Comparison question

The name of the pictureThe name of the pictureThe name of the pictureClash Royale CLAN TAG#URR8PPP











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U is concave and increasing function



I know that



$$w-t_nge 1/2$$



$$U(w-t_a)ge U(1/2)$$



How can I compare $t_a$ and $t_n$



All $w>t_i>0$ for all i=n,a.




calculus real-analysis self-learning




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  • What does the "I know that" part mean?
    – copper.hat
    Jul 16 at 3:18










  • Shifting the axes preserves both monotonicity and convexity, so it can be assumed WLOG that $,t_n = 0,$, $,U(1/2)=0,$, but I don't think there is enough information to answer the question.
    – dxiv
    Jul 16 at 3:27















up vote
0
down vote

favorite












U is concave and increasing function



I know that



$$w-t_nge 1/2$$



$$U(w-t_a)ge U(1/2)$$



How can I compare $t_a$ and $t_n$



All $w>t_i>0$ for all i=n,a.




calculus real-analysis self-learning




share|cite|improve this question



















  • What does the "I know that" part mean?
    – copper.hat
    Jul 16 at 3:18










  • Shifting the axes preserves both monotonicity and convexity, so it can be assumed WLOG that $,t_n = 0,$, $,U(1/2)=0,$, but I don't think there is enough information to answer the question.
    – dxiv
    Jul 16 at 3:27













up vote
0
down vote

favorite









up vote
0
down vote

favorite











U is concave and increasing function



I know that



$$w-t_nge 1/2$$



$$U(w-t_a)ge U(1/2)$$



How can I compare $t_a$ and $t_n$



All $w>t_i>0$ for all i=n,a.




calculus real-analysis self-learning




share|cite|improve this question











U is concave and increasing function



I know that



$$w-t_nge 1/2$$



$$U(w-t_a)ge U(1/2)$$



How can I compare $t_a$ and $t_n$



All $w>t_i>0$ for all i=n,a.





calculus real-analysis self-learning





share|cite|improve this question










share|cite|improve this question




share|cite|improve this question









asked Jul 16 at 3:02









B11b

2,75211548




2,75211548











  • What does the "I know that" part mean?
    – copper.hat
    Jul 16 at 3:18










  • Shifting the axes preserves both monotonicity and convexity, so it can be assumed WLOG that $,t_n = 0,$, $,U(1/2)=0,$, but I don't think there is enough information to answer the question.
    – dxiv
    Jul 16 at 3:27

















  • What does the "I know that" part mean?
    – copper.hat
    Jul 16 at 3:18










  • Shifting the axes preserves both monotonicity and convexity, so it can be assumed WLOG that $,t_n = 0,$, $,U(1/2)=0,$, but I don't think there is enough information to answer the question.
    – dxiv
    Jul 16 at 3:27
















What does the "I know that" part mean?
– copper.hat
Jul 16 at 3:18




What does the "I know that" part mean?
– copper.hat
Jul 16 at 3:18












Shifting the axes preserves both monotonicity and convexity, so it can be assumed WLOG that $,t_n = 0,$, $,U(1/2)=0,$, but I don't think there is enough information to answer the question.
– dxiv
Jul 16 at 3:27





Shifting the axes preserves both monotonicity and convexity, so it can be assumed WLOG that $,t_n = 0,$, $,U(1/2)=0,$, but I don't think there is enough information to answer the question.
– dxiv
Jul 16 at 3:27
















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