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I am not able even after a whole hour spent on figuring this out to understand the following passage. Please, can you help me out somehow? It is part of the explanation of how a tax affect a monopoly. We start by the assumption that marginal revenue equals margina cost (plus the tax):

$a-2by = c+t$

and we solve for y which leads to:

$y=\frac{a-c-t}{2b}$

Than I don't understand how I can get to this: $\frac{\Delta y}{\Delta t}=- \frac {1}{2b}$

and finally I don't understand why the demand is: $p(y)=a-by$

Thanks for the help in advance!

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    sorry @Merci but I still don't fully understand, is this a partial derivative? are a and c variables (t is a variable right?). thanks so much so far!2012-09-26

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By definition $y'=\lim_{\Delta t\to 0}\frac{\Delta y}{\Delta t}$ so when $\Delta t$ is so small , $y'\thickapprox\frac{\Delta y}{\Delta t} $ and then you have : $y'=\frac{-1}{2b}$ Moreover, you know that $\int MR=TR$ This means that: $TR=\int (a-2bt)dt=at-bt^2$ Regarding the definition of Total Revenue, $TR=p(y)y$ wherein $p$ is your demand function, so: $at-bt^2=(a-bt)t\longrightarrow p(y)=a-by$

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    Hello! I've been "waiting" for you, dear friend!2013-03-22