2 Government and Economic Activity Consider the following two period model with a government. The household likes consumption (c1, C2) and dislikes labor (1, 12), with utility function log(c1) - (1)2 ( 12) 3 2 - + Blog C2 3 The household budget constraints are b1 (1 + Tc) Ci + R = 1 -T1 (1 + Tc)C2 = (1 - 71) 12 + bi - T2 where Ti, T2 are lump-sum taxes, Tc is a consumption tax, 7 is a labor income tax and b1 denotes government debt. For simplicity it is assumed that wages are equal to 1 in both periods. The government levies taxes and issues government debt (as described above) and purchases goods and services in the amount gi in period 1 and g2 in period 2. It needs to repay the government debt it has issued in period 1. The resource constraints for both periods are therefore given as C1 + 91 = 1 C2 + 92 = 12 1. Solve the household maximization to derive the the intratemporal opti- mality conditions, relating (c1, l1) and (c2, 12), respectively, and the in- tertemporal Euler equation (relating c1, C2).2. State the government budget constraints in both periods and use them to derive the intertemporal government budget constraint. 3. Starting from a world without government (no taxes, no government spend- ing), determine the impact of an increase in government spending g; fi- nanced by an increase in the lump sum tax 7; on private consumption and labor (c1,11,c2,l2) as well as on government debt b; and the equilib- rium interest rate R. I am looking for qualitative answers (goes up, goes down, stays the same), but you need to show your work using the house- hold optimality conditions, the resource constraints and the intertemporal government budget constraint from above. 4. Repeat the previous question, but now suppose the government uses the lump-sum tax in period, 7%, to finance the increase in g;. Explain the similarities and differences between your answer in parts 3 and 4. 5. Now suppose the increase in government spending g; is financed by an increase in the labor income tax 7;. Repeat question 3 and explain the similarities and differences in your findings, relative to part 3. You do not have to discuss the impact on the interest rate R (as this is ambiguous)