Suppose that there is a credit market imperfection because of limited commitment. As in the setup with collateralized wealth, each consumer has a component of wealth which has value pH in the future period, cannot be sold currently, and can be pledged as collateral against loans. Suppose also that the government requires each consumer to pay a lump-sum tax t in the current period and a tax t' in the future period. Also suppose there is a limited commitment with respect to taxation. That is, if a consumer refuses to pay his or her taxes, the government can seize the consumer's collateralizable wealth but cannot confiscate the consumer's endowment. Assume that if a consumer fails to pay off 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.
a. Show how the limited commitment problem puts a limit on how much the government can spend in the current and future periods.
b. Write down the consumer's collateral constraint, taking into account the limited commitment problem with respect to taxes.
c. Now suppose the government reduces t and increase t' so that the government's budget constraint continues to hold. What will be the effects on an individual consumer's consumption in the present and the future? Explain when the collateral constraint is binding for the consumer and when not. Does Ricardian equivalence hold in this economy? Explain why or why not.