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##### Alex and Carrie plan to study together for a game theory test.

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**Question**

1. Alex and Carrie plan to study together for a game theory test. Alex prefers to study in the library.;Carrie prefers to study in the Student Union. If they study apart, they will each get a C on the;exam. If they study in the library, Alex will get an A and Carrie will get a B (feeling isolated she will;get on facebook and get distracted). If they study in the Student Union they will both get an A-.;They cannot reach each other and both leave for a study space.;Write down the rules of the game. Who are the players? What are the strategy choices? What is the;order of play? What are the payoffs?;Represent the game in normal (or strategic form). Represent the game in extensive form, with Alex;making her choice at the root of the game tree. Does it matter if Alex leaves home first? Why or why;not?;Now suppose that Alex does reach Carrie and tells her where she is going. Represent the game in;extensive form.;(Note: You are not being asked to solve the game.);2. Use the first order condition to find the critical points for the following functions. Show if the;critical point is a local or global maximum, or local or global minimum, or neither using the second;order condition.;f(x) = x2 +4x 8;f(x) = ln x x for all x>0;3. A firm has the following production function for engines;f(K,L) = 10 K1/2 L1/2;The cost of labor is 8/unit of labor and the cost of capital is 2/unit of capital. The firm must produce;400 engines.;Write the optimization problem.;Using the Lagrange method find the amount of capital and labor the firm should use. What is the;value of the Lagrange multiplier?

Paper#30696 | Written in 18-Jul-2015

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