# How does Limited Friction affect a two-period model? Does the Ricardian Equivalence hold?

Consider a two period model with limited commitment involved.

Each consumer has a component of wealth which has value $pH$ in the future period, cannot be sold in the current period, and can be pledged as collateral against loans. The government uses lump-sum taxes $t$ and $t'$ in the current and future period, respectively, to fund its expenditures.

Suppose that there is limited commitment with respect to taxation as well. More precisely, while all consumers pay their taxes in the current period, consumers might refuse to pay their taxes in the future period.

Assume that in that case the government can seize the consumer’s collateralisable wealth, but cannot confiscate income. Moreover, assume that if a consumer fails to pay off his or her debts to private lenders, and also fails to pay her taxes, the government has to be paid first from the consumer’s collateralisable wealth.

I'd like to say I don't think the RE holds here. But there's some other things I'm not sure about in a model like this.

How does the limited commitment friction affect the government’s budget constraint?.

Would the Lifetime Budget Constraint for the Government in this model be $G+\frac{G'}{1+r}=T+\frac{T'+pH}{1+r}$? Or would this be incorrect?

Also, how does a consumers collateral constraint change taking into account the limited commitment friction with respect to taxes? I have an idea it would look something like. $c\leq{y}$$-t+\frac{pH}{1+r}$? This is my work so far on constructing it, I'm not sure if just plodding pH into the constraint is correct though. But it does imply much like the model suggests that any pH owed is collected in the future period only due to illiquidity.

Also, what do you all think happens when the government reduces $t$ and increases $t'$ so that it's budget constraint will continue to hold? I'm sure the RE equivalence doesn't hold here. I think the optimal consumption choices of the household in the present and the future will lead to a consumption increase. But hey, I'm not exactly sure. Edit: Ignore this for now, working with it for a possible solution. $c+\frac{c'}{1+r}=y-t_cc+y'-\frac{t'_{c'}c'}{1+r}$

• The model description seems to me insufficient. How does the capital market work? Does the government have any advantage as a financial intermediary? Where does the government invest so that they can save at a rate $r$? (small open economy?). – Fato Oct 3 '17 at 7:06