Hello, I would like help with the following question:

Exercise 1 (30 points) Consider a one period economy in which the representative consumer has preferences over leisure {I} and consumption {c} described by the utility function \"(a)\" : C'f' This consumer has 1 unit of time h to spend between leisure, I, and labor supply, NS. The representative rm's production funstion is Y = zN'f where Nd is labor demand and z = 2 is total factor productivity. The government buys one unit of consumption good, meaning that, G = 1. (a) Explain what an indifference curve is. Does the consumer prefer allocation c = 4 and I = (1.25 to the allocation c = 5 and I = 11.2? Explain. (b) Find the Production possibility frontier {PPF} equation. (c) From the lm's maximization problem, nd the consumer's real wage and firms prots. (d) Explain why it is possible to determine the competitive equilibrium of the present economy by obtaining the social planner's solution? (e) What are the conditions characterizing the social planner's solution? (E) Show that the competitive equilibrium of this economy is c" = 0.5 and l\" = (1.25