This is the question regarding Labor Income Taxation. Could you check my answer from (1) to (2) and give me the answer from (3) to (9)? I would appreciate it if you could give me the graph illustration and explanation each.

Note: I know this utility function is quasi-linear so income effect should be all 0 (only focus on substitution effect).

1. Write the budget constraint faced by the individual. [0.5 points]

c = wl

2. Set up the individual maximization problem and solve for the optimal choices of labor and consumption. [1 point]

U = wl + log(10-l)

FOC: U/l = w - [/(10 - l)] = 0

l* = 10 - (/w), c* = w[10 - (/w)]

3. Suppose now that the market wage w is equal to $10h/hour. Draw the consumption-labor trade-off for a representative individual. [0.5 points]

Suppose that the government introduces an Earned Income Tax Credit (EITC) such that for the first $40 in earnings, the government pays 50 cents per dollar on wages earned. After $40 the credit is reduced at a rate of 50 cents per dollar earned. When the credit reaches zero, there is no additional EITC.

4. Draw the relationship between consumption and labor (Hint: there are two brackets). Label the x and y values of the kink point, and the slope of each segment of the graph. [1 point]

5. Draw the relationship between pre-tax/transfer income and post-tax/transfer income.

Label the x and y values of the kink point, and the slope of each segment of the graph. [1 point]

6. For each of the two brackets in your budget constraint, indicate the sign (direction) of the substitution and income effects on an individual's choice of labor supply. Also indicate the sign (direction) of the total (combined) effect of the two, if it is possible to know for certain, or indicate with a question mark if the total effect is uncertain. [1 point]

7. Consider now two individuals with different relative valuations of labor and consumption. Individual 1 has a of 45 and individual 2 has a of 20. For each of these individuals, find the optimal choice of labor in the no-tax context and under the EITC setting previously described. [1 points]

8. Plot the solutions you found in a consumption-labor graph for each individual separately. Does someone bunch in response to the EITC? If so, who responds by bunching? [2 points]

9. What is the effect of the EITC on the labor supply of individual 1? What does this tell you about the relative magnitudes of the substitution and income effects? What about for individual 2? [2 points]

Assume that individuals have the same utility function over consumption and labor given by U(c,l) = c+ log(10 1) > where c represents consumption, l represents hours of labor, and 0 is a given positive parameter. Assume that the only income individuals have comes from labor and that the hourly wage rate is given by w. Bracket 1 Bracket 2 Substitution Effect: Income Effect: Total Effect: Labor Supply Theory Individual has utility over labor supply l and consumption c: u(c,l) increasing in c and decreasing inl [= increasing in leisure] max u(c,l) subject to cel c= w:[+R with w =.(1 ) the net-of-tax wage (w is before tax wage rate and T is tax rate), and R non-labor income FOC wa + W au ac ai = 0 defines Marshallian labor supply 1 =1(w, R) = W ai Uncompensated labor supply elasticity: E" = 1 - I Income effects: n= w where c represents consumption, l represents hours of labor, and 0 is a given positive parameter. Assume that the only income individuals have comes from labor and that the hourly wage rate is given by w. Bracket 1 Bracket 2 Substitution Effect: Income Effect: Total Effect: Labor Supply Theory Individual has utility over labor supply l and consumption c: u(c,l) increasing in c and decreasing inl [= increasing in leisure] max u(c,l) subject to cel c= w:[+R with w =.(1 ) the net-of-tax wage (w is before tax wage rate and T is tax rate), and R non-labor income FOC wa + W au ac ai = 0 defines Marshallian labor supply 1 =1(w, R) = W ai Uncompensated labor supply elasticity: E" = 1 - I Income effects: n= w