1. Given that the demand function x (p, w) is homogeneous degree 1 for income w and satisfies Walras law, find the income elasticity of demand (p is price, w is income). 2. Assume that the consumers choice satisfies the weak axiom of revealed preference. In this case, mathematically prove the compensated law of demand using the Walras law. 4.Answer the problem by watching two Bayesian simultaneous games: Two workers can do one work. When the work is done, each person gets 1 reward, and if its not done, he gets zero. The cost of doing work is Ci (i = 1, 2), which varies from person to person. Each person knows the cost of his own work but not the other. It is common knowledge that each Ci comes from a uniform distribution in [0,3 / 2]. In other words, the cost information is private information. The games rewards are summarized below. The first value in the complement matrix is player 1s complement, and the second value is player 2s complement. Get the Bayesian Nash Equilibrium from the game above. Player 2 Dont work 1-4,1 0,0 Player 1 Work 1-4,1-C2 1,1-cz Work Dont work
1. Given that the demand function x (p, w) is homogeneous degree 1 for
1. Given that the demand function x (p, w) is homogeneous degree 1 for income w and satisfies Walras law, find the income elasticity of demand (p is price, w is income). 2. Assume that the consumers choice satisfies the weak axiom of revealed preference. In this case, mathematically prove the compensated law of demand using the Walras law. 4.Answer the problem by watching two Bayesian simultaneous games: Two workers can do one work. When the work is done, each person gets 1 reward, and if its not done, he gets zero. The cost of doing work is Ci (i = 1, 2), which varies from person to person. Each person knows the cost of his own work but not the other. It is common knowledge that each Ci comes from a uniform distribution in [0,3 / 2]. In other words, the cost information is private information. The games rewards are summarized below. The first value in the complement matrix is player 1s complement, and the second value is player 2s complement. Get the Bayesian Nash Equilibrium from the game above. Player 2 Dont work 1-4,1 0,0 Player 1 Work 1-4,1-C2 1,1-cz Work Dont work
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