# Questions tagged [real-analysis]

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### Relationship between strictly convex preference and convex preference

Let X be a convex subset of linear topological space and let binary relation >= be a complete preordering. prove: If preference relation is strictly convex and continuous, then it is convex. Since ...
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### Real wages fluctuation as per classical economics

I have just started studying Macroeconomics and have noticed that as per the Classical economics, the real wage level will always remain same because any change in price level in the market is ...
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### Calculating elasticity between terms in a regression equation

Given the following regression: $ln(w_i)=\beta_1+\beta_2age+\beta_3age_i^2+\beta_4Y_i+\beta_5T_i+\beta_6Mar_i+\epsilon_i$ I am asked to calculate the elasticity of wages with respect to age. Is the ...
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### Calculating elasticity between log term and non-log term [duplicate]

Given the following, I am asked to calculate the elasticity of wages with respect to age: $$𝑙𝑛(𝑤_𝑖)=𝛽_1+𝛽_2𝑎𝑔𝑒_i+𝛽_3𝑎𝑔𝑒^2_𝑖+𝛽_4𝑌_𝑖+𝛽_5𝑇_𝑖+𝛽_6𝑀𝑎𝑟_𝑖+𝜖_𝑖$$ How does one ...
My notes says that if $u(.)$ is strictly quasiconcave and differentiable, by the supporting hyperplane theorem, there exists $p >>0$ and $w \geq 0$ such that $x = x(p,w)$ $\forall x$. I am ...