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Part A - Question 1.
Household budget constraint - income increase
income
i
i2
b
a
i1
ui
h
h2 h1
home time
a) Budget line 'ih' constrains choice in a household so maximum utility is
achieved on the indifference curve furthest from the origin at a, with 'i1' income
and 'h1' home time.
b) With unearned income 'ui' the budget line shifts parallel to 'hi' with a new
maximum utility at 'b'. If home time is an inferior good as income rises
households will choose to spend less time at home. The new income at 'i2'
results in less home time at 'h2'. Thus, when income goes up, if more work is
offered, home time is an inferior good.
Household wage increase
income
c
i2
b
i1
h2
a
h1
home time
c) The overall effect of an increase in wage rate for this household is pivot the
budget line as arrow and move the point of maximum utility from 'a' to 'c', as
income rises from'i1' to 'i2' and home time reduces from 'h1' to 'h2'. The total
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move a made up from a substitution effect 'a' to 'b' and an income effect 'b' to
'c'. Both acting to reduce home time with home time an inferior good.
Household labour supply curve
wage rate
w2
w1
m1 m2
market work hours
d) From c) as wages rise from 'w1' at 'i1' to 'w2' at 'i2', because home time has
reduced from 'h1' to 'h2', market work hours must rise from 'm1' to 'm2'.
Household income increase - home time a normal good.
income
i2
i1
wage
rate
b
a
home time
h1 h2
1
Labour supply
w2
w1
m2
m1
market work hours
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e) If home time were a normal good, as wages rise from 'w1' at income 'i1' to
'w2' at 'i2' home time would rises from 'h1' to 'h2' thus market work would
decrease from 'm1' to 'm2'. The income effect would outweigh the substitution
effect. The substitution effect would still act in the same direction to increase
market work hours as wages rise.
The labour supply curve would be backward sloping.
Part A - Question 2
wife's utility
Household utilities non-altruists
W
W*
N
T1
T
M*
M
husband's utility
a) The concave to the origin curve shows the boundary of all feasible
combinations of utility for a husband and wife; the consumption possibility
frontier. The concave shape indicating the additional utility partners get over
and above their separate utilities as a result of combined efforts within a
household, the result of synergies from specialisation and scale, for example.
Outside of the boundary, further from the origin, there are higher utilities for
husband and wife but they are constrained by income and capability and not
feasible.
b) Pareto efficiency is this context is a concept of maximum household utility
within the constraints which cannot be improved without adversely affecting one
partner or the other. All points within the feasible can be improved by moving
away from the origin until the constraint line. The poits on the boundary from 'W'
to 'M' are Pareto efficient.
c) At 'W' the wife's feasible utility is maximum and at 'M' the husband's is
maximised. A combination of household utility choices at 'T' will deliver half the
maximum utility the wife could gain at 'W' and half the husband's at 'M'.
Utility is not confined to consumption of market goods like meat purchased from
the butcher. It also includes Z-goods which are sources of utility which are not
purchased. The stroganoff a loving wife produces from the butcher's meat is a
Z-good.
Utility and it's measurement has a long economic history. Starting with Bentham
and Pigou who considered utility as the consumption of market or 'cardinal'
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goods which could be measured followed by Hicks' idea of preference
satisfaction, indifference curves and 'ordinal' choices where preferences are
ranked, with the criteria of Pareto efficiency.
Weber highlighted this fundamental difference as 'formal rationality' which
calculates and 'substantive rationality' which is value based.
Hick's approach was underpinned by Wittgenstein's logical positivism, where
only the individual knew his own mind but was constrained by avoiding harm to
others.
McClements, Engel and Rathberg all recognised the institutional context of the
individual and proposed measurement enhancements where household utilities
could be analysed after composition adjustments.
Nozick suggested further sophistication by pointing out that experience alone
was an incomplete guide to preferences, aspirations for the future were involved
as well.
Sen highlighted the difference between the 'capacity' to function and the
satisfying 'function' itself. Utility involved the concept of 'capability'.
Mishan pointed to a problem with economic growth as a source of utility
because of unmeasurable side effects and Marx went even further suggesting
capitalist growth was nothing to do with utility but was all a class conspiracy!
Becker's attempt at a generalised economic overview of utility preferences in his
model of New Household Economics raised the issue of 'the predictive worth of
a model which includes unobservable and unmeasurable variables' [1].
Nash proposed a household utility from bargaining as the product of individual
utility and von Neumann attempted to measure individual utilities by more
measurement intrigue based on hypothetical wagers which tease out
preferences.
But the fundamental problem remains; the utility the wife gets at 'W' and half of
it at 'T' is a perception of value in an individual brain, it is immensely complex
and constantly changing. However, the infuriating issue for theorists is that
perceptions of utility affect behaviour and they do not seem to be random, there
are patterns, and patterns require explanations.
d) The threat point in a bargaining situation is the combination of utilities below
which positions become unacceptable. Participants would be prepared to either
withdraw co-operation or withdraw from the household and go their separate
ways. Outcomes below the horizontal through 'T' would leave the wife with less
utility than she is prepared to accept and the area to the left of 'T' would
unacceptably reduce the utility of the husband. This leaves the set of feasible
combinations which are acceptable, confined to those above and to the right of
the threat point.
Bargaining between wife and husband would tend to produce a combination of
Pareto efficient outcome utilities between 'W*' and 'M*' which is maximised for
the household. Such a maximum could be the Nash Equilibrium which is on the
boundary of the feasible set to the right and above the threat point at a point 4
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which maximises the added utility of the husband multiplied by the added utility
of the wife, i.e. maximises the product of the bargain hunter's utility gains at 'N'.
e) One interpretation of a threat point is the ultimate position of divorce and total
sacrifice of all household synergy gains. An increase in the prospects of market
employment for the wife would move the threat point up to 'T1'.
i) Indicating the possibility of improved utility if she left the home and entered
employment.
ii) For the employed wife there would be no such prospect because she is
already employed, unless such prospects led to increased rewards in her
current or alternative job.
Part B
Introduction. The welfare of Debbie and her children increases through cooperation in the household. This is an uncomfortable truth because of the
implied insecurity and dependence on decisions of others with minds of their
own.
Whether Debbie is right not to worry about her husband David receiving the
Working Family Tax Credit depends on the theory used to explain behaviour.
However, everyone should worry about the wider consequences of the
Chancellor's tax policy.
Economic theory attempts to predict outcomes and is dominated by the decision
making process. A particular problem for theory is 'collective' decision making
and how manifestly different individual preferences are reconciled.
There are two main theories of household decision making, significantly they
predict different outcomes.
1 Becker's Household Utility Function. Becker resolved the collective decision
making problem by showing how individual decisions of a household head could
reflect the interests of all. The crucial assumption is that the self interest of
everybody is enhanced by co-operation because of the synergistic gains, so
'altruistic' decisions are taken to secure these benefits.
Debbie's
utility
W
Household utility - altruistic decisions
W1
N
C
T
M1
M
David's utility
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The boundary of the feasible combinations of utility for altruistic David and
Debbie (even if she is not altruistic) would move from a maximum for Debbie
herself at 'W' to 'C' as co-operative gains are secured and David gains more
utility than Debbie looses. At 'C' any further increase David's consumption
would decrease his utility because as an altruist he is concerned about further
falls in Debbie's utility. Eventually at 'M' Debbie's consumption and utility are
zero and although David's consumption is maximum, as an altruist, his utility is
also zero because of his wife's plight.
It is clear the husband would choose point 'C'. Continuing to take decisions to
increase his utility and through redistribution also increasing Debbie's until the
critical point 'C'.
If 'T' represents the combination of utilities of Debbie and David alone outside of
the household, it is also clear that Debbie would accept any point in the feasible
set above 'T', see 2 c), and she would be happy with 'C'. Thus the husband's
altruistic choice is OK for Debbie.
In this model it is irrelevant who receives the Working Families Tax Credit and
the policy switch from Family Credit benefit does not affect the Household Utility
Function because the husband is altruistic and in maximising his utility he also
considers Debbie and the children.
However although Debbie is better off than if separated, this model says
nothing about her welfare under alternative decision making systems.
2 Bargaining. An alternative model assumes Debbie and David bargain over the
spoils of household co-operation. In this case a Nash equilibrium 'N' would
result which maximises the product of the added utilities, see the diagram
above and 2 c). Depending on the shape of the feasible set boundary and the
position of 'T', points 'N' and 'C' could be different.
A model with a more realistic feel involving household members bargaining and
not involving the counterintuitive idea of altruism is shown below.
Debbie's
utility
Household utility - bargaining
W
C1
1
C2
T1
T2
M
David's utility
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The boundary of the feasible set of combinations of utility in this model and the
bargaining analysis is similar to 2 above. However in this case the threat point
is affected by the identity of the recipient of the WFTC.
Currently Debbie receives the child benefit and family credit and the threat point
is represented by 'T1' giving a Nash bargaining outcome of 'C1'. If in future
David receives the WFTC the threat position changes to 'T2' with a Nash
bargaining outcome at 'C2', reflecting Debbie's lower separate utility.
The significance of the bargaining model is that the outcome is dependent on
the threat position and therefore on Extra-household Environmental Parameters
such as the WFTC.
It is this potential loss of utility suffered by Debbie if the benefit recipient is
David which prompted pressure from women's groups on the Chancellor for
choice in the identity of the beneficiary.
This reflects Ruth Listers view, 'benefits are more likely to be spent on children
if paid direct to the caring parent'. The Chancellor's original policy was designed
to help the family unit by encouraging work. The modification to differentially
help Debbie with the objective of helping the children, may have unintended
consequences of disrupting the cohesion of the family unit. Lister's well intention
concern for children may have the opposite effect!
The crucial question is whether the result of bargaining at 'C2' provides the
children with more utility than Becker's HUF at 'C'? Who knows?
Clearly the choice of explanatory theory determines policy!?
Becker's model suggests men have comparative advantage in market work,
make the major contribution, are altruistic, have the power to make decisions.
Bargaining models suggest gender specific environmental social norms,
perceptions of contributions and rewards, and bargaining powers are important.
However, the models are not alternatives but 'as if' explanations of the benefits
of co-operation.
Critique. The maximising calculations underpinning these neo-classical theories
are not performed in reality, theory predicts behaviour only 'as if' individuals
calculate.
Becker is explicit, 'the economic approach does not assume that decision units
are conscious of their efforts to maximise' [2].
Although Becker is clear that, 'the economic approach is not restricted to
material goods and the market sector' [2], an almost universal criticisms of
these models is that they don't reflect people's real experience in households.
Regardless of Z-goods concepts and ordinal preferences they appear 'money'
focused and materialistic. Cold calculation doesn't reflect the pleasures and
pains of the real emotional experience in households.
The point is conceded by Himmelweit, 'Models of household decision making do
not have to be interpreted as claiming that husbands and wives openly pit
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their bargaining strengths against each other' [1]. There is no 'power', no
'calculation', merely outcomes which are based on perceptions (Sen) or
discovery (Becker) and embedded in social culture.
Reality is evolution. Nevertheless, the 'as if' theories do provide useful insights
into understanding and prediction of outcomes.
Dawkins has made the point extravagantly, 'Genes behave 'as if' they make
cost benefit calculations' [3].
Kant also believed that, 'there is a reciprocal dependence of parts and wholes
which cannot be explained by cause and effect and we should investigate
nature 'as if' there were a design' [4]. This is how all science progresses.
Debbie and David don't calculate the merits of each decision. They learn from
experience by associating behaviour with outcomes and they experiment to
discover improved outcomes. This is Dennett's 'satisficing' [5].
However the patterns of experience and discovery indicate that co-operative
behaviour is economically efficient. Co-operation creates value in excess of
resource costs because of the advantages of specialisation, scale, synergy,
science, investment, imitation and innovation which all respond positively to cooperation.
The tendency, as everyone manoeuvres to try to secure advantages is that cooperation benefits will be maximised and differentially survive. It maybe
counterintuitive but Debbie and David's own selfish interests are served by
altruistic decisions, sometimes Debbie, sometimes David but without cooperation they and the children are impoverished.
The Becker and the bargaining models are 'as if' models which illuminate the
benefits of co-operation but it is blind evolution which secures the gains.
Interference. If reality is evolution the Chancellor's interference with tax and
spend policy will always be a problem.
The problem on the 'tax' side is not only the resentment of confiscation of
scarce resources, but also the problems of distortion of the price mechanism,
which is an inevitable consequences of replacing dispersed markets with
centralised taxation.
A tax credit, the WFTC, distorts in the same way as a tax. The intention is to
encourage work but it only encourages market work, children may benefit from
home work. Do paid carers care more than unpaid mothers? It may shift some
from being wholly dependent to more being partially dependent. It may distort
the incentive to gain utility through effort and innovation. As it is means tested It
may encourage dishonesty and it may distorts thrift as savings investment
decisions are made by others.
The problem on the 'spend' side for the Chancellor is a of lack of knowledge,
particularly concerning the very personal benefits from Z-goods and the myriad
of unintended consequences and knock on distortions of complex decisions [6].
Conclusion. Debbie should continue her strategy of co-operation as it is the
best bet because of in-built economic advantages. In an uncertain world with 8
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inadequate information Debbie and David will always have to strive to secure
the benefits of co-operation. They will sometimes win, sometimes lose, but by
building on past success and experimenting they will increase their chances of
improvement.
Their task is made more difficult by the well intentioned interference by the
Chancellor which destroys their 'market information system' by the ever
increasing distortions of taxes and benefits.
The Chancellor's objective should be to speed up evolution by removing
barriers to experiment and the discovery of improvements. He should stop
taking decisions on behalf of others and attempting to second guess the
evolution of co-operation by designing and interfering.
[1] Himmelweit (1964) - D319 Households, OU.
[2] Becker (1976) - The Economic Approach to Human Behaviour, University of
Chicago.
[3] Dawkins (1976) - The Selfish Gene, Oxford University Press.
[4] Losse (1993) - The Philosophy of Science, Oxford University Press.
[5] Dennett (1996) - Darwin's Dangerous Idea, Touchstone.
[6] D G Green (1999) - An End To Welfare Rights, Institute of Economic Affairs.
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