Suppose there is a credit market imperfection due to limited commitment

. As in the setup with collateralizable wealth we examined in thischapter, each consumer has a component of wealth that has value pH in the futureperiod, that cannot be sold in the currentperiod, and that can be pledged as collateral against loans. Suppose also that the government requires each consumer to pay alump-sum tax t in the currentperiod, and a tax t in the future period. Also suppose that there is limited commitment with respect to taxation. Thatis, if a consumer refuses to pay his or hertaxes, the government can seize the consumer's collateralizable wealth but cannot confiscate income(the consumer' endowment). Assumethat, if a consumer fails to pay off his or her debts to private lenders and also fails to pay his or hertaxes, 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.

The maximum present value of government spending is represented by: