ANSWER ALL PARTS OF THE QUESTION AND I WILL GIVE THUMBS UP. DO NOT COPY OTHER CHEGG ANSWERS FOR THIS QUESTION OR I WILL GIVE THUMBS DOWN.

Question 2 ( 70 points). Consider an agent that has preferences represented by: u(c,l)=cl1 where 0T. (a) Show that the utility function u(c,l)=cl1 satisfies the Inada conditions. (b) Show that the utility function u(c,l)=cl1 is strictly concave in c and strictly concave in l. (c) Write down the consumer's optimization problem. What variables are taken as given by the consumer? What variables are the consumer's choices? (d) Obtain the consumer's Lagrangian and first-order conditions. Interpret the first-order conditions. (e) Solve for the consumer's optimal consumption and labor supply as a function of the wage, profits and taxes. Hint: You should arrive to the following formula for the optimal labor supply NS=h(1)wT (f) What happens to the optimal consumption when taxes increase? Discuss the income and/or substitution effects to explain your results. (g) What happens to the optimal labor supply when wages increase? Discuss the income and/or substitution effects to explain your results. (h) What happen to the optimal consumption and labor supply and when increases? Interpret to explain your results. Remember that 0T. (a) Show that the utility function u(c,l)=cl1 satisfies the Inada conditions. (b) Show that the utility function u(c,l)=cl1 is strictly concave in c and strictly concave in l. (c) Write down the consumer's optimization problem. What variables are taken as given by the consumer? What variables are the consumer's choices? (d) Obtain the consumer's Lagrangian and first-order conditions. Interpret the first-order conditions. (e) Solve for the consumer's optimal consumption and labor supply as a function of the wage, profits and taxes. Hint: You should arrive to the following formula for the optimal labor supply NS=h(1)wT (f) What happens to the optimal consumption when taxes increase? Discuss the income and/or substitution effects to explain your results. (g) What happens to the optimal labor supply when wages increase? Discuss the income and/or substitution effects to explain your results. (h) What happen to the optimal consumption and labor supply and when increases? Interpret to explain your results. Remember that 0