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There is another way to compute the symmetric BNE in increasing strategy. Let $U(v)$ denote the expected utility of a player in equilibrium when his type is $v$: Given that the bidding strategy is increasing, a player with type $0$ will get the good with probability zero. Thus he/she must bid zero and $U(0) = 0$. For any other $v > 0$, the probability ...


Value, Competition and Exploitation by Cogliano, Flaschel, Franke, Fröhlich and Veneziani, Classical Political Economics and Modern Capitalism by Tsoulfidis and Tsaliki provide formalizations of classical/Marxian approach, you can find them on libgen.


You want to show $$ \frac{dMR}{dQ} < 0. $$ As you point out in the comments $$ \frac{dMR}{dQ}= Q\frac{d^2P(Q)}{dQ^2} + 2\frac{dP(Q)}{dQ}. $$ The linear case When $P(Q) = a - bQ$, assuming $a,b>0$, you get $$ \frac{dMR}{dQ}= Q \cdot 0 - 2b = - 2b< 0. $$ The general case $$ Q\frac{d^2P(Q)}{dQ^2} + 2\frac{dP(Q)}{dQ} < 0 $$ does not hold for all ...


Your calculation is correct. There's probably just a mistake in the book and (4) should really be $(1+π)\frac{d Z_t}{d π} = \frac{M_t/P_t}{1+π} - e π$. Since presumably the RHS is then set to zero, this doesn't change the maximizer, so the mistake is innocent.


Take a consumer with utility $$ U = x - x^2 - \theta x d, $$ where $x$ is the amount of information given to the firm and $d$ is the disclosure set by the firm. The optimal level of $x$ is given by the first order condition: $$ 1 - 2 x - \theta d = 0 \to x = \frac{1 - \theta d}{2} $$ A consumer will buy from the firm if her utility is greater than zero. ...

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