Two-period Model Consider the two-period model. The households receive exogenous income y in the first period and y’ in the second period. Remember that N is the number of households. The government taxes the individual with a lump-sum tax t in the first period and t’ in the second period. Therefore, the government receives tax revenues T = N* t in the first period and T’ = N* t’ in the second period. Besides taxes, the government also issues government debt (B) in the first period to finance its government spending in the first period (G) and second period (G’ ). In the first period, the household can save (s) with a real interest rate r and can choose his/her optimal consumption path(c and c’ ). The credit market clearing condition implies that N*s = B. The credit market is perfect.
In reality, when consumers save by investing in financial assets, they need to pay capital gain taxes. The capital gain taxes are proportional to capital gains. Suppose now the consumer in our baseline two period model also needs to pay proportional capital gain tax to the government and the tax rate is τ , i.e., for each unit of interest payment received, the consumer can only keep (1-τ ), how will the capital gain tax change the consumer’s budget constraint and the optimality condition? For simplicity, only consider the case where the consumer is a saver, i.e., we assume s > 0 always. (Hint: You will need to work with the period by period budget constraints and identify which part of the budget constraints is capital gain. )
