Basic Neoclassical Theory
In this chapter, we develop a simple theory (based on the neoclassical perspec-tive) that is designed to explain the determination of output and employment (hours worked). The object is to construct a model economy, populated by in-dividuals that make certain types of decisions to achieve some speciﬁed goal. The decisions that people make are subject to a number of constraints so that inevitably, achieving any given goal involves a number of trade-oﬀs. In many respects, the theory developed here is too simple and suﬀers from a number of shortcomings. Nevertheless, it will be useful to study the model, since it serves as a good starting point and can be extended in a number of dimensions as the need arises.
For the time being, we will focus on the output of consumer goods and services (hence, ignoring the production of new capital goods or investment); i.e., so that I ≡ 0. For simplicity, we will focus on an economy in which labor is the only factor of production (Appendix 2.A extends the model to allow for the existence of a productive capital stock). For the moment, we will also abstract from the government sector, so that G ≡ 0. Finally, we consider the case of a closed economy (no international trade in goods or ﬁnancial assets), so that NX ≡ 0. From our knowledge of the income and expenditure identities, it follows that in this simple world, C ≡ Y ≡ L. In other words, all output is in the form of consumer goods purchased by the private sector and all (claims to) output are paid out to labor.
A basic outline of the neoclassical model is as follows. First, it is assumed that individuals in the economy have preferences deﬁned over consumer goods and services so that there is a demand for consumption. Second, individuals also have preferences deﬁned over a number of nonmarket goods and services, that are produced in the home sector (e.g., leisure). Third, individuals are endowed
22 CHAPTER 2. BASIC NEOCLASSICAL THEORY
with a ﬁxed amount of time that they can allocate either to the labor market or the home sector. Time spent in the labor market is useful for the purpose of earning wage income, which can be spent on consumption. On the other hand, time spent in the labor market necessarily means that less time can be spent in other valued activities (e.g., home production or leisure). Hence individuals face a trade-oﬀ: more hours spent working imply a higher material living standard, but less in the way of home production (which is not counted as GDP). A key variable that in part determines the relative returns to these two activities is the real wage rate (the purchasing power of a unit of labor).
The production of consumer goods and services is organized by ﬁrms in the business sector. These ﬁrms have access to a production technology that transforms labor services into ﬁnal output. Firms are interested in maximizing the return to their operations (proﬁt). Firms also face a trade-oﬀ: Hiring more labor allows them to produce more output, but increases their costs (the wage bill). The key variables that determine the demand for labor are: (a) the productivity of labor; and (b) the real wage rate (labor cost).
Thereal wageis determinedbytheinteractionofindividuals in thehousehold sector and ﬁrms in the business sector. In a competitive economy, the real wage will be determined by (among other things) the productivity of labor. The productivity of labor is determined largely by the existing structure of technology. Hence, ﬂuctuations in productivity (brought about by technology shocks) may induce ﬂuctuations in the supply and demand for labor, leading to a business cycle.
2.2 The Basic Model
The so-called basic model developed here contains two simplifying assumptions. First, the model is ‘static’ in nature. The word ‘static’ should not be taken to mean that the model is free of any concept of time. What it means is that the decisions that are modeled here have no intertemporal dimension. In particular, choices that concern decisions over how much to save or invest are abstracted from. This abstraction is made primarily for simplicity and pedagogy; in later chapters, the model will be extended to ‘dynamic’ settings. The restriction to static decision-making allows us, for the time-being, to focus on intratemporal decisions (such as the division of time across competing uses). As such, one can interpret the economy as a sequence t = 1,2,3,...,∞ of static outcomes.
The second abstraction involves the assumption of ‘representative agencies.’ Literally, what this means is that all households, ﬁrms and governments are assumed to be identical. This assumption captures the idea that individual agencies share many key characteristics (e.g., the assumption that more is pre-ferred to less) and it is these key characteristics that we choose to emphasize. Again, this assumption is made partly for pedagogical reasons and partly be-cause the issues that concern us here are unlikely to depend critically on the fact
2.2. THE BASIC MODEL 23
that individuals and ﬁrms obviously diﬀer along many dimensions. We are not, for example, currently interested in the issue of income distribution. It should be kept in mind, however, that the neoclassical model can be (and has been) extended to accommodate heterogeneous decision-makers.
2.2.1 The Household Sector
Imagine an economy with (identical) households that each contain a large num-ber (technically, a continuum) of individuals. The welfare of each household is assumed to depend on two things: (1) a basket of consumer goods and services (consumption); and (2) a basket of home-produced goods and services (leisure). Let c denote consumption and let l denote leisure. Note that the value of home-produced output (leisure) is not counted as a part of the GDP.
How do households value diﬀerent combinations of consumption and leisure? We assume that households are able to rank diﬀerent combinations of (c,l) ac-cording to a utility function u(c,l). The utility function is just a mathemati-cal way of representing household preferences. For example, consider two ‘al-locations’ (cA,lA) and (cB,lB). If u(cA,lA) > u(cB,lB), then the household prefers allocation A to allocation B; and vice-versa if u(cA,lA) < u(cB,lB). If u(cA,lA) = u(cB,lB), then the household is indiﬀerent between the two allo-cations. We will assume that it is the goal of each household to act in a way that allows them to achieve the highest possible utility. In other words, house-holds are assumed to do the best they can according to their preferences (this is sometimes referred to as maximizing behavior).
It makes sense to suppose that households generally prefer more of c and
to less, so that u(c,l) is increasing in both c and l. It might also make sense to suppose that the function u(c,l) displays diminishing marginal utility in both c and l. In other words, one extra unit of either c or l means a lot less to me if I am currently enjoying high levels of c and l. Conversely, one extra unit of either c or l would mean a lot more to me if I am currently enjoying low levels of c and l.
Now, let us ﬁx a utility number at some arbitrary value; i.e., u0. Then, consider the expression:
u0 = u(c,l). (2.1)
This expression tells us all the diﬀerent combinations of c and l that generate the utility rank u0. In other words, the household is by deﬁnition indiﬀerent between all the combinations of c and l that satisfy equation (2.1). Not surprisingly, economists call such combinations an indiﬀerence curve.
Deﬁnition: An indiﬀerence curve plots all the set of allocations that yield the same utility rank.
If the utility function is increasing in both c and l, and if preferences are such thatthere is diminishing marginal utilityin both c and , then indiﬀerencecurves
24 CHAPTER 2. BASIC NEOCLASSICAL THEORY
have the properties that are displayed in Figure 2.1, where two indiﬀerence curves are displayed with u1 > u0.
FIGURE 2.1 Indifference Curves
Direction of Increasing Utility
Households are assumed to have transitive preferences. That is, if a house-hold prefers (c1,l1) to (c2,l2) and also prefers (c2,l2) to (c3,l3), then it is also true that the household prefers (c1,l1) to (c3,l3). The transitivity of preferences implies the following important fact:
Fact: If preferences are transitive, then indiﬀerence curves can never cross.
Keep in mind that this fact applies to a given utility function. If preferences were to change, then the indiﬀerence curves associated with the original prefer-ences may cross those indiﬀerence curves associated with the new preferences. Likewise, the indiﬀerence curves associated with two diﬀerent households may also cross, without violating the assumption of transitivity. Ask your instructor to elaborate on this point if you are confused.
An important concept associated with preferences is the marginal rate of substitution, or MRS for short. The deﬁnition is as follows:
Deﬁnition: The marginal rate of substitution (MRS) between any two goods is deﬁned as the (absolute value of the) slope of an indiﬀerence curve at any allocation.
2.2. THE BASIC MODEL 25
The MRS has an important economic interpretation. In particular, it mea-sures the household’s relative valuation of any two goods in question (in this case, consumption and leisure). For example, consider some allocation (c0,l0), which is given a utility rank u0 = u(c0,l0). How can we use this information to measure a household’s relative valuation of consumption and leisure? Imag-ine taking away a small bit ∆l of leisure from this household. Then clearly, u(c0,l0 − ∆l) < u0. Now, we can ask the question: How much extra consump-tion ∆c would we have to compensate this household such that they are not made any worse oﬀ? The answer to this question is given by the ∆c that satis-ﬁes the following condition:
u0 = u(c0 +∆c,l0 −∆l).
For a very small ∆l, the number ∆c/∆l gives us the slope of the indiﬀerence curve in the neighborhood of the allocation (c0,l0). It also tells us how much this household values consumption relative to leisure; i.e., if ∆c/∆l is large, then leisure is valued highly (one would have to give a lot of extra consumption to compensate for a small drop in leisure). The converse holds true if ∆c/∆l is a small number.
Before proceeding, it may be useful to ask why we (as theorists) should be interested in modeling household preferences in the ﬁrst place. There are at least two important reasons for doing so. First, one of our goals is to try to pre-dict household behavior. In order to predict how households might react to any given change in the economic environment, one presumably needs to have some idea as to what is motivating their behavior in the ﬁrst place. By specifying the objective (i.e., the utility function) of the household explicitly, we can use this information to help us predict household behavior. Note that this remains true even if we do not know the exact form of the utility function u(c,l). All we really need to know (at least, for making qualitative predictions) are the general properties of the utility function (e.g., more is preferred to less, etc.). Second, to the extent that policymakers are concerned with implementing poli-cies that improve the welfare of individuals, understanding how diﬀerent policies aﬀect household utility (a natural measure of economic welfare) is presumably important.
Now that we have modeled the household objective, u(c,l), we must now turn to the question of what constrains household decision-making. Households are endowed with a ﬁxed amount of time, which we can measure in units of either hours or individuals (assuming that each individual has one unit of time). Since the total amount of available time is ﬁxed, we are free to normalize this number to unity. Likewise, since the size of the household is also ﬁxed, let us normalize this number to unity as well.
Households have two competing uses for their time: work (n) and leisure (l), so that:
n+l = 1. (2.2)
Since the total amount of time and household size have been normalized to unity,
nguon tai.lieu . vn