(c) (10%) Let c, k and _w denote the consumption tax rate, the capital income tax rate and the labor income tax rate. How will the taxes affect the agent's budget constraint? Write down the agent's budget constraints in periods 1 and 2 as well as the intertemporal budget constraint. Illustrate the intertemporal budget constraint under consumption tax, capital income tax and labor income tax in figures, respectively.

(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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