Consider an overlapping generations model with capital that produces 2k0.5 at +1 if a person creates k, units of capital at t. Assume that there is a subsidy to production: government subsidizes the old person of 0.5 goods for each unit of output newly produced. (Hint: the subsidy is to new output, not to capital as in homework). Assume that the subsidy is paid for by a lump- sum tax of goods on each young person. Each agent lives for two periods and is endowed with w units of the good when young and nothing when old. The preference of an agent is represented by the following utility: In(c) + 2ln(c) (1)(15') Find the new budget constraints of the individual. (2)(15) Assume that the endowment at young age w is 10 and lump-sum tax of is 2, find the optimal capital. Verify that the government budget is balanced. (3)(15) Assume that endowments at young age increases from 10 to 21 units of goods and the lump-sum tax increases from 2 to 3, what is the new optimal capital? Is the government's budget still balanced with this policy change? (4)(20) Show that you can't achieve the golden rule capital with such a subsidy policy.