In this figure PPF 1 is the original PPF and it shifts to PPF 2 when z

In this figure ppf 1 is the original ppf and it

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In this figure PPF 1 is the original PPF and it shifts to PPF 2 when z increases from z 1 to z 2 . The initial equilibrium input is at point A, and the final equilibrium is at point B after z increases. The equation for PPF 2 is given by C = z 2 F(K, h – l) – G. Now consider constructing an artificial PPF, called PPF 3 , which is obtained by shifting PPF 2 downwards by a constant amount. The equation is given by C = z 2 F(K, h – l) – G –C 0. Here,
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C0 is a constant that is large enough so that PPF3 is just tangent to the initial indifference curve I1. What we are doing here is taking consumption away from the representative consumer to obtain the pure substitution effect of an increase in z. The substitution effect is the movement from D to B. The substitution effect is for consumption to increase and leisure to decrease, so that hours worked increases. The income effect is for both consumption and leisure to increase, consumption must increase as both goods are normal goods, but leisure may increase or decrease due to opposing income and substitution effects. Why must the real wage increase in moving from A to B, even if the quantities of leisure and employment rise or fall? Firstly, the substitution effect involves an increase in MRS l, c (the indifference curve becomes steeper) in moving along the indifference curve from A to D. Secondly, because PPF 2 is just PPF 3 shifted by a fix amount, the slope of PPF 2 is the same as the slope of PPF 3 for each quantity of leisure. As the quantity of leisure is higher at point B than at point D, the PPF is steeper at B than at D, and so MRS l, c also increases in moving from D to B. Thus the real wage, which is equal to the marginal rate of substitution in equilibrium, must be higher in equilibrium when z is higher. The increase in total factor production causes an increase in the marginal productivity of labour, which increases the demand for labour by firms, driving up the real wage. Workers now have more income given the hours worked, and they spend the increased income on consumption goods. Because they are offsetting income and substitution effects on the quantity of labour supplied, hours worked may increase or decrease. An important feature of the increase in total factor productivity is that the welfare of the representative consumer must increase. Therefore, the representative consumer must consume on a higher indifference curve when z increases. As a result, increases in total factor productivity unambiguously increase the aggregate standard of living.
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A Simplified One-Period Model with Proportional Income Taxation We use this model to study the incentive effects of the income tax, and to derive the “Laffer curve”. In this section we modify the model by including proportional tax on wage income, instead of a lump sum tax. This tax will then distort the labour supply decision, and the competitive equilibrium will not be Pareto optimal.
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