Because the slope of the indifference curve is MRS lc and the slop of the PPF

Because the slope of the indifference curve is mrs lc

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PPF is bowed out from the origin and is concave. Because the slope of the indifference curve is –MRS l,c , and the slop of the PPF is –MRT l,c , or -MP N. The Pareto optimum has the property that MRS l,c = MRT l,c =MP N This is the same property that a competitive equilibrium has. We can easily see that the Pareto optimum and the competitive equilibrium are the same thing, because a competitive equilibrium is the point where an indifference curve is tangent to the PPF, and the same is true of the Pareto optimum. A key result of this chapter is that competitive equilibrium identical to the Pareto optimum. First and Second Welfare Theorems These theorems apply to any macroeconomic model. The first fundamental theorem of welfare economics states that, under certain conditions, a comparative equilibrium is Pareto optimal. The second fundamental theorem of welfare economics states that, under certain conditions, a Pareto optimum is a competitive equilibrium. Using the Second Welfare Theorem to Determine a Competitive Equilibrium Because the competitive equilibrium and the Pareto optimum are the same thing, we can analyse a competitive equilibrium by working out the Pareto optimum, which is point B in the figure. At the Pareto optimum, an indifference curve is tangent to the PPF, and the equilibrium real wage is equal to negative the slop of the PPF and negative the slop of the indifference curve at B. In the figure, the PPF is curve AH, and the competitive equilibrium (or Pareto
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optimum) is at point B, where an indifference curve I 1 , is tangent to the PPF. The equilibrium is the quantity of consumption in then C*, and the equilibrium quantity of leisure is l*. The quantity of employment is N* = h – l*, and the quantity of output is Y* = C* + G . The real wage is determined by negative the slope of the PPF, or negative the slope of the indifference curve I 1 at point B. The real wage is determined in this way because we know that, in equilibrium, the firm optimizes by setting the marginal product of labour equal to the real wage, and the consumer optimizes by setting the MRS equal to w . The Effects of a Change in Government Purchases An increase in G from G1 to G2 shifts the PPF from PPF1 to PPF2, where the shift down is by the same amount as G2-G1 for leisure. This shift leaves the slope of the PPF constant for each unit of leisure. The effect of shifting the PPF downward by a constant amount is very similar to shifting the budget constraint for the consumer through a reduction in his nonwage disposable income. Because G = T , an increase in government spending will increase taxes by the same amount, which reduces the consumer’s disposable income. Therefore, the effects of an increase in government spending essentially involve a negative income effect on consumption and leisure.
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