# How to set a variable between 1 and 0, and how to check the FOC is greater or small than 0 by assumption?

I have the following notebook:

\$Assumptions = Flatten[{Thread[{c0, c1, p, w, e} > 0],Thread[0 <= {{r, i, x, alpha, beta, gamma, {1 - alpha - beta - gamma}, {1 + r - i}, {1 - x}} <= 1}], Element[{c0, c1, p, w, e, r, i, x, alpha, beta, gamma, {1 - alpha - beta - gamma}, {1 + r - i}, {1 - x}}, Reals]}] case11 = ((1 - x)*alpha*(c0 + e + w + w/(1 + r - i))); case12 = ((1 - x)*gamma*(c0 + w - p/(1 + r - i))); case13 = x*(c0 - p); case21 = ((1 - x)*(1 - alpha - beta - gamma)*(c0 + c1/(1 + r - i) + e+ w+ w/(1 + r - i))); case22 = ((1 - x)*beta*(c0 + c1/(1 + r - i) - p/(1 + r - i) + w)); case23 = (x*(c0 - p)); f = case11 + case12 + case13; h = case21 + case22 + case23; g = e + w + w/(1 + r - i); occc=g/h; ocdc=g/f; I would like to check if D[occc,p] is positive, i tried to run the Positive, but seems it does not work, it did not give me True of False as a result. I believe I need to have more condition to make D[occc,p to be positive, I would like to know those conditions,the word "conditions" i would like to see is something like c0>p, can Mathematica tell me?
Thanks

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It is impossible to help until you clarify your assumptions. As written, they make no sense.
– Bob Hanlon
Aug 27 ’14 at 14:16

Hi, my assumption is c0, c1, w, e, p all greater than 0 and they are all real number. but r, i, x, alpha, beta, gamma are all between 0 and 1. Particularly, x, alpha, beta, gamma are probabilities; r, i are nominal interest rate and inflation respectively. Sorry, I am completely newbie to mathematica, and do not know what it the meaning of each syntax, the assumption syntax is from some question’s answer. Sorry if I made any misunderstanding.
– Chris_Lam
Aug 27 ’14 at 16:07

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