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Income Distribution and the Tax System

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Income Distribution and the Tax System CHAPTER 9 Income Distribution and the Tax System LEARNING OBJECTIVES After reading this chapter, you should understand • how marginal productivity theory explains the distribution of income; • why a tax on capital hurts workers and how our welfare and personal income tax systems interact to create a poverty trap; and • how replacing the income tax with a progressive expenditure tax could simulta- neously increase average incomes and decrease income inequality. Introduction One thing that many people find unappealing about a decentralized market- oriented economy is that it seems to produce a wide distribution of incomes. Some individuals become extremely wealthy, while others remain very poor. The analysis in this chapter helps to explain why this distribution of incomes occurs. It also explores several features of our tax and welfare systems with the intention of identifying an efficient way of redistributing income from the rich to the poor. But before we explore these questions of tax policy, we must understand how the pattern of high and low incomes occurs in the first place. This pat- tern depends on the productivity of the factors of production owned by each individual, so we start with a review of marginal productivity theory. Marginal Productivity When developing the law of diminishing marginal returns in Chapter 4, we simplified the analysis by concentrating on just two inputs to the production process: labour and capital. We continue that simplification here. In Chapter 4, we considered the firm hiring increasing amounts of labour while holding its amount of capital fixed. The left-hand panel of Figure 9.1 shows the dimin- ishing marginal productivity of labour. When we first derived this curve, it had an increasing portion for very low quantities of labour, but from now on we deal only with the downward-sloping portion. Recall the rationale for the neg- ative slope: as the labour force gets bigger and the stock of machines does not, each individual worker has a smaller quantity of machines to work with and so is less productive. There is a second way of viewing this phenomenon of diminishing mar- ginal returns and that is to consider the firm hiring more and more capital 110 NEL CHAPTER 9: INCOME DISTRIBUTION AND THE TAX SYSTEM 111 Quantity of Quantity of Figure 9.1 Output Output Two Ways of Measuring Total Output The sum of all additions to output equals total output. As a result, the area under a marginal product curve Marginal equals total output. Product of Capital Marginal Product of Labour 6 Quantity of 4 Quantity of Labour Capital while holding the size of its labour force fixed. The right-hand panel of Figure 9.1 follows this approach, and it shows the diminishing marginal productivity of capital. As the quantity of capital increases, with the size of the labour force fixed, each additional machine has a smaller quantity of labour to work with, so it adds less to the firm’s total output. It is important to remember that the sum of all the additional outputs yields total output. Thus, the area under a firm’s marginal productivity curve measures the total amount that the firm has produced. We can apply this idea to both graphs in Figure 9.1. To have a concrete discussion, we assume that the firm whose operations are shown in the graphs has hired six units of labour and four units of capital. The total output of the firm is shown by the shaded area in either panel. (The shaded regions are intended to represent the same area.) If the firm keeps its machine stock constant but hires one more worker, its total output would increase. The amount of additional output is shown by the darkly shaded area in the left-hand panel of Figure 9.2. The firm has moved out along the labour input axis by one more unit (from six workers to seven workers), and the extra output is the additional area under the marginal product curve. This extra output is shown in a different way in the right-hand panel of Figure 9.2. Since we are discussing a case in which the firm has not hired any more machines, there is no movement out to the right along the capital input axis. Instead, the four units of capital now have seven instead of six units of labour to work with, so each unit of capital becomes more pro- ductive. The entire marginal product of capital curve shifts up, as shown in Figure 9.2. The extra output that results is shown by the additional darkly shaded area under the new higher marginal product of capital curve. It is worth emphasizing once more that the two panels in Figure 9.2 are just alternative ways of showing the same thing. Thus, the total output of the firm before hiring the seventh worker is the lightly shaded area, and the addi- tional output that follows from the hiring of that seventh worker is the darkly shaded area, whether we view these areas in the left or the right panel of Figure 9.2. The two lightly shaded regions are the same area, and the two darkly shaded regions are the same area. NEL 112 MICROECONOMICS Figure 9.2 Quantity of Quantity of Two Ways of Measuring Output Output Additional Output When a firm hires an addi- tional worker, it moves along its marginal product of labour curve, while its mar- Marginal ginal product of capital curve Product of Capital shifts out to the right. The additional area under both Marginal curves is the same. Product of Labour 67 Quantity of 4 Quantity of Labour Capital How Incomes Are Determined We are now in a position to see how these marginal productivity relationships determine people’s incomes. We know from the optimal hiring rule discussed in Chapter 4 that the marginal product curve is the firm’s demand curve for that factor. Thus, to find out whether a certain factor, say, labour, receives a high or low payment, we simply add together the marginal product curves for all firms (to get the overall demand curve for labour), and then we see where that demand curve intersects the supply curve for labour. Equilibrium in the labour market is shown in Figure 9.3. The overall supply curve for labour is shown as completely inelastic. You might find this surprising since you probably know some people who move in and out of the labour force, depending on the wage rate. For example, so-called second earners in families, especially low-income families, tend to respond positively to wage rate changes. Higher wages provide an incentive for second earners to leave the home and enter the work force. However, other individuals, such as some lawyers and other professionals, tend to cut hours of work when their wages go up. Higher wages allow these individuals to achieve all the income they want by working less, so higher wages induce them to opt for more leisure (leading to a smaller labour supply). When we add up everyone’s reac- tions, the positive and negative responses to higher wages appear to cancel each other out, so that overall the supply of labour is quite inelastic. The labour supply and demand curves shown in Figure 9.3 are for the whole economy. As a result, the total income available to all citizens is equal to the value of total goods produced, and graphically this is the area under the marginal product curve (up to the quantity of labour available). The intersec- tion of supply and demand determines the wage rate received by each worker. This rate multiplied by the number of workers gives the total wage bill received by all workers. Geometrically, this total wage earnings is given by the area of the white rectangle in Figure 9.3. (The height of this rectangle is the wage rate, and the width is the number of workers. Total labour income [the area of the rectangle] is the product of these two items.) By subtracting this NEL CHAPTER 9: INCOME DISTRIBUTION AND THE TAX SYSTEM 113 Figure 9.3 Quantity of Output Income Distribution as Seen from the Labour Market Supply of Total income created in the Labour Earnings production process is the of Capital area under the marginal product curve. Labour’s income equals the equilib- Marginal rium wage times the number Total Product = Wage Demand for of people receiving that Bill Labour wage (the white rectangle), and the income of capitalists is the remaining (shaded) triangle. Quantity of Labour wage bill from the total value of output (the entire trapezoid under the mar- ginal product curve), we see that the owners of capital receive the shaded tri- angle. So the graph shows how national income is divided between labourers and the owners of capital. The second thing that follows from this marginal productivity explana- tion of income distribution is that the owners of scarce factors of production receive very high incomes, while the owners of abundant factors of produc- tion get very low incomes. Let us consider each case in turn. If labour is scarce, the supply curve would be far over to the left in Figure 9.3, indicating that only a few units are available. An example might be famous singers or hockey players. The equilibrium wage (which clears the market for such a scarce factor) is very high. Similarly, if labour is abundant, the supply curve would be far over to the right, indicating that there are many units of this factor of production available. An example might be unskilled labourers.
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