Please give the table or the process of the calculation

Assume that there are two agents in an economy. Agent A has an (after tax) income stream of Period 1 Period 2 Period 3 30 20 10 and no assets at the beginning of period 1. Agent B has an (after tax) income stream of Period 1 Period 2 Period 3 10 30 20 and also has no assets at the beginning of period 1. Assume that there exist borrowing constraints for both agents and that all agents are hypersmoothers. Also, assume that all taxes are non-distortionary and that the real interest rate is 0. a) (9 points) Compute national savings in period 1 in this economy, assuming that government savings in period 1 are 0 (i.e. the government budget is balanced). Answer: The first agent will consume 20 in each period. The second agent is borrowing constrained in the first period and hence will onlyconsume 10. Hence, private savings is equal to 10. Since government savings are 0, national savings is 10. b) (9 points) Assume now that the government wants to boost aggregate consumption in period 1 by 5 units. It will attempt to do so by cutting taxes of the two agents in period 1, and then raising taxes by the same amount in period 2. Its spending behavior will not be altered. Importantly, the government has to impose the same tax payment (or cut) on both agents. What is the smallest period 1 tax cut that would achieve the stated objective? How large will the resulting budget deficit be in period 1? Answer: The government will have to reduce the tax it collects from each agent by 5 and raise taxes by 5 on each agent in the next period. Agent A's consumption will not be affected by the tax cut, since he is not borrowing constrained and hence will save the tax cut. However, agent B will consume the 5 dollars of the tax cut. Government savings (i.e. the government's budget surplus) will become -10