Suppose we have the following market-clearing condition for the goods market within a New-Keynesian setting:

$$ c_t = (1-\alpha)(1-\frac{\phi}{2}\pi_t^2)y_t + \alpha (1-\frac{\phi}{2}\pi_{t-1}^2)y_{t-1}, $$

where $\pi$ denotes inflation. Can I consider $\pi_t \equiv\pi_{t-1}$ here in this equation? I know we do this in the case of steady-state. Is it the same for inflation here in the equilibrium too?

Moreover, as a general question, can we have GDP ($y_t$) from the previous period in the market-clearing condition as I have here? I came up with this equation since part of the labor income from the previous period is invested in period $t$.

  • 2
    $\begingroup$ Is it a homework problem? What do you mean by "can I consider..." - do you want to assume that always..., or there exists a case such that...? Whether the equilibrium is a steady state or nonstationary depends on the model. There may be multiple equilibria. Depends on the model whether past GDP is in the market clearing condition or not. $\endgroup$ Mar 31 '21 at 6:58
  • $\begingroup$ Thank you for the answer. No it's not homework. I mean "is there a goods market-clearing condition that includes the previous GDP?" In my model, there are two agents. One agent invests part of her wage at time $t$, and at time $t+1$, the profit is shared between two agents.That is why when I write down the equilibrium for total consumption, there is profit that actually comes from output of the previous period. $\endgroup$
    – Giordano
    Mar 31 '21 at 10:04

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