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High income earners work more. Is it consistent, or can it be explained by consumer theory?

1)      Definition of terms

a)      Consumer theory – standard neo-classical consumer theory models the behaviour of humans by taking

i)        individual rationality

ii)       dislike for work

iii)     Walrasian economy (perf. comp, no transaction costs or assym. information)

iv)     Utility function of the form U=f(C,1-l) where utility is derived from consumption (C) and work(l). Ramsey model will do.

v)      Showing other assumptions is just a show off that one should not remember in an exam anyway.

2)      Basic theory

a)      Representative household maximises the expected value of

where rho is the discount rate and u(.) is the instantaneous utility function. Households maximise this function subject to (assuming no capital accumulation). Thus one can see that when the real wage function w(t) increases people can automatically afford more consumption )ie in equilibrium consumption must be higher). Furthermore, assuming a convex instantaneous utility function that satisfies Inada conditions, we can see that work, l(t), is now more productive and makes people more willing to substitute work for labour. However, since they already have higher consumption possibility due to increased wage, the leisure has become more valuable in terms of consumption, thus people might start working less (income effect). At low incomes substitution effect is likely to dominate (people work more when wage increases), however, at higher incomes the combined effect of inc. and subst. effect is ambiguous.

b)      graphical approach:

Income and substitution effect:










l1->l2 substitution, l2->l3 income. As seen final effect ambiguous.






Resulting Labour supply function:






3)      Extensions to basic theory

a)      Normally people are paid overtime, so wage is not just increased. Thus budget constraint becomes   where w1<w2 and L bar corresponds to the “normal” working hours. The second term thus shows the payment for overtime. This eliminates the income effect as the income of the person is not actually increased before he starts working more (ie before substitution from leisure has occurred).

b)      Graphically










As seen, l1>l3, thus leisure has been reduced, and people work more.

4)      Conclusions

a)      Basic theory can be realistically modified to show the overtime effects

b)      Other effects:

i)        More likely going to enjoy job (higher satisfaction with better pay)

ii)       Promotion prospects

iii)     Rules of thumb instead of optimisation (automatically increase working hours with pay rise, thinking that permanent increase is temporary)

c)      Criticism

i)        Very little evidence of any intertemporal substitution in reality

ii)       Efficiency wage and other non-walrasian arguments meaning that real wage does not affect employment

iii)     Fear of unemployment – people can either work or be unemployed. Reduction in hours not feasible. The “normal” hours of work historically higher for managerial positions irrespective of wage.

5)      References

D. Romer Advanced macro. Intro. to Ramsey model (Ch.2) and baseline RBC (p. 154).

A. Fisher lecture notes from last year (ie Begg “Macroeconomics”).

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