Suppose there is a credit market imperfection due to limited commitment. As in the setup with we examined in chapter 10, each consumer has a component of wealth that has value pH in the future period, that cannot be sold in the current period, and that can be pledged as against loans. Suppose also that the government requires each consumer to pay a lump-sum tax t in the current period, and a taxtin the future

is, if a consumer refuses to pay his or her taxes, the government can seize the consumer's collateralizable wealth but cannot confiscate income (the consumer's endowment). Assume that, if a consumer fails to pay off his or her debts to private

lenders and also fails to pay his or her taxes, the government has to be paid first from the consumer's collateralizable wealth. Show how the limited commitment problem puts a limit on how much the government can spend in the current and future periods. Write down the consumer's collateral constraint, taking into account the limited commitment problem with respect to taxes. (2 points)