Suppose there is a credit market imperfection due to limited commitment. Each consumer has a component of wealth that has value pH in the future period, cannot be sold in the current period, and can be pledged as collateral against loans. Suppose 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 that there is limited commitment with respect to taxation as well. That 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 taxes, the government has to be paid first from the consumer's collateralized wealth.
1. Show how the limited commitment problem puts a limit on how much the government can spend in the current and future periods.
2. Write down the consumer's collateral constraint, taking into account the limited commitment problem with respect to taxes.
3. Draw the consumer's lifetime budget constraint.
4. Suppose now that the government reduces (t) and increases (t') so that the government budget constraint continues to hold. What will be the effects on an individual consumer's consumption in the present and the future? Does Ricardian equivalence hold in this economy? Explain why or why not.