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Q = K 1 =4 L 1 =8 Then, answer the following questions. (a) In the short run, the …rm is committed to hire a …xed amount of capital K(+1), and can vary its output Q only by employing an appropriate amount of labor L . Derive the …rm’s short-run total, average, and marginal cost functions. (b) In the long run, the …rm can vary both capital and labor. Derive the …rm’s

(a) The intersection of any pair of open sets is an open set. (b) The union of any (possibly infinite) collection of open sets is open. (c) The intersection of any (possibly infinite) collection of closed sets is closed. (You can use (b) and De Morgan’s Law without proofs.)

   If the stage game has a unique NE, then for any T , the finitely repeated game has a unique SPNE: the NE of the stage game is played in every stage irrespective of the histor[r]

(a) If an agent is risk averse, her risk premium is ALWAYS positive. (b) When every player has a (strictly) dominant strategy, the strategy profile that consists of each player’s dominant strategy MUST be a Nash equilibrium. (c) If there are two Nash equilibria in pure-strategy, they can ALWAYS be Pareto

(c) Solve for the total saving S by all types who save and the total borrowing B.. by all types who borrow.[r]

    5. Bayesian Nash Equilibrium (12 points)  There are three different bills, $5, $10, and $20. Two individuals randomly receive one  bill each. The (ex ante) probability of an individual receiving each bill is therefore 1/3.  Each  individual  knows  only  her  own  bill,  and  is  simultaneously  given  the  option  of  exchanging her bill for the other individual’s bill. The bills will be exchanged if and only  if  both  individuals  wish  to  do  so;  otherwise  no  exchange  occurs.  That  is,  each  individuals can choose either exchange (E) or not (N), and exchange occurs only when  both  choose  E.  We  assume  that  individuals’  objective  is  to  maximize  their  expected  monetary payoff ($). 

Find (all) pure‐strategy Nash equilibrium if it exists.  iii.[r]

e z . The prices of the three goods are given by (p, q, 1) and the consumer’s wealth is given by ω. (a) Formulate the utility maximization problem of this consumer. (b) Note that this consumer’s preference can be expressed in the form of U (x, y, z) = V (x, y) + z. Derive V (x, y).

elimination of strictly dominated strategies can never be selected (with positive probability) in a mixed-strategy Nash equilibrium.[r]

Combination of dominant strategies is Nash equilibrium. There are many games where no dominant strategy exists[r]

Prove that if a firm exhibits increasing returns to scale then average cost must strictly decrease with output. 4.[r]

政府（官僚組織、政治家）はどのように行動するのか？
政治の経済学 政治の経済学 政治の経済学 政治の経済学
私企業の中でなにが起こっているのか？
組織の経済学、企業統治（コーポレート・ガバナンス） 組織の経済学、企業統治（コーポレート・ガバナンス） 組織の経済学、企業統治（コーポレート・ガバナンス） 組織の経済学、企業統治（コーポレート・ガバナンス）

Prisoners’ Dilemma: Analysis
   ( Silent , Silent ) looks mutually beneficial outcomes, though    Playing Confess is optimal regardless of other player’s choice!    Acting optimally ( Confess , Confess ) rends up realizing!!

Solve the following problems in Snyder and Nicholson (11th):. 1.[r]

Solve the following problems in Snyder and Nicholson (11th):. 1.[r]

Solve the following problems in Snyder and Nicholson (11th):. 1.[r]

  A tree starts with the initial node and ends at2. terminal nodes where payoffs are specified..[r]

  A strategy in dynamic games is a complete action plan which prescribes how the player will act in each possible.. contingencies in future..[r]

  4. Incomplete Information (16 points, think carefully)  There are four different bills, $1, $5, $10, and $20. Two individuals randomly receive  one bill each. The (ex ante) probability of an individual receiving each bill is therefore  1/4.  An individual knows only her own bill, and  is  simultaneously given the option of  exchanging her bill for the other individual’s bill. The bills will be exchanged if and only  if  both  individuals  wish  to  do  so;  otherwise  no  exchange  occurs.  That  is,  each  individuals can choose either exchange (E) or not (N), and exchange occurs only when  both  choose  E.  We  assume  that  individuals’  objective  is  to  maximize  their  expected  monetary payoff ($). 

B) Nash equilibrium outcomes are always Pareto efficient. C) A strategy used in Nash equilibrium can never be eliminated in the process of iterated elimination of dominated strategies. D) In a mixed-strategy Nash equilibrium, each player must completely randomize his/her (pure-) strategies, i.e., taking every strategy with exactly equal probability. E) The Zermelo’s theorem says that the second mover always has a winning strategy.