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In pure exchange GE models, a typical goods market clearing condition for good $n$ looks like:

$$\sum\limits_{i=1}^Ic_n^i=\sum\limits_{i=1}^Ie_n^i.$$

Consider a model with production where firms can pay dividends and invest in new capital. New capital can be produced from output goods using a linear technology.

My Question: Taking the existence of dividends and investment into account, how does the goods market clearing condition look like in this case?

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Look at textbook definitions of equilibrium in macro models of General Equilibrium with production and investment. Basically, the Equation $Y_t=C_t+I_t$ that says that the amount produced at a certain period must equal the consumption plus investment in that period is the relevant market-clearing condition in the market for goods.

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