I would like to check my work from 1 to 3 and answer further questions from 4 to 9. I don't know how to draw a graph.
Thank you for checking and answering my questions.
I really need your help!!
Assume that individuals have the same utility function over consumption and labor given by U(c, 1) = c+ 0log(10 -1) where c represents consumption, I 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. R= D 1. Write the budget constraint faced by the individual. [0.5 points] Budget constraint : 2. Set up the individual maximization problem and solve for the optimal choices of labor and consumption. [1 point] max V ( L , R ) = CT B loy ( 1 0 - 2) s. t. C = wl V L L J = W I T 8 log ( 10 - 2 ) Q - W - = D ( 0 - l W= 10 - e low - wl = 0 We = low- 0 w / (= w ( 10 - W) = low - Q3. 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) W = 1D 1 1 4 = 10 - Q 1 = 150 - 0 A (OD ( = 100 - 0 10 150Suppose that the government introduces an Earned Income Tax Credit (EITC) such that for the rst $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. . 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 pretax/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] Bracket 1 Bracket 2 Substitution Effect: Income Effect: Total Effect: 7. Consider now two individuals with different relative valuations of labor and consumption. Individual 1 has a 9 of 45 and individual 2 has a 9 of 20. For each of these individuals, nd the optimal choice of labor in the notax context and under the EITC setting previously described. [1 points] 8. Plot the solutions you found in a consumptionlabor 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 sustitution and income effects? What about for individual 2? [2 points]

Question

I would like to check my work from 1 to 3 and answer further questions from 4 to 9. I don't know how to draw a graph.

Thank you for checking and answering my questions.

I really need your help!!

Assume that individuals have the same utility function over consumption and labor given by U(c, 1) = c+ 0log(10 -1) where c represents consumption, I 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. R= D 1. Write the budget constraint faced by the individual. [0.5 points] Budget constraint : 2. Set up the individual maximization problem and solve for the optimal choices of labor and consumption. [1 point] max V ( L , R ) = CT B loy ( 1 0 - 2) s. t. C = wl V L L J = W I T 8 log ( 10 - 2 ) Q - W - = D ( 0 - l W= 10 - e low - wl = 0 We = low- 0 w / (= w ( 10 - W) = low - Q3. 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) W = 1D 1 1 4 = 10 - Q 1 = 150 - 0 A (OD ( = 100 - 0 10 150Suppose that the government introduces an Earned Income Tax Credit (EITC) such that for the rst $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. . 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 pretax/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] Bracket 1 Bracket 2 Substitution Effect: Income Effect: Total Effect: 7. Consider now two individuals with different relative valuations of labor and consumption. Individual 1 has a 9 of 45 and individual 2 has a 9 of 20. For each of these individuals, nd the optimal choice of labor in the notax context and under the EITC setting previously described. [1 points] 8. Plot the solutions you found in a consumptionlabor 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 sustitution and income effects? What about for individual 2? [2 points]