Question 2 (35 points]. Consider an agent that has preferences represented by: u(C,) = 0711? where 0 T. (a) Show that the utility function satises the Inada conditions. {5) Write down the consumer's optimization problem. What variables are taken as given by the consumer? What variables are the consumer's choices? (c) Obtain the consumer's Lagrangian and rst order c0nditions. Interpret the rst order c0n ditions. (d) Solve for the consumer's optimal consumption and labor supply as a function of the wage, prots and taxes. Hint: You should arrive to the following formula for the optimal labor supply 1T T w N3=7h(17) (e) What happen to the optimal labor supply and consumption when w increases? Explain the intuition behind your results. Make sure to discuss income and substitution effects. (f) What happen to the optimal labor supply and consumption when 7 increases? Interpret 7 to explain the intuition your results