Jensen’s inequalityWritten by Felix Lazebnik. Let f be a function concave up on (a, b), i.e., for any x1 , x2 ∈ (a, b),   x1 + x2

Source URL: www.math.udel.edu

Midterm Exam, Econ 210A, FallElmer Kink’s utility function is min{x1 , 2x2 }. Draw a few indifference curves for Elmer. Find each of the following for Elmer: • His Marshallian demand function for each good.

Source URL: econ.ucsb.edu

• Concave function
• Convex function
• Quasiconvex function
• Utility
• Hessian matrix
• Expected utility hypothesis
• Insurance
• Dracula
• Logarithmically concave function
• Mathematical analysis
• Mathematical optimization
• Convex analysis

Midterm Examination: Economics 210A October 2011 The exam has 6 questions. Answer as many as you can. Good luck. 1) A) Must every quasi-concave function must be concave? If so, prove it. If not, provide a counterexample.

Source URL: econ.ucsb.edu

Deformable Free Space Tilings for Kinetic Collision Detection Pankaj K. Agarwaly Julien Baschz Leonidas J. Guibasz John Hershbergerx

Source URL: www.cs.duke.edu

• Euclidean plane geometry
• Pseudotriangle
• Tessellation
• Simple polygon
• Polygon
• Collision detection
• Internal and external angle
• Convex and concave polygons
• Convex hull
• Geometry
• Polygons
• Triangulation

Proving that a Cobb-Douglas function is concave if the sum of exponents is no bigger than 1 Ted Bergstrom, Econ 210A, UCSB If you tried this problem in your homework, you learned from painful experience that the Hessian

Source URL: econ.ucsb.edu

Midterm Exam, Econ 210A, FallElmer Kink’s utility function is min{x1 , 2x2 }. Draw a few indifference curves for Elmer. These are L-shaped, with the corners lying on the line x1 = 2x2 . Find each of the follow

Source URL: econ.ucsb.edu

• Concave function
• Convex function
• Hessian matrix
• Quasiconvex function
• PROPT
• Logarithmically concave function
• Mathematical analysis
• Mathematical optimization
• Convex analysis

Rooftop Theorem for Concave functions This theorem asserts that if f is a differentiable concave function of a single variable, then at any point x in the domain of f , the tangent line through the point (x, f (x)) lies

Source URL: econ.ucsb.edu

Name Midterm Examination: Economics 210A November 7, 2012 Answer Question 1 and any 4 of the other 6 questions. Good luck. 1) Let f be a real-valued concave function whose domain is a convex subset of

Source URL: econ.ucsb.edu

• Consumer theory
• Economics
• Revealed preference
• PROPT
• Consumer choice
• Microeconomics
• Utilitarianism

Name Midterm Examination: Economics 210A October 2011 The exam has 6 questions. Answer as many as you can. Good luck. 1) A) Must every quasi-concave function must be concave? If so, prove it. If not,

Source URL: econ.ucsb.edu

Two Properties of Expenditure functions Proof that e(p, u) is a concave function of p. Proof: We want to show that for any u and any two price vectors p and p0 , and for any λ between 0 and 1, λe(p, u) + (1 − λ)e(p0

Source URL: econ.ucsb.edu

• Quantum mechanics
• Ordinary differential equations
• Spectral theory
• Representation theory of Lie groups
• Operator theory
• Physics
• Mathematical analysis