Determination of the equilibrium wage rate

Determination of the equilibrium wage rate.


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Finally, Figure 7.10c displays an intermediate situation of moderate inequality or average wealth, where sizable numbers of people are shut out of credit markets, while another sizable fraction are not. Demand and supply curves intersect at some wage rate that lies between subsistence z and the high wage .

The inefficiency of inequality Two features of this model are worth noticing. First, return to the high inequality case in which industrial wages are reduced to the subsistence alternative. In this situation there are some individuals in the subsistence sector. What if a fraction of these individuals could have become entrepreneurs? They would then have generated profits for themselves, which exceed the subsistence level of income to be sure, and then would have pulled more workers into the industrial sector. This scenario creates an efficiency improvement (indeed, a Pareto improvement): some section of the population can be made better off while no one else is made worse off. This is just another way to state that the market equilibrium under high inequality is inefficient: alternatives exist that can improve the lot of some individuals by hurting no one else.

Why doesn’t the market permit these improvements to arise of their own accord? The reason is that the improvements require additional access to credit, and such access is barred because of the inequality in wealth. Thus we see here another functional implication of inequality: by hindering access to credit markets, it creates inefficiency in the economy as a whole. Even if we do not care about the inequality per se, the inefficiency might still matter to us.

This inefficiency is not restricted to high inequality regimes alone, although with sufficient equality it will go away. For instance, consider Figure 7.10b, in which entrepreneurial access is so easy that industrial wages rise to their maximum level. In this case, further easing of the credit market serves no function at all: the outcome is efficient to begin with. In the moderate inequality regime depicted by Figure 7.10c, inefficiency continues to persist. If some additional workers could become entrepreneurs, their incomes would rise23 and the incomes of the remaining workers would rise as well, because of the resulting upward pressure on wages (demand rises, supply falls). Again, these efficiency improvements are barred by the failure in credit markets.

If you have been following this argument closely, you might raise a natural objection at this point. Look, you might say, all these problems occur only in the here and now. Over time, people will save and their wealth will increase. Sooner or later everybody will be free of the credit constraint, because they will all have sufficient collateral to be entrepreneurs if they so wish. Thus after some time, everything should look like Figure 7.10b. The inefficiency you speak of is only temporary, so what is all the fuss about?

This is a good question.24 The way to seriously address it is to think about just what constitutes the startup cost that we’ve so blithely blackboxed with the label I. Presumably, the startup cost of a business includes the purchase of plant and equipment—physical capital, in other words. If we go beyond the very simple model of this section, we also see a role for startup human capital: skilled technicians, researchers, scientists, trained managers, and so on. All of this goes into I. If we begin to think about the economy as it runs over time, surely these startup costs will change as overall wealth changes. For instance, we would expect the costs that are denominated in terms of human capital to rise along with national wealth: the wages of scientists and engineers will rise. It is even possible that the costs of physical capital will rise as well. Thus startup costs are endogenous in an extended view of this model and will presumably increase as wealth is accumulated. The whole question then turns on how the ratio of startup costs to wealth changes over time. For instance, if wealth is accumulated faster than startup costs increase, your objection would indeed be correct: the inefficiency is only an ephemeral one. If this is not the case—if startups keep pace with wealth accumulation—then these inefficiencies can persist into the indefinite future and inequality has sustained (and negative) effects on aggregate performance.25

Inequality begets inequality The second feature of this model is that it captures an intrinsic tendency for inequality to beget itself. Look again at Figure 7.10a. Its outcome is generated by the fact that the majority of individuals are shut out from access to credit, so that the labor market is flooded from the supply side and is pretty tightfisted on the demand side. This market reaction goes precisely toward reinforcing the inequalities that we started with. People earning subsistence wages are unable to acquire wealth, while wealthy entrepreneurs make high profits off the fact that labor is cheap. The next period’s wealth distribution therefore tends to replicate the wealth distribution that led to this state of affairs in the first place.




Thus high inequality not only gives rise to inefficient outcomes, it tends to replicate itself, which prolongs the inefficiency. The lack of convergence (among economic agents) stems from the fact that the poor are shut out of projects (such as entrepreneurship) that yield high rates of return. Consequently, wealth disparities do not go away with time.

It is of interest to note that low inequality may also be self-perpetuating. Consider, for instance, the situation depicted in Figure 7.10b. In this case all economic agents earn the same, and as time passes, there is no reason for this state of affairs to change (unless rates of savings are different across individuals, but that is another matter). The Appendix to this chapter contains a very simple algebraic description of these “multiple steady states.”

Pulling together the discussion in the last two paragraphs, we see here another example of possible history dependence. The model tells us nothing about how a history of high inequality comes about in the first place, but does suggest that a history of high inequality may persist into the indefinite future, carrying with it inefficiencies in production. The very same economy may exhibit different levels of output and investment if its history were to change to one of low initial inequality.

This history-dependent multiplicity of development paths suggests that the market system may lack a self- correcting device for large initial inequalities, especially if the credit market is constrained by the need for adequate collateral. One-time redistributive policies (such as a land reform) may well spur an economy onto a different (and faster paced) growth path. This sort of theory goes well with the empirical observations discussed earlier.

Summary We summarize by listing the three main lessons to be learned from this model.

(1) If capital markets were perfect, an individual’s wealth would not matter in deciding the amount of credit that she can obtain for consumption or investment, as long as the amount is one that she can feasibly pay back. In contrast, once default becomes a possibility, then what can be feasibly repaid may not correspond to what is actually repaid. In such situations the incentive to repay becomes important in determining credit allocations. To the extent that wealth matters in the ability to put up collateral, it matters in communicating the credibility of repayment and therefore in determining access to the credit market.

(2) Inequality has an effect on aggregate output. In this model, the greater the equality in wealth distribution, the greater the degree of economic efficiency as the constraints that hinder the capital market are loosened.

(3) Finally, there is no innate tendency for inequality to disappear over the long run. A historically unequal situation perpetuates itself unless changed by government policy such as asset redistribution. This means, in particular, that two countries with exactly the same parameters of production and preferences may nevertheless not converge with each other as far as wealth distribution and output levels are concerned.

7.2.9. Inequality and development: Human capital What we have discussed so far is just a fascinating sample of the many and diverse links between inequality and

development. It is difficult to include a comprehensive treatment of all these connections, so we will not try. Here are a few general comments.

The previous section is of great importance because it illustrates a general principle that is of widespread applicability. Inequality has a built-in tendency to beget inefficiency, because it does not permit people at the lower end of the wealth or income scale to fully exploit their capabilities. In the previous section we illustrated this by the inability of a section of the population to become entrepreneurs, even though this choice would have promoted economic efficiency. However, this is only one example. For instance, in Chapter 13, we explore the theme that inequality prevents the buildup of adequate nutrition, which is certainly bad in itself, but in addition contributes to inefficiencies in work productivity. Replace nutrition by human capital, a more general concept which includes nutritional capital as well as skills and education, and you can begin to see a more general point.

Low levels of wealth hinder or entirely bar productive educational choices, because of the failure of the credit market. Educational loans may be difficult to obtain for reasons such as those described in Section 7.2.8. Actually, in the case of education, matters are possibly worse, because human capital cannot be seized and transferred to a creditor in the event of default. Thus human capital cannot be put up as collateral, whereas a house or business can be pledged, at least to some extent, as collateral in the event of failure to repay. It follows that the constraints on human capital loans are even more severe, dollar for dollar.

Thus the poor have to fund educational choices out of retained earnings, wealth, or abstention from currently 160



productive work. Because they are poor, the marginal cost of doing so may be prohibitively high. (It is also true that the marginal returns from such investments are high, but after a point the marginal cost effect dominates.) If a wealthier person were to loan a poor person money for educational purposes, an economywide improvement in efficiency would be created. By investing money in the acquisition of human capital, the poor person can possibly earn a higher return on this money than the rich person (who has already made use of his educational opportunities to the fullest) and can therefore compensate the rich person for the opportunity cost of investment. However, this credit market is missing, because loan repayment may be difficult or impossible to enforce.

Thus high-inequality societies may be characterized by advanced institutes of education and research that rank among the best in the world. At the same time, the resources devoted to primary education may be pathetically low. There is no paradox in this, as long as we recognize the credit market failure that is at the heart of this phenomenon.

To be sure, inequalities in education feed back and reinforce the initial differences in inequality. This part of the story is also analogous to the model of the previous section. Multiple development paths can result: one characterized by high inequality, low levels of primary education, and inefficient market outcomes; the other characterized by low inequality, widespread primary education, and equalization of the rates of return to education across various groups in society, which enhances efficiency. As Loury [1981] puts it,

. . . Early childhood investments in nutrition or preschool education are fundamentally income constrained. Nor should we expect a competitive loan market to completely eliminate the dispersion in expected rates of return to training across families. . . . Legally, poor parents will not be able to constrain their children to honor debts incurred on their behalf. Nor will the newly-matured children of wealthy families be able to attach the (human) assets of their less well-off counterparts, should the latter decide for whatever reasons not to repay their loans. (Default has been a pervasive problem with government guaranteed educational loan programs, which would not exist absent public underwriting.) . . . The absence of inter-family loans in this model reflects an important feature of reality, the allocative implications of which deserve study.

Loury was writing about the U.S. economy, and so was Okun [1975] when he judged the constrained accumulation of human capital to be “one of the most serious inefficiencies of the American economy today.” Consider the same phenomenon magnified severalfold for developing countries.

7.3. Summary In this chapter, we studied the functional aspects of inequality: its connections with other features of development, such as per capita income and rates of income growth.

We began with an empirical investigation of the inverted-U hypothesis, due to Simon Kuznets, which states that inequality rises at low levels of per capita income and then falls. Early evidence suggests that developing countries appear to have higher inequality, on average, than their developed counterparts. More detailed investigation runs into data problems. There are no sufficient data to comprehensively investigate inequality in a single country over time, so the majority of studies rely on analysis of inequality over a cross section of countries.

The first cross-section study with evidence for the inverted-U was that of Paukert. Even though his data set of fifty-six countries displayed wide variation in inequality, there appeared, on the whole, to be an inverted-U relationship over the cross section. More recent (and more comprehensive) data sets support this observation, and so (at first glance) do more formal statistical methods such as regression analysis. We discussed in this context the study of Ahluwalia, whose regressions delivered additional support for the inverted-U over a larger sample of countries than studied by Paukert.

These studies are qualified by various caveats. Cross-country variation in inequality is too much to be predicted by per capita income alone. Some measures generate inverted-U behavior even when there is ambiguity in the comparisons of underlying Lorenz curves. Finally, the exact specification of the functional form in a regression might matter.

There is a more serious objection than any of the foregoing; it stems from what we termed the Latin effect. What if the middle-income countries (in which inequality is highest) are mainly Latin American (which they are) and these countries exhibit high inequality simply because of structural features that are common to Latin America, but have nothing to do with their per capita income? Put another way, do different countries have their own Kuznets curves? The way to examine this is to put regional or country dummies into the regression—an approach taken by Fields and Jakubson as well as by Deininger and Squire. Of course, this approach requires several years of data for each country in the sample, a condition that is fortunately satisfied by recent data sets. When these fixed effects are allowed for, the Kuznets hypothesis fails to hold up.

The failure of the inverted-U hypothesis over the cross section (once country fixed effects are accounted for) provokes a way of thinking about income changes. We identified two sorts of changes. Uneven changes in income




bolster the fortunes of some subgroup of people or some sector of the economy. Such changes are by their very nature inequality enhancing. In contrast, compensatory changes in income occur as the benefits of an initially uneven change percolate more widely through the society; such changes reduce inequality. Recasting the inverted-U hypothesis in this language is roughly equivalent to the assertion that development is like one giant uneven change followed by one giant compensatory change. That would create first a rise and then a fall in inequality. Although there is some support for this point of view, there is no reason for it to be an ironclad law.

We then studied several connections between inequality and income (and its growth). One is through savings. We showed that if marginal savings increase with income, then an increase in inequality raises savings. On the other hand, if marginal savings decreases with income, then an increase in inequality lowers national savings. We went on to discuss the possible behavior of marginal savings as a function of income. Subsistence needs, conspicuous consumption, and aspirations are all concepts that are useful in this context. We discussed the effect of inequality on savings and, consequently, growth. Conversely, we discussed the effect of savings and growth upon inequality.

We turned next to another connection between inequality and growth. High inequality might create a political demand for redistribution. The government might respond with a once-and-for-all redistribution of assets, but this takes political will and information regarding asset owners, so more typically the government reacts with taxes on incremental earnings. However, such taxes are distortionary: they reduce the incentive to accumulate wealth and therefore lower growth.

Is there evidence that inequality lowers subsequent growth, as these models suggest? This was the subject of our next inquiry. We discussed papers by Alesina and Rodrik and others that suggest that there is indeed such an empirical relationship, but its sources are unclear. Specifically, it is hard to tell from the available empirical evidence whether the effect of inequality on growth works through savings and investment, through the demands for public redistribution, or through some entirely different channel.

Encouraged by this evidence (blackboxed though it may appear), we went on to study other connections between inequality and development. We studied the relationship between inequality and the composition of product demand. People consume different goods (perhaps of varying technical sophistication) at different levels of income, so it must be the case that at any one point in time, the overall inequality in income distribution influences the mix of commodities that are produced and consumed in a society. The production mix, in turn, affects the demand for inputs of production, in general, and various human skills, in particular. For instance, if the rich consume highly skill-intensive goods, the existence of inequality sets up a demand for skills that reinforce such inequalities over time.

Self-perpetuating inequality can only happen if certain skills are out of bounds for the poorer people in the society. Why might this happen? After all, if credit markets are perfect, individuals should be able to borrow enough to invest in any skill they like. This paradox motivated us to study the nature of credit markets in developing societies (much more of this in Chapter 14). We saw that in the presence of potential default, loans are offered only to those people with adequate collateral, so that inequality has an effect in the sense that certain segments of the population are locked out of the credit market (because they have insufficient collateral). We showed that this creates an inefficiency, in the sense that certain Pareto improvements are foregone by the market. Thus inequality has a negative effect on aggregate economic performance. The greater the equality in wealth distribution, the greater the degree of economic efficiency as the constraints that hinder the capital market are loosened.

We also observed that there is no innate tendency for inequality to disappear over the long run. A historically unequal situation might perpetuate itself unless changed by government policy such as asset redistribution. This means, in particular, that two countries with exactly the same parameters of production and preferences may nevertheless not converge with each other as far as wealth distribution and output levels are concerned.

Appendix: Multiple steady states with imperfect capital markets We complement the study of imperfect credit markets in Section 7.2.8 with a simple algebraic description of wealth accumulation. This account is only meant to be illustrative: many realistic extensions, such as the growth story sketched in the text, are possible.

Just as in the growth models of Chapter 3, we are going to track variables over time, so values like t and t 1 in parentheses denote dates. Thus W(t) denotes a person’s wealth at date t, w(t) denotes the wage rate at time t, and so on.




Consider a person with initial wealth W(t), who faces the choice between the three occupations described in the text. Whatever income is received from these occupations is added to her wealth (plus interest at fixed rate r), and a fixed fraction is consumed from the total. The remaining fraction becomes the new wealth level Wt 1 at date t 1. you like, you can just as easily think of this as being the new wealth level of the descendant of this individual, so that each period or date corresponds to the entire “life history” of a particular generation.

If subsistence production is chosen, then the individual produces for herself an income of z. Total assets a ailable are then (1 r)W(t) z, where, if you remember, r stands for the interest rate. If a given fraction s of this is passed on to the next date (or to the next generation), then

is the equation that describes future starting wealth. Alternatively, she might choose employment in the labor market for wage income, the going value of which is

w(t) (remember this is endogenous). What happens in this case looks just like the subsistence option, with w(t) taking the place of z. Future wealth is now given by

Finally, she might choose to be an entrepreneur. Recall that profits in this case are given by ( − w ) − (1 r)I. Add this to her starting wealth. As before, a fraction s is passed on to the next generation, so the corresponding equation that describes the evolution of wealth for an entrepreneur is

Assumption 1. Repeated subsistence cannot make someone indefinitely rich over time: s(1 r) < 1.

Assumption 2. Being an entrepreneur when wages are at subsistence levels is better than being a worker: (q − mz) − (1 r)I > z.

Assumption 1 states that repeated subsistence cannot cause an indefinite rise in wealth. Look at equation (7.5) to understand just why this requires the algebraic inequality at the end of that assumption. [Hint: Reverse the inequality and see what happens to wealth over time as you repeatedly apply (7.5).]

This assumption gets us away from complicated issues that pertain to growth (recall our discussion in the text about changing startup costs.) Don’t take the assumption seriously, but think of it as a tractable way to study a long- run wealth distribution (see the following text).

Assumption 2 already is implicit in the exposition of the text. We want to study the steady-state distributions of wealth in this model; that is, a distribution that precisely

replicates itself. Ask yourself, What is the long-run wealth of an individual (or a sequence of generations, depending on your interpretation) who earns the subsistence wage z year after year? The long-run level of “subsistence wealth” Ws will replicate itself: if W(t) = Ws, then W(t 1) Ws as well. Using this information in (7.5) [or (7.6), which is the same here because wages are at subsistence], we see that

Ws = s(1 r)Ws sz,

and using this to solve for Ws tells us that

Now, to arrive at this wealth level, we presumed two things. First, we assumed that such individuals had no access to the credit market. In the language of our model, this means that Ws cannot satisfy the minimum wealth requirement (7.4), with z substituted for w. Second, we presumed that the wages were driven down to subsistence, so that the crossing of demand and supply curves was as depicted in Figure 7.10a. This means that a sufficiently large fraction of the population must be at this subsistence level.26

What about the entrepreneurs? Well, they are earning profits in each period to the tune of (q − zm) − (1 r)I, 163


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