please explain by details and graphs.

2. Suppose a representative consumer has preference over consumption (6) and leisure (l). Her indifference curve is deseribed by the following utility function: u(c, l) = 3ln(c) + 2111(1) Her endowment over time is given by h = 1. Her wage rate is 2 in terms of consumption goods. Suppose she has 2 units of dividend income from rm and pays 1 unit of lump-sum tax to the government. (a) Write down the budget constraint for this consumer. (b) Compute this consumer's optimal choice over consumption, leisure and working time. Plot his indifference curve, budget constraint and optimal choice. You need to label the intersection of the budget constraint with Xaxis and y-axis, and the optimal choice. Now, suppose that the government imposes a prOportional income tax on the representative consumer's wage income. That is, the consumer's wage income is now w(1 1-)N'S where 0