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... with x = (y, z) where y is a scalar, z is an n-dimensional consumption vector, and V (·) is a real valued function. The consumption set X = R n+1 + . (a) Show that if V is concave, U is quasi-concave. (b) Show ... 完全なドキュメントを参照

... with x = (y, z) where y is a scalar, z is an n-dimensional consumption vector, and V (·) is a real valued function. The consumption set X = R n+1 + . (a) Show that if V is concave, U is quasi-concave. (b) Show ... 完全なドキュメントを参照

... (a) Show that the above data satisfy the Weak Axiom of revealed preference. (b) Show that this consumer’s behavior cannot be fully rationalized. Hint: Assume there is some preference relation % that fully ... 完全なドキュメントを参照

... (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. ... 完全なドキュメントを参照

... u(x 1 , x 2 ) and v(x 1 , x 2 ) are both homogeneous of degree r, then s (x 1 , x 2 ) := u(x 1 , x 2 ) + v(x 1 , x 2 ) is also homogeneous of degree ...u(x 1 , x 2 ) and ... 完全なドキュメントを参照

... 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 ... 完全なドキュメントを参照

... long-run total, average, and marginal cost functions. 7. Expected Utility Suppose that an individual can either exert e¤ort or not. The cost of e¤ort is c. Her initial wealth is 100. Her probability of facing a loss 75 ... 完全なドキュメントを参照

... endowment of time is 2ω 1 units. There is no (initial) endowment of consumption good. Each individual has a common utility function U (x) = ln x 1 + 2a ln x 2 . Sup- pose that only Ann owns the firm and its ... 完全なドキュメントを参照

... (a) Suppose % is represented by utility function u(·). Then, u(·) is quasi-concave IF AND ONLY IF % is convex. (b) Marshallian demand function is ALWAYS weakly decreasing in its own price. (c) Lagrange’s method ... 完全なドキュメントを参照

... St Petersburg Paradox (1) The most primitive way to evaluate a lottery is to calculate its mathematical expectation, i.e., E[p] = P s∈S p(s)s. Daniel Bernoulli first doubt this approach in ... 完全なドキュメントを参照

... Consider the following exchange economies with two agents and two goods. Derive competitive equilibrium prices (price ratio) and allocations in each case. (a) Two agents, a and b, have the following indirect utility ... 完全なドキュメントを参照

... Explain. (b) Show that any risk averse decision maker whose preference satisfies indepen- dence axiom must prefer L 2 to L 3 . 3. Question 3 (4 points) Suppose a monopolist with constant marginal costs prac- tices ... 完全なドキュメントを参照

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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） ... 完全なドキュメントを参照

... i (p, u) denote the Hicksian demand function of good i and e(p, u) denote the expenditure function. Then, state the Shephard’s lemma. (c) Using envelope theorem, derive either (a) Roy’s identity, or (b) ... 完全なドキュメントを参照

... Overlapping Generations Model (2) Proof. Suppose that each member of generation t + 1 transfers one unit of its endowment to generation t. Now generation 1 is better off since it receives 3 unit of ... 完全なドキュメントを参照

... Pareto Efficiency (1) A situation is called Pareto efficient if there is no way to make someone better off without making someone else worse off. That is, there is no way to make all agents better off. To put it ... 完全なドキュメントを参照

... Second Welfare Theorem (1) Theorem 12 Consider an exchange economy with P i∈I e i ≫ 0, and assume that utility function u i is continuous, strongly increasing, and strictly quasiconcave for all i ∈ I. Then, any ... 完全なドキュメントを参照

... Second Welfare Theorem Theorem 9 Suppose the conditions stated in the existence theorem are satisfied. Let (x ∗ , y ∗ ) be a feasible Pareto efficient allocation. Then, there are income transfers, T 1 , ..., T I ... 完全なドキュメントを参照

... Solve the following problems in Snyder and Nicholson (11th):. 1.[r] ... 完全なドキュメントを参照

... (! x ; ! y ) = (1; 1) (a) Assume there are only two individuals in this economy. Then, draw the Edgworth-box and show the contract curve. Find a general equilibrium (equilibrium price and allocation) if it ... 完全なドキュメントを参照