Suppose a representative consumer has preference over consumption (c) and leisure (l). Her indifference curve is described by the following utility function:

u(c, l) = 3 ln(c) + 2 ln(l)

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 firm and pays 1 unit of lump-sum tax to the government.

(a) Write down the budget constraint for this consumer.

(b) Compute this consumers 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 x-axis and y-axis, and the optimal choice.

Now, suppose that the government imposes a proportional income tax on the representative consumers wage income. That is, the consumers wage income is now w(1 )N^s where 0 < < 1 is the tax rate.

(c) What effect does this new income tax have on consumption and labor supply? Explain your results in terms of income and substitution effects. Show the income and substitution effects in the graph.

(d) Is your answer in (c) consistent with the observation that hours of work in European countries is about 30% less than in the U.S, while the average income tax rate is about 60% in European countries and 40% in the U.S.? In other words, under what condition can you justify this observation using your model? (hint: do we need income effect dominates the substitution effect or the other way around?)

I have done for question a and b, please help me for c and d.Clear answer and steps is betterthank you.