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Suppose that the government imposes a proportional labor tar, where agents have to pay TWN (and assume that T = 0)

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Suppose that the government imposes a proportional labor tar, where agents have to pay TWN (and assume that T = 0). (a) Write down the budget constraint (BC) and show in a graph how the BC shifts after the labor tax is imposed. (b) Does the slope of the BC change? Explain. 5. Suppose that consumer's utility function ulc, 2) depends on consumption c and leisure l, and has all the standard properties we typically assume. (a) Write down the maximization problem assuming that the agent is subject a proportional income tax (as in the question above) and that lump sum txaes T=0. (b) Write down the 'optimality condition'. (c) Show the optimal choices in a plot which has c in the y-axis and l in the x-axis for two cases: (i) when t = 0 (denote this by point A) and when (ii) T > 0 (denote this by B). Assume that preferences are such that the substitution effect is stronger than the income effect. (d) Draw the implied labor supply in a plot where w is in the y-axis and N$ is in the x-axis. (e) Re-do the plot from the previous question, but assuming that the income effect is stronger than the substitution effect. 6. Assume that the labor supply curve is upward sloping. Should the labor supply curve shift to the left or to the right if any of the following changes happen? Show each case in a graph. (a) the dividends paid by the firms decrease (increase)? (b) the government raises the lump sum taxes? (c) the government introduces a proportionate labor income tax?