Chapter 5 A Closed-Economy One-Period Macroeconomic Model

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6. The representative consumer chooses C and N s to maximize utility. The representative firm chooses N d to maximize profits. s d Market-clearing: N = N = N. Government budget constraint: T = G. Chapter 5 A Closed-Economy One-Period Macroeconomic Model 45 7. The slope of the production possibilities frontier is equal to − MPN . The slope of the production possibilities frontier is also identified as − MRTlC , , where MRT lC , is identified as the marginal rate of transformation between leisure and consumption. 8. The competitive equilibrium is Pareto optimal because it lies at a tangency point between the production possibilities frontier and a representative consumer’s indifference curve. 9. The first theorem: A competitive equilibrium can be Pareto optimal. This theorem assures us that the competitive equilibrium is a good outcome. The second theorem: A Pareto optimum is a competitive equilibrium. This theorem allows us to directly analyze Pareto optima with the assurance that these points are also competitive equilibriums. The second theorem is useful because Pareto Optima are often easier to work with than competitive equilibriums. 10. Externalities, noncompetitive behavior, and distorting taxes. 11. G↑⇒Y ↑, C↓, N ↑, l↓, and w↓ . 12. Government competes with the private sector in buying goods. An increase in government spending implies a negative wealth effect, which results in lower consumption. 13. z↑⇒Y ↑, C↑, and w↑ . The sign of the effects on N and l are ambiguous. 14. The substitution effect of an increase in z is that the representative consumer works more hours. The income effect of an increase in z is that the representative household works more hours. The sign of the net effect is ambiguous. 15. A distorting tax makes that households equalize their marginal rate of substitution between leisure and consumption to the after tax wage, which is different from the before tax wage that firms equalize their marginal rate of transformation to. Thus, one cannot achieve the Pareto optimum where the same wage (before tax) is equal to both marginal rates above. 16. The Laffer curve takes into account that higher proportional tax rates give incentives to households to work less. While tax revenue increases with the tax rate for a given tax base, that tax base is reduced by the tax rate. 17. When the income tax rate falls, households are willing to supply additional labor more in such quantities that the tax base increases more than what the tax rate decreases, thus increasing tax revenue.
46 Williamson Macroeconomics, Third Edition Problems 1. Although we often think about the negative externalities of congestion and pollution in cities, there may also be some positive externalities. A concentrated population is better able to support the arts and professional sports; cities typically have a greater variety of good restaurants, etc. Perhaps a more basic issue is that there may be some increasing returns to scale at low output levels that make industrial production more costly in small towns. There may also be externalities in production in being located close to other producers. One example would be the financial industry in financial centers like New York, London, Tokyo, etc. Another example would be large city medical centers that enhance coordination between primary physicians and specialists. One market test of whether productivity is higher in cities would be to look at the wages in cities versus the wages in smaller towns and rural areas. Wages are often higher in cities for individuals of comparable skills. Market efficiency suggests that the higher wages be reflective of a higher marginal product of labor, and that the higher wages compensate those choosing to live in cities for the negative externalities that they face. 2. In a one period model, taxes must be exactly equal to government spending. A reduction in taxes is therefore equivalent to a reduction in government spending. The result is exactly opposite of the case of an increase in government spending that is presented in the text. A reduction in government spending induces a pure income effect that induces the consumer to consume more and work less. At lower employment, the equilibrium real wage is higher because the marginal product of labor rises when employment falls. Output falls, consumption rises, employment falls and the real wage rises. 3. The only impact effect of this disturbance is to lower the capital stock. Therefore, the production possibility frontier shifts down and the marginal product of labor falls (PPF is flatter). (a) The reduction in the capital stock is depicted in the figure below. The economy starts at point A on PPF 1 . The reduction in the capital stock shifts the production possibilities frontier to PPF 2 . Because PPF 2 is flatter, there is a substitution effect that moves the consumer to point D. The consumer consumes less of the consumption good and consumes more leisure. Less leisure also means that the consumer works more. Because the production possibilities frontier shifts down, there is also an income effect. The income effect implies less consumption and less leisure (more work). On net, consumption must fall, but leisure could decrease, remain the same, or increase, depending on the relative strengths of the income and substitution effect. The real wage must also fall. To see this, we must remember that, in equilibrium, the real wage must equal the marginal rate of substitution. The substitution effect implies a lower marginal rate of substitution. The income effect is a parallel shift in the production possibilities frontier. As the income effect increases the amount of employment, marginal product of labor must fall from point D to point B. This reinforces the reduction in the marginal rate of substitution from point A to point D.
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Chapter 5 A Closed-Economy One-Period Macroeconomic Model

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