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I'm working on a Ramsey problem for taxation, and am a little confused on the meaning/intuition behind the transversality conditions below:

$\lim_{T \to \infty} \lambda_T b_{T+1} = 0$

$\lim_{T \to \infty} \lambda_T K_{T+1} = 0$

These are coming from substituting the FOCs for $b_{t+1}$ and $K_t+1$ into the HH budget constraint and iteratively forward substituting.

BC: $(1-\tau^w_t)w_tL_t + (1-\tau^K_t)R_tK_t + (1+(1-\tau^K_t)r_t)b_t = c_t b_{t+1} +K_{t+1} -(1-\delta)K_t$

FOC:

[$b_{t+1}$] $\lambda_t = \lambda_{t+1}(1+(1-\tau^K_{t+1})r_{t+1})$ [$K_{t+1}$] $\lambda_t = \lambda_{t+1}(1-\tau^K_{t+1})R_{t+1} + (1-\delta))$

After forward substituting and forward iterating to t=T I get:

$\lambda_T(K_{T+1} + b_{T+1}) = \sum_{t =0}^T \{\lambda_t((1-\tau^w_t)w_tL_t - c_t\} + \lambda_{-1}(K_0 + b_0)$

Taking the limit as T-> $\infty$ you get the sum to $\infty$ and the TVC.

I know the transversality conditions have to hold, but what are their meanings/what is the intuition? I can't seem to figure it out.

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