Consider an economy populated by a representative consumer, that has preferences over leisure (I) and consumption (c). The consumer's utility function in this one-period model is: \"(31\": game) + gin\") The consumer has 1 unit of time [h = 1} at his disposal to spend between leisure and work. With T being a xed lump-sum tax, 11' being prots from dividends, and in being wage, the consumer's budget constraint can be written as: c + an! = w + 1r T The representative rm's production function is Y = E K\"? N1}? Assume that K = 1, z = 10, and that the goverment buys two units of consumption good, meaning G = 2. (a) Dene and Calculate the marginal rate of substitution of leisure for consumption {MRSicl Show why it is not optimal for the consumer to choose the allocation c=5 andl=|l64 ifthe wageisn: = ll]. (b) Show why this rm does not maximize prots in" if it chooses N = 0.64 when w = 10. What should this rm do? Explain. (c) The Production Possibility Frontier [PPF) is useful to determine the social planneris solution of an economy. Dene PPF. Find the PPF for this model. (d) The social planner's solution must also satisfy the condition llafRS;c = MPN = MRth- Show that the social planner's solution is c = 3 and I = U.T5 (e) Find the equilibrium wage and the rm's prots in a competitive equilibrium.Using your results, calculate the GDP using the income approach. Justify your answer fully. (f) List all the conditions that an allocation c\" and l\" must satisfy to be a competitive equilibrium. (3;) Suppose that higher production lowers the consumer's welfare because producing more goods leads to more pollution by rms. Explain in which way this new infor- mation is likely to affect the planner's solution found in question (d). Would the planner's solution coincide with the competitive equilibrium in this particular case