# Tag Info

8

Your statement is in fact not true. Consider for example the lexicographic ordering ($X \subset \mathbb{R}^2$, and for $x, y \in X$, $x \preceq y \iff x_{1} < y_{1}$ or $x_{1} = y_{1}$ and $x_{2} < y_{2}$. (It is called lexicographic as it reminds one of the dictionary). This total ordering doesn't allow for a utility function, as can be seen in ...

5

This is not a valid proof, because your sequence $x_1, x_2, \dots$ cannot contain all the points of $\mathbb R^n$, because the latter is not countable. (You haven't assumed that it is recursively enumerable, but you have assumed that it is enumerable at all, and it isn't!) I believe your statement isn't true, even for the $n = 1$ case. If $\preceq$ is a ...

2

For risk-averse people with many good alternatives for spending small sums of money, an occasional lottery play is portfolio diversification. For poor people or ones without good alternative micro-investments (and, typically, many bad options), there are all sorts of reasons why saving one more coin is not necessarily more appealing than using it sometimes ...

1

If you have an equation of the form $$\log(W - p) = \frac{a\log b + c\log d + e\log f}{g}$$ then you should solve this equation for $p$ by getting rid of the $\log$s. The easiest way to do this is boil the RHS down to one $\log$ by combining terms using the rules $p\log q$ = $\log (q^p)$ and $\log p + \log q$ = $log (pq)$. Hence $$\log(W - p) = ... 1 Let me make a couple of observations up front: You're facing two standard problems in forecasting the sales volume of a product. First, you probably don't have much information as to whether past fluctuations in sales were due to shifts in the demand curve or the supply curve (or, gasp, both!). E.g., while you appear to have data on the quantity sold and ... 1 The map g only exists if f with the required properties exist. If g exists then you reach a contradiction and so g can not exist which implies f with the required properties can not exist. Similarly h only exists if such an f exists (as if f fixes a point then you can not extend a segment from x through f(x) in any well-defined continuous ... 1 Let W=2X-Y. Then W has mean (2)(10)-5. Becuase X and Y are independent, 2X-Y has normal distribution with variance 2^2\text{Var}(X)+(-1)^2\text{Var}(Y). Now that you know that W is normal, and you know its mean and variance, I am sure you can find \Pr(W\gt 18). 1 Yes. This appears to be a simple application of the implicit function theorem. Think of p as a function of A. Then your first equality must hold for all values of A. Hence the derivative of the difference must equal zero. Thus,$$GU'(A) + (1-G) U'(A+L) - U'(A+L-p) \Big(1-\frac{dp}{dA}\Big)=0. Solve for $dp/dA$.

1

Assumptions for existence of a utility function In your question you imply that the only assumptions needed on preference to produce a a real-valued function (a utility function) that represents those preferences are completeness and transitivity. This is incorrect. To represent preferences with a real-value function, you need (1) completeness, (2) ...

1

Following @Michael, I do not think the Arrow-Pratt coefficient was constructed with the differential geometry curvature notion in mind. Rather, it was coined as a way to encompass some characteristics of the utility function which have economic interpretations. In the case of expected utility theory, economists want to identify features of the utility ...

1

As you can see the $MRS$ increases as you move along an indifference curve, $x_1\nearrow$ and $x_2\searrow$. That means the consumer likes specialization, the more he or she gets of $x_1$ the more she is willing to give-up of good $x_2$ to get more of good $x_1$ and also the other way around. Consumers have the same amount of $x_1$ and $x_2$ but they like ...

Only top voted, non community-wiki answers of a minimum length are eligible