Recent content by michonamona

Is this a counter example?

Let v be a random variable distributed according to F(.). Let X be a set containing the objects x1 and x2. Suppose E(v|x1) = b AND E(v|x2) = b (The expected value of v conditional on x1 is b, etc) where b is some constant. Does it follow that E(v|x1,x2) = b? If so, why...

Homework Statement For a given fixed value, z, how would the level curves of the function below look like? (i.e. the graph of the function in the xy plane, for some given value z. z = min(2x+1, x+y, 2y+1) Homework Equations The Attempt at a Solution Ive been working on...

Its called Microeconomic Theory by Mas-Collel, Winston, and Green. I thought concavity was a general mathematical property, I learned it in Real Analysis.

I'm trying to show that if the function f is discontinuous, then it cannot be concave. Here's the general definition of concavity Let f be a function of many variables defined on the convex set S. Then f is concave on the set S if for all x ∈ S, all x' ∈ S, and all λ ∈ (0,1) we have...

Hello, It's a class in Microeconomic Theory Thanks

Homework Statement Let f be a function from (1,0) to (1,0). Suppose that f is discontinuous. Show that f is not concave. Homework Equations The Attempt at a SolutionLet f:(0,1)-->(0,1). Suppose f is discontinous. Show that it is not concave.I've been working on this problem for over an hour...

Thanks everyone for your response. I'm an amateur in physics so could someone explain why it is not theoretically possible for a spaceship to travel at the speed of light? Does it have something to do with Einstein's E=mc^2? Also, does ".99c" stand for ".99 percent of the speed of light"...

My brother-in-law proposed the following thought experiment: Suppose a person was sitting on the nose of a spaceship traveling at the speed of light through outer space. Now suppose that person pushed off against the spaceship launching himself ahead of it. Is it the case that that person will...

Homework Statement Suppose i and j take on values from {0,1,2,...,7}. We say that i and j are 'happy' if i - j (their difference) is congruent to 1.4 or 7 modulo 8. Note: 'happy' is some mathematical property not relevant to the question. What does 7 modulo 8 mean? What does it...

Homework Statement Why is the size of the power set 2^n ? To elaborate, suppose we have a set B that has n elements. Let C be the set that contains all the possible subset of B. Why is it that |C|=2^n ? It boggles my mind why the base is 2 for all size of sets. Thank you, M...

Ok, |x|^p is definitely continuous everywhere. I graphed it and it looks differentiable at x=0 (seems to be the local min). Is the following a valid proof? Show that |x|^p, p>1 is differentiable at x=0 lim_{h->0^{+}} \frac{|0+h|^{p} - |0|^p}{h}= lim_{h->0^{+}} \frac{|h|^{p}}{h}=lim_{h->0^{+}}...

Homework Statement Let p>0. What is the derivative of |x|^{p}? Homework Equations The Attempt at a SolutionI know that if p is even, then the derivative is just px^{p-1} . But what if x is odd? Would it turn out to be some piecewise function, such as px^{p-1},\: if x \geq 0 and -px^{p-1}...

You mean using: lim_{\textbf{h} \rightarrow \textbf{0}} \frac{f(\textbf{0} + \textbf{h}) - f(\textbf{0}) - Df(\textbf{a})(\textbf{h})}{||\textbf{h}||} = \textbf{0} . directly?

Hi Euler, Thank you for your reply. There's a theorem in my textbook that says that if the first-order partial derivatives of a vector-valued function f exists at a, and if these first-order partial derivatives are continuous at a, then f is differentiable at a. I know how to show the...