Market Economy | 市場経済
In previous lectures, we studied the behavior of individual consumers, describing optimal behavior when market prices were fixed and beyond the agent’**s** control. We begin to explore the consequences of that behavior when consumers (and firms) come together in markets. First, we consider price and quantity determination in a single market.

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R n + := {(x 1 , ..., x n )|x i ≥ 0, i = 1, ..., n} ⊂ R n .
For any x, y ∈ X, x % y means x is at least as preferred as y. Consumption set contains all conceivable alternatives.
A budget set is a set of feasible consumption bundles, represented as B(p, ω) = {x ∈ X|px ≤ ω}, where p is an n-dimensional positive vector interpreted as prices, and ω is a positive number interpreted as the consumer’**s** wealth.

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Two neighboring homeowners, 1 and 2, simultaneously choose how many hours to spend maintaining a beautiful lawn (denoted by l 1 and l 2 ). Since the appearance of one’**s** property depends in part on the beauty of the surrounding neighborhood, homeowner’**s** benefit is increasing in the hours that neighbor spends on his own lawn. Suppose that 1’**s** payoff is expressed by

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This is an advanced course in microeconomics, succeeding to Advanced Microeconomics I (ECO600E) in which we study individual economic decisions and their aggregate [r]

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Introduction to Market Design and its Applications to School Choice.. Yosuke YASUDA.[r]

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If the two pennies match, then player 2 wins player 1’**s** penny; if the pennies do not match, then 1 wins 2’**s** penny.
Although the existence of Nash equilibrium is not guaranteed, the natural extension of strategies, mixed strategies, will almost always assure the existence of equilibrium.

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Similarly, player 2 must be indi¤erent amongst choosing X and Y , which implies **4**q + 6(1 q) = 7(1 q)
, 5q = 1 , q = 1=5.
Thus, the mixed-strategy equilibirum is that player 1 takes A with probability 1=5 (and B with probability **4**=5) and player 2 takes X with probability 3=**4** (and Y with probability 1=**4**).

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2 units of the firm 1’**s** good and A − p 2 + p 1
2 units of the firm 2’**s** good. Assume that the firms have identical (and constant) marginal costs c(< A), and the payoff for each firm is equal to the firm’**s** profit, denoted by π 1 and π 2 .

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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]

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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!!

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Prisoners’ Dilemma: Analysis (3)
(Silent, Silent) looks mutually beneficial outcomes, though
Playing Confess is optimal regardless of other player’**s** choice!
Acting optimally ( Confess , Confess ) rends up realizing!!

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payoff) while M gives 1 irrespective of player 1’**s** strategy.
Therefore, M is eliminated by mixing L and R .
After eliminating M , we can further eliminate D (step 2) and L
(step 3), eventually picks up ( U , R ) as a unique outcome.

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

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

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

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3(a - e)/4, is greater than aggregate quantity in the Nash equilib- rium of the Cournot game, 2(a - e)/3, so the market-clearing price is lower in the Stackelberg game.. Thus, i[r]

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Exist exactly one for ANY exchange problem. Always Pareto efficient and individually rational[r]

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Paul Romer (1955-, 内生的成長理論) → 学界から消えた！？
Ben Bernanke (1953-, マクロ、金融) → FRB議長を辞めた**の**は好材料？ Douglas Diamond (1953-, 銀行取付) → 金融は無い？
清滝信宏 (1955-, マクロ、金融) → まだ早い

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December **4**, 2010, “Soukairou Hall ( 想海樓ホール )” 1 st floor ,
GRIPS, National Graduate Institute for Policy Studies, Tokyo
Organized by GRIPS, Hitotsubashi University Global COE program “Innovation in the Japanese Corporation-Education and Research Center for Empirical Management Studies” and Osaka University and Kyoto University Global COE program “Human Behavior and Socioeconomic Dynamics”

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Consider a consumer problem. Suppose that a choice function x(p; !) satis…es Walras’**s** law and WA. Then, show that x(p; !) is homogeneous of degree zero. 6. Lagrange’**s** Method
You have two …nal exams upcoming, Mathematics (M) and Japanese (J), and have to decide how to allocate your time to study each subject. After eating, sleeping, exercising, and maintaining some human contact, you will have T hours each day in which to study for your exams. You have …gured out that your grade point average (G) from your two courses takes the form

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