patriots in 2007, the Colts had a fourth down and inches play. Rather than punt the ball and turn it over to their opponent, the Colts decided to go for a first down. Suppose the Colts have two play options: a fullback running up the middle or a screen pass to a wide receiver. The Patriots also have two play options: setting up to defend against the run or setting up to defend against the screen pass. The coaches of the two teams simultaneously choose their plays. If the Colts run the ball and the Patriots set up to defend against the run, then the Colts' payoff is and the Patriots' payoff is 1. If the Colts pass and the Patriots set up to defend against the pass, then the Colts' payoff is and the Patriots receive 2. If the Colts run and the Patriots set up to defend against the pass, the Colts' payoff is 6 and the Patriots' is If the Colts pass and the Patriots set up to defend against the run, the Colts' payoff is 10 and the Patriots' is
a. Show the payoff matrix for this simultaneousmoves game. What is the Nash equilibrium? Is it a pure-strategy or mixed-strategies Nash equilibrium?
b. Now suppose instead that if the Colts pass and the Patriots set up to defend again the pass, the Colts' payoff is 8 and the Patriots' -8. is Write the payoff matrix for this simultaneous-moves game. What is the Nash equilibrium? Does this Nash equilibrium involve pure or mixed strategies?
If the firms collude to maximize their combined profit, find the price, output per firm, and profit per firm assuming they split the profits evenly.
Verify that the relationship between the AP and MP curves
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Calculate the equilibrium output if he discriminates perfectly.
An economy is operating with output $400 billion below its natural rate, and fiscal policymakers want to close this recessionary gap. The central bank agrees to adjust the money supply to hold the interest rate constant
Wealth statistics on the very rich are compiled every year by Forbes magazine.
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An industry consists of two firms, each of which have variable costs of $10 per unit but no fixed costs. The industry demand curve is P = 70 - Q. Solve for the Cournot equilibrium. In doing so, derive the reaction function of each firm (call Q1 an..
The forecasting staff for the Prizer Corp has developed a model to predict sales of its air cushioned ride snowmobiles. The model specifies that sales S vary jointly with disposable personal income Y and the population between ages 15 and 40 Z.
Can the United States establish a dialog with your group? What are the risks? What are the advantages?
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the purchaser of the metal pipe will only accept deliveries of pipe where the diameters fall in the range of 1" +/- 0.0030". Using Chebyshev's Theorem, what is the minimum percentage of acceptable metal pipe in a given shipment. (K must be in "st..
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