(b) (3%) Derive the two-period intertemporal budget constraint for the agent. Plot it on the (c1, c2)-space. Suppose that there is a government collecting taxes from and providing services to the agents in the economy. The government can choose to impose a consumption tax, a capital income tax or a labor income tax on the household.

(d) \((10\%)\) Suppose that the government collects labor income taxes only. In both periods, the government provides services to all the agents in the economy, inclusive of public health services, national defense, and etc. Denote government expenditure by \(G\). Suppose that the technology scaling factor in the two periods, \(A{1}\) and \(A{2}\), are different and \(A{1} > A{2}\). Now the total taxes collected in period 1 is greater than \(G_{1}\). Do you think that the government should return the "excess" tax revenue to the agents in the economy? Discuss.

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