Consider an economy populated by a representative consumer, that has preferences over leisure (E) and consumption (c). The consumer's utility function in this one-period model is: 1 5 a(c,l) = ln(e) + $1130) The consumer has 1 unit of time (h = 1) at his disposal to spend between leisure and work. With T being a xed lumpsum tax, 7r being prots from dividends, and a) being wage, the consumer's budget constraint can be written as: e+wlzw+7rT The representative rm's production function is Y : ZKleNI/E Assume that K = 1, z = 10, and that the govermcnt buys two units of consumption good, meaning G = 2. (a) Dene and Calculate the marginal rate of substitution of leisure for consumption (M R315). Show why it is not optimal for the consumer to choose the allocation (3 = 5 and l 2 0.64 if the wage is m 2 10. (b) Show why this rm does not maximize prots 7? if it chooses N = 0.64 when w z 10. What should this rm do? Explain. (c) The Production Possibility Frontier (PPF) is useful to determine the social planner's solution of an economy. Dene PPF. Find the PPF for this model. (d) The social planner's solution must also satisfy the condition M R5215 = MPN = MRTgc. Show that the social planner's solution is c = 3 and l = 0.75 (c) Find the equilibrium wage and the rm's prots in a competitive equilibrium.Usiug your results, calculate the GDP using the income approach. Justify your answer fully. (f) List all the conditions that an allocation c\" and 1\" must satisfy to be a competitive equilibrium. (g) 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 folmd in question (d). Would the planncr's solution coincide with the competitive equilibrium in this particular case