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2. Consider the game in which the following are commonly known. First, Ann chooses between actions a and b. Then, with probability 1/3, Bob observes which action Ann has chosen and with probability 2/3 he does not observe the action she has chosen. In all cases (regardless of whether he has observed Ann chose a, or he has observed Ann chose b, or he has not observed any action), Bob chooses between actions and . The payoff of each player is 1 after (a, ) and (b, ) and 0 otherwise. (a) Write the above game in extensive form. (b) Write the above game in normal form. 3), where s1 {, } , denotes the choice of the information set (numbered as 1 B = (s1 2 Strategy of Ann is simple: {a, b}. 2 {, } , s3 {, }. 1 2 in the picture) and s Strategy of Bob is s , s , s s s 3 is for node 2, and s is for node 3. Utility of outcomes is in the following table. a b 1,1 0,0 1,1 1 3 , 1 3 2 3 , 2 3 0,0 2 3 , 2 3 1 3 , 1 3 1 3 , 1 3 2 3 , 2 3 1 3 , 1 3 1,1 0,0 2 3 , 2 3 0,0 1,1 3. Consider the following variation of the above game. First, Ann chooses between actions a and b. Then, Bob decides whether to observe the chosen action of Ann or not, by choosing between the actions Open and Shut, respectively. In all cases, Bob then chooses between actions and . The payoff of Ann is 1 after (a, ) and (b, ) and 0 otherwise, regardless of whether Bob chooses Open or Shut. The payoff of Bob is equal to the payoff of Ann if he has chosen Shut, and his payoff is equal to the payoff of Ann minus 1/2 if he has chosen Open. (a) Write the above game in extensive form. (b) Write the above game in normal form. Strategy of Ann is simple: {a, b}. Strategy of Bob is sB = (s1, s2, s , s4), where s 3 {O, S} , s2 {, } , s3 {, } , s4 {, }. s2 denotes the choice of the node 1 (the left one) and s3 is for node 2, s4is for the information set on the right side (numbered as 3 in the picture). Utility of outcomes is in the following table. a b O 1, 0.5 0,-0.5 O 1, 0.5 0,-0.5 O 1, 0.5 1, 0.5 O 1, 0.5 1, 0.5 O 0,-0.5 0,-0.5 O 0,-0.5 0,-0.5 O 0,-0.5 1, 0.5 O 0,-0.5 1, 0.5 S 1,1 0,0 S 0,0 1,1 S 1,1 0,0 S 0,0 1,1 S 1,1 0,0 S 0,0 1,1 S 1,1 0,0 S 0,0 1,1 the question is complete plz

4. Federal government is planning to build an interstate highway between two states, named A and B. The highway costs C > 0 to the government, and the value of the highway to the states A and B are vA 0 and vB 0, respectively. Simultaneously, each state i {A, B} is to bid bi [0, ). If bA + bB C the highway is constructed. For any distinct i, j {A, B}, state i pays C bj to the federal government if bj < C bA + bB. (There is no payment otherwise.) The payoff of a state is the value of the highway to the state minus its own payment to the government if the highway is built, and 0 otherwise. (You can focus on the case vA + vB < C.) (a) Write this in the normal form. Strategy of player i is choice of bi [0, ). Utility from strategy profile x of player i is ui(bA, bB) = vi C + bj if bA + bB C = 0 if bA + bB < C (b) Check if there is a dominant strategy equilibrium, and compute it if there is one. There is a unique dominant strategy equilibrium, (vA, vB). In other words, bidding own value is the dominant strategy equilibrium. From player A's point of view, there are three cases. If bB C, then uA = vA, regardless of what bA is. If C vA bB < C, then A wants to build the highway as uA = vA C + bB 0. Thus, bA C bB is the best response. Lastly, if bB < C vA, then A does not want to build the highway as uA = vA C +bB < 0. The best response for this case is bA < C bB. 4 For bB = C vA + t (0 < t < vA), we need bA C bB = vA t. As this inequaility has to hold for all 0 < t < vA, we need bA vA. Similarly, for bB = C vA t (0 < t < C vA), we need bA < C bB = vA + t. As this inequaility has to hold for all 0 < t < C vA, we need bA vA. Therefore, the dominant strategy is bA = vA. For example, if A chooses bA = vA + ( > 0), when bB = C vA 2 , uA = 2 < 0 while bA = vA gives uA = 0.

State whether you think each of the following questions is true (T), false (F), or uncertain (U) and briefly explain your answer. No credit will be given for an answer without any explanation (1) [5 points] Staggering makes the overall level of wages and prices adjust quickly, because individual wages and prices change frequently (2) [5 points] If Congress raises taxes, the response of the economy to the tax increase depends on how the central bank responds (3) [5 points] The Mundell-Fleming model shows that a fiscal policy is more effective than a monetary policy Part B (15 points) Briefly answer the following questions in words. (1) [5 points] Can an IS curve be vertical? Give an example (2) [5 points] What is an advantage to fixed exchange rates? (3) [5 points] Why do firms have motives for holding inventories of goods? Give an example

Dynamic Life Cycle Model is used to evaluate an individual's life-time choices over consumption and working.

Use your understanding of this model to answer the following questions:

a) Suppose Mary lives three periods: childhood, adulthood and elderhood. For simplification, use "c", "a" and "e" as the subscriptions attached to the variables that describe Mary's choices in different periods. Write down Mary's life-time income constraint. Suppose the interest rate is r. b) Assume that Mary's life is no longer divided into 3 periods. Instead, Mary is known to live to 105-years old. Use the summation sign, (sigma), to write down Mary's life-time income constraint. The interest rate is still r. c) Draw a diagram to show three possible reasons for Mary to experience wage increases in the framework of Dynamic Life Cycle Model. Give an example to each of the three cases. Then, determine which wage increases are anticipated or unanticipated, and permanent or transitory? d) Conduct an income effect and substitution effect analysis on the three wage increases discussed in Part c). Rank the magnitudes of the total effects in the three cases from smallest to largest and explain why.