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I have one question in the proof for section 4.1. in Cole, Mailath, and Postlewaite (2001). $$\lim_{\varepsilon \to 0}\frac{1}{2\varepsilon}\int_{\overline{l}-\varepsilon}^{\overline{l}+\varepsilon} …

Suppose that we have the following inequality: $u( y- d) - u(y-d') \ge u(y' - d) - u( y' -d')$. The concavity of $u$ together with $y\le y'$ then implies that $d \le d'$. I sometimes come across thi …

I am struggling with understanding one result in Buera and Nicolini (2004) published in JME. In page 538, they write $$A_t(h^t) b_{t-1}(h^{t-1}) = Z_t(h^{t-1})$$ where $A_t(h^t)$ is a $N \times J$ mat …

$\int_a^b u(x)dF(x)$ (1)$ = u(t)F(t)|_a^b - \int_a^b F(t)u^\prime(t)dt$ (2)$ = u(b)-\int_a^b F(t)u^\prime(t)dt$ $= u(b)-(\Phi(t)u^\prime(t)|_a^b-\int_a^b \Phi(t)u^{\prime\prime}(t)dt=u(b)-\Phi(b)u^\p …

This is from Hopkins and Kornienko (2010). In this model, $x$ is investments, $s$ is status, and $y=z-x$ is leisure, where $z$ is endowments. $x(r)$ is the optimal investment, and the relative investm …

I am reading George J. Mailath and Andrew Postlewaite (2001), and this is the lemma 1 in this paper. I don't understand the induction process in this proof. I think that we should use the fact that …