Only Exceptional Proff

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The Household: Asset Accumulation and The Search for Income The individual’s offer of labor and saving is viewed by the neoclassical economist as

falling out of a more fundamental decision over how much leisure and consumption to engage in.

To understand this it’s important to remember that the neoclassical views the individual as an

extreme hedonist, driven by an insatiable appetite to consume (own) as much as possible with the

least amount of effort as possible. Labor is viewed as a bad, something to be avoided, but entered

into out of necessity to purchase the goods being desired. At the same time, the individual’s

desire for consumption is infinite. What’s more, the individual is impatient and would much

rather consume (own) now than postpone current consumption for future gain. If money were no

object, the individual would never stop wanting to own more. The only thing constraining the

amount that can be owned is the amount of money available, and this, in turn, is largely

determined by the wages that can be earned from working. (There is also the possibility of

borrowing money or of earning interest income, rental income or profits – but here we’ll only

focus on the case of labor income, i.e. wages. The logic of the individual’s utility maximizing

choice remains the same regardless of the source of income, so understanding the case of wage

income can be easily extended to the case of property income, i.e. interest, rent and profits.). At

the same time, the only thing constraining the individual’s impulse to consume all of current

income is the possibility of even greater consumption in the future (which in turn, is obtained

from saving a portion of current income – not consuming – and earn interest on it for even

greater consumption in the future).

Let’s consider first the individual’s offer of labor. The decision confronting the

individual, from the neoclassical perspective, is how much consumption and leisure to engage in.

The term leisure, in this context, is unfortunate since it really doesn’t capture what the

neoclassical has in mind; a more appropriate term or phrase would be non-paid-labor. The word

leisure, as originally intended, doesn’t mean absence of work or non exertion of energy, it

instead means time taken to pursue one’s own personal inclinations which could include

exercise, painting, music, dancing, contemplation, reading, writing, etc.; it was traditionally

associated with the idea that the individual is pursuing activities that gives vent to what he/she

wants to become or learn. As such it doesn’t really mean the absence of exertion, it instead

means exertion that is undertaken for personal, non-pecuniary, ends. Leisure was generally

assumed to include a range of activities available only to those who had the means to pursue

them, i.e. the wealthy, or the leisured class – as Veblen would have said.

But, of course, for a very large swath of the working population, leisure in that sense is

fleeting. This is particularly true for women and more specifically married women with children

in a traditional patriarchal family structure. For this class of people, time spent away from paid

labor doesn’t necessarily imply leisure in the classic sense of the word; it instead means another

form of labor, namely carrying out the necessary duties of maintaining the household. In the case

of patriarchal households this form of labor can involve a complex mixture of both caring labor

(work carried out for the love of family, or desire to see one’s children do well) and exploitative

labor (the husband demanding that his dinner be served on time), and in the worse case nothing

but exploitative labor (a domineering husband controlling the wife’s household labor). Under

ideal circumstances one could imagine this class of workers having the time to not only engage

in caring labor (without exploitative household labor) but leisure as well. That is, after the

necessary duties of taking care of the family are done, the person would now have time to pursue

hobbies, that is, engage in true leisure. But, of course, this is seldom possible for large sections of

the working class. For this class of people, non-paid labor generally means other forms of labor

(usually household labor) that seldom incorporate the notion of leisure in its classic sense.

This diversion was necessary to underscore the idea that the utility maximizing choice of

how much non-paid labor to engage in does not mean that the non-paid labor is leisure in the

classic sense; for most workers the choice of how much non-paid labor to engage in does not

mean that leisure is being pursued, it instead means that the necessary drudgery of organizing life

must still go on. Nevertheless, in what follows I’ll often resort to using the term leisure simply

because it’s less cumbersome than the awkward phrase “non-paid-labor.”

Let’s now lay out the basic analytics of the offer of labor as envisioned by the

neoclassicals. The following graph lays out the structure of the decision confronting the

individual. Leisure (i.e., non-labor – NL) is measured on the horizontal axis and consumption is

measured on the vertical axis. The individual is presumed to have a strictly convex indifference

space displaying the rate at which he/she is willing to substitute one more unit of leisure for

consumption (i.e. the Marginal Rate of Substitution of NL for C, MRSNL,C). Another way of

thinking of this trade off is that the indifference curves incorporate the individual’s estimation of

the amount of consumption he/she is willing to give up, at the margin, for a bit more leisure.

The budget constraint includes the element of time, in particular the maximum amount of

time the individual can engage in leisure. As in all of these graphs, the information displayed on

the axis always assumes a given repeatable unit of time, for example it might be per day or per

week, per month or per year. To keep things simple let’s imagine that the unit of time is daily.

Then, the maximum amount of time the individual would be able to dedicate to non-labor would

be 24 hours. So, T on the horizontal axis represents 24 hours per day, the maximum amount of

non-labor the individual can engage in on a daily basis.

The point at which the budget constraint intercepts the vertical axis represents the

maximum amount of consumption the individual could engage in, on a daily basis, which would

have to be the wages that could be earned if the individual worked 24 hours per day (or stated

differently, if the individual had no leisure time). The slope of the budget constraint is the wage

rate and represents not only the wages that can be earned per hour of work but, as well, the

opportunity cost of leisure. The cost of an hour of leisure must be equal to the wages that are

foregone by not working during that hour.

Now, assuming a given budget constraint (determined by time and the wage rate) the

individual will choose a combination of leisure and consumption that will maximize his/her

utility. As always, this will occur at the point at which the consumer has exhausted his/her

budget and found that combination of leisure and consumption for which the marginal rate of

substituting leisure for consumption just equals the wage rate. Another way of saying the same

thing is that the individual will pick that combination of leisure and consumption such that the

w1*T

w2*T

NL1NL2 NL3

marginal utility per dollar of leisure just equals the marginal utility per dollar of consumption

foregone. In the diagram this occurs at NL1 units of non-labor. The horizontal distance between

the origin and NL1 represents the leisure “purchased” by the individual, and the horizontal

distance between NL1 and T represents the amount of labor the individual must offer to sustain

the leisure and consumption desired.

If the wage rate were to increase then the consumer would pick another utility

maximizing choice of leisure and consumption, which in turn would lead to another offer of

labor. A change in the wage rate (the price of leisure) will induce income and substitution

effects. The substitution effect represents the rate at which the individual is willing to substitute

leisure for consumption as a result of change in the relative price of leisure (which is the wage

rate). If the wage rate increases then the relative price of leisure increases and this would induce

the consumer to purchase less leisure and more consumption (that is, the individual would be

induced to offer more labor). This would occur even if we could somehow hold the consumer’s

income constant, which in the above diagram would be represented by keeping the choice along

the first indifference curve U1. The move from NL1 to NL2 represents the substitution effect.

But, of course, a change in the wage rate also represents a change in income, so as the

wage rate increases so too does income. Since leisure is a normal good, this means that an

increase in income brought on by an increase in wages would induce the individual to consume

more leisure (which in turn means that the individual would be induced to offer less labor). The

move from NL2 to NL3 represents the income effect.

Notice that the income and substitution effects work at cross purposes; when the wage

rate increases, the substitution effect brings about an increase in the offer of labor, while the

income effect brings about a decrease in the offer of labor. The net effect will depend on the

relative influence of the income and substitution effect. In the above diagram the income is less

than the substitution effect. If we were to graph the labor supply curve for this particular

individual, the resulting graph would look like a traditional upward sloping supply curve with the

offer of labor positively related to the wage rate.

But this need not always be the case. It’s also possible for the income effect to just equal

the substitution effect, or for the income effect to be greater than the substitution effect. These

possibilities are displayed below.

In the first case, below, the income effect is just equal to the substitution effect, causing

the offer of labor to remain unchanged as the wage rate increases. The labor supply curve for this

individual would be perfectly inelastic, meaning that an increase in the wage rate would not

change the amount of labor offered. The supply curve would be vertical at the amount of labor

offered per time period.

In the second case, below, the income effect is greater than the substitution effect. In this

case the labor supply curve would be negatively related to the wage rate, meaning that as the

wage rate increases the amount of labor offered by this individual would decrease.

w1*T

w2*T

NL1=NL3NL2

U2 U1

w1*T

w2*T

NL1NL2 NL3

Given these possible responses it’s common to portray the individual’s supply of labor as

backward bending, as shown in the next diagram. The upward sloping portion of the supply

curve represents the range of wages over which the individual’s income effect is less than the

substitution effect. The vertical portion would represent the region over which the individual’s

income effect is the same as the substitution effect, and the backward bending portion would

represent the range of wages over which the individual’s income effect is greater than the

substitution effect.

The logic underlying this backward bending supply curve is that the individual’s offer of

labor will vary depending on the level of the wage rate. When wages are fairly low, an increase

in the wage rate will motivate the individual to offer more labor, but as the wage rate moves into

the middle range, the offer of labor remains fairly inelastic, and when the wage rate is already

high, a further increase in the wage rate will motivate the individual to offer less labor.

It’s important to remember that this interpretation of the individual’s labor supply curve

ignored the idea of subsistence or necessary consumption. We can easily amend the above

argument by introducing the notion of necessary consumption and see what impact it has on the

offer of labor. When the notion of necessary consumption is introduced, the individual’s labor

supply curve takes on characteristics more easily understood by the working classes, namely that

the offer of labor remains fairly inelastic (at the maximum amount of labor that can be offered

Income e!ect > Substitution e!ect

Income e!ect = Substitution e!ect

Income e!ect < Substitution E!ect

per time period) until the necessary wage rate is attained. Further wage increases beyond that

point will then induce the backward bending effect.

The following diagram shows one possible way of envisioning a worker’s indifference

space over leisure and consumption, where a minimal level of consumption is seen as necessary.

The Cn point on the consumption axis represents the minimal level of consumption that must be

attained to cover social subsistence, which can be thought of as the minimal standard of living

that must be attained to participate in society, call it socially necessary consumption. For

consumption levels below that amount the individual would not want any leisure since his/her

concern would be with first attaining the minimal bundle of goods to get by. There is, in short,

no substitutability between leisure and consumption when consumption is below the socially

necessary amount. This idea is represented by showing the indifference curves at, or below, the

Cn amount as horizontal lines; no consumption would be traded for a little bit more leisure.

But once consumption starts moving above the socially necessary amount then the

consumer would begin to consider trading off a little less consumption for a little bit more

leisure. Thus the indifference curves above Cn begin to take on more of a convex shape showing

the individual’s willingness to trade off various amounts of consumption for leisure.

Let’s now reexamine the utility maximizing choice of leisure and consumption for an

individual with a preference pattern like the one depicted in the previous diagram, where there

exists a need for a minimal standard of living.

The following diagram depicts how the choices would play out as wages begin to grow

from a level that’s below the socially necessary level to one that exceeds the minimal amount.

Note that when wages (w·T) are below or equal to the socially necessary standard (Cn) the

individual would not purchase any leisure and would instead offer all of his/her labor so as to

attain, or come close to attaining, the socially necessary bundle of goods. But once the wage

begins to move above the socially necessary level, the individual would begin to purchase some

leisure (i.e. begin to offer less labor). In this diagram we are only showing the concluding

choices, we are not showing the income and substitution effects that are inevitably built into each

choice.

The following graph shows what the labor supply curve would look like when the notion

of a socially necessary standard of living is introduced. Under these conditions, which capture

the behavior of the vast majority of the labor force, the supply of labor remains inelastic until the

socially necessary standard of living is achieved. But once the wage rate begins to move beyond

that point then the supply of labor begins to slope backward.

w1*T Cn=U2

w2*T

w3*T

NL1 NL2 NL3

w0*T

Of course, the extent to which the supply curve would bend backward for wages above

the socially necessary amount would vary from individual to individual, and it’s reasonable to

imagine that, even above the socially necessary level, further wage increases would still be

accompanied by an inelastic supply of labor. But eventually, the supply curve would begin to

bend backward.

The Individual’s offer of Saving:

Before exploring the neoclassical theory of individual saving, we need to clarify what

saving and savings mean. Saving refers to the amount of income (money) not consumed,

whereas savings represents the accumulated total of saving over time. For example, I might be

saving $100 each month for 10 months. My monthly saving would be $100, but at the end of the

10-month period my savings would be $1,000 (the accumulation of saving over a ten month

period). In this section we will only be looking at saving.

The neoclassical sees the offer of saving as falling out of the individual’s intertemporal

choice of consumption, that is, it’s a byproduct of the individual’s decision to consume now

versus the future. The basic idea is that the individual is thought to be impatient (once again, the

hedonistic interpretation of human behavior) and would prefer to consume all of his/her income

now. The only thing that might induce the individual to consume less than his/her total income

(that is, to save) would be the possibility of consuming even more in the future; and the

inducement to cut back on current consumption, so as to consumer more in the future, would be

the interest that could be earned on saving. As the interest rate increases, the inducement to

consume less now (to save more now) would increase.

The easiest way to model this idea is to imagine that there are two time periods, now and

the future. We’ll imagine that the individual is earning the same amount of income (money) in

both time periods and must decide how much to consume in both time periods. The individual

will end up choosing a utility maximizing combination of current and future consumption, given

his/her intertemporal consumption preferences, money per time period and the going interest

rate.

The following diagram captures this idea. The horizontal axis measures levels of current

consumption (C1) while the vertical axis measures future consumption (C2). We can think of C1

as representing consumption in this year and C2 as representing consumption in the following

year. The budget constraint provides information on the maximum amount of C1 and/or C2 the

individual can consume, given yearly income (money) and the going interest rate. The point at

which the budget constraint intersects the vertical axis represents the maximum amount of future

consumption, C2, the individual can engage in. This would have to be the amount of money the

consumer gets in each time period plus the interest earned on the money that was saved (not

consumed) in the first time period; i.e. 2·M + i·M = M·(2+i).

The point at which the budget constraint intersects the horizontal axis represents the

maximum amount of current consumption, C1, the individual can engage in. This would have to

be the amount of money the consumer gets in the current time period plus the present value of

the money that will be earned in the future, i.e. M + M/(1+i) = M·(2+i)/(1+i).

The slope of the budget constraint represents the relative price of C1 in terms of C2, that

is, it represents the rate at which the market is willing to exchange future consumption for

current consumption, and this, in turn, will equal (1+i). Notice also that the budget constraint

must cross the point at which current income (money) is equal to future income (money), since

we’re assuming that the amount of income (money) in both time periods is the same.

The indifference set over current and future consumption provides information on the

extent to which the individual is willing to trade off current consumption for future consumption;

that is, the rate at which the individual is willing to substitute a little bit more of current

consumption for a little bit less of future consumption, MRSC1,C2.

Given the individual’s intertemporal budget constraint and his/her intertemporal

consumption preferences (as depicted by the indifference curves), the individual will pick that

combination of current and future consumption that will maximize his/her utility over time. This

will occur at the point at which the budget constraint is exhausted and the MRSC1,C2 just matches

the relative price of C1 in terms of C2, that is MRSC1,C2 = (1+i). Another way of saying this is that

the individual maximizes intertemporal consumption when the present value of the amount by

which future consumption is changed just matches the change in current consumption.

Note that the initial utility maximizing choice occurs, in this particular case, at C11. Since

C11 is less than the amount of money received in the current time period, M1, the difference

between C11 and M represents saving in the current time period. So, in this case, the utility

maximizing choice of the individual is leading him/her to save.

If the interest rate were to increase then a new utility maximizing choice of C1 and C2

would be made. In the above diagram, as the interest rate increases from i to i’ the budget

constraint rotates about the point where M in the current time period is equal to M in the future

time period, and the individual would end up picking C13 amounts of current consumption. But,

C11C12 C13 M*(2+i)/(1+i)

M*(2+i)

M*(2+i')

M*(2+i')/(1+i')

as always this outcome is the result of two forces that are taking place at the same time, namely

the substitution effect and the income effect.

The substitution effect captures the impact that a change in the interest rate has on the

individual’s opportunity cost of current consumption and consequently the amount of current

consumption he/she willing to substitute for future consumption. In this particular example, an

increase in the interest rate means that the opportunity cost of current consumption has increased,

inducing the consumer to cut back on current consumption and increase future consumption. In

the diagram this is represented as the move from C11 to C12, that is current consumption

decreases and, as a result, saving increases. Note that the substitution effect will always be

positive: that is, an increase in the interest rate will cause current consumption to fall and

consequently saving to increase.

The income effect captures the impact that a change in the interest rate has on the

individual’s income and consequently the amount of current and future consumption he/she is

willing to engage in. As the interest rate increases the future value of current saving (i.e.,

sc•(1+i)) increases, while the present value of future saving (i.e. sf/(1+i)) falls. The combination

of these two effects is to encourage the individual to increase current consumption, C1, since it is

considered a normal good. In the above diagram this is shown as the move from C12 to C13. Note

that the income effect will always be negative: that is, an increase in the interest rate will cause

current consumption to increase, causing saving to decrease.

Note that, as with the offer of labor, the offer of saving has two contradictory impulses:

on the one hand, the substitution effect which is always positive (rising interest rates increase

saving); on the other hand, the income effect is always negative (rising interest rates will

decrease saving). The extent to which the substitution effect is greater than, equal to, or less than

the income effect will depend on the preferences of the individual and the range over which

interest rates are changing.

In this particular case the substitution effect is greater than the income effect and, as a

result, the net outcome is that this individual ends up cutting back on current consumption (i.e.

increasing saving) when the interest rate increases. If we were to graph the saving curve over this

range of interest rates, it would be upward sloping, i.e. saving would increase with increases in

the interest rate.

But, as in the case of the individual’s offer of labor, the supply of saving can be inelastic

or negatively related to the interest rate. That is, in some cases the substitution effect is equal to

the income effect, and in other cases the substitution effect might be less than the income effect.

The following graph shows how, as in the case of the offer of labor, the supply of saving can be

represented by a backward bending supply curve, reflecting the various possible ways in which

the substitution and income effects might interact.

Saving

interest rate

Income e!ect < Substitution e!ect

Income e!ect = Substitution e!ect

Income e!ect > Substitution e!ect