While he has often gone beyond orthodox economics, David never leaves economics behind. "I reaﬃrm my faith in models in which individuals maximize (albeit as best they can) and admit that my objective is to convert the heathens to economics by mild cooption. (Kreps, 1996, p.593)" Responding to Kreps (1990), he himself develops a formal, although static, decision-theoretic model of unforeseen contingencies by identifying preferences for ﬂexibility with them, and it is further extended by Dekel, Lipman, and Rustichini (2001). As for the notion that an individual's desires can change and be changed, he argues that it "should become part of economic orthodoxy (Kreps, 2014, p.2)."
0 (a o , θ) ≤ 0
which contradicts ˆ a > a o . Q.E.D.
Proposition S2 identifies a suﬃcient condition for the well-known result of Che and Hausch (1999) to hold when alternative-use value depends on a. Formal contracts cannot improve the seller’s eﬀort incentives from the no contract case if the eﬀects of uncertainty θ is not too large to alter the sign of the eﬀects of investment a on the negotiated price. For example, this condition holds if both v(a, θ) and m(a, θ) are additively separable in terms of a and θ: v(a, θ) = v(a) + x(θ) and m(a, θ) = m(a) + y(θ), with αv(a) + (1 − α)m(a) being monotone in a. It also holds if θ does not aﬀect the negotiated price because, either (as in our paper) there is no uncertainty in the value for the buyer and the alternative-use value, or, as in Edlin and Hermalin (2000), the parties can renegotiate only before uncertainty resolves. 1 Finally,
Absolute Risk Aversion (2)
The next proposition gives a rationale for this measure.
Thm (Pratt’s Theorem) Let u 1 and u 2 be twice differentiable,
increasing, and strictly concave vNM utility functions. Then, the following properties are equivalent.
Problem Set 2: Posted on November 18
Advanced Microeconomics I (Fall, 1st, 2013)
1. Question 1 (7 points)
A real-valued function f (x) is called homothetic if f (x) = g(h(x)) where g : R → R is a strictly increasing function and h is a real-valued function which is homo- geneous of degree 1. Suppose that preferences can be represented by a homothetic utility function. Then, prove the following statements.
Open Set and Closed Set (2)
Boundary and interior
◮ A point x is called a boundary point of a set S in R n
if every ε-ball centered at x contains points in S as well as points not in S. The set of all boundary points of a set S is called boundary, and is denoted ∂S .
Problem Set 2: Due on May 14
Advanced Microeconomics I (Spring, 1st, 2013)
1. Question 1 (6 points)
(a) Suppose the utility function is continuous and strictly increasing. Then, show that the associated indirect utility function v(p, ω) is quasi-convex in (p, ω). (b) Show that the (minimum) expenditure function e(p, u) is concave in p.
Dual Problem - Theory | 双対問題 - 理論 (3)
Thm Suppose the consumer’s preference is continuous, monotone and strictly convex. Then, we have the following relations between the Hicksian and Marshallian demand functions for p ≫ 0, ω ≥ 0 and u ∈ R, and i = 1, 2, ..., n:
Problem Set 2: Due on May 10
Advanced Microeconomics I (Spring, 1st, 2012) 1. Question 1 (2 points)
Suppose the production function f satisfies (i) f (0) = 0, (ii) increasing, (iii) con- tinuous, (iv) quasi-concave, and (v) constant returns to scale. Then, show that f must be a concave function of x.
u i ( i ; i ) u i (s i ; i ) for all s i 2 S i . (2)
7. Mixed strategies: Application
A crime is observed by a group of n people. Each person would like the police to be informed but prefers that someone else make the phone call. They choose either “call” or “not” independently and simultaneously. A person receives 0 payo¤ if no
テスト生成複雑度 [Fujiwara, et al, IEEE Trans. Comp, 1982]
• Strategy 1: In each step of the algorithm, determine as many signal values as possible that can be uniquely implied .
Strategy 2: Assign a fault signal D or D’ that is uniquely determined or implied by the fault in question.