richardian equivalence

Student number: 557699

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Question A

Ricardian equivalence observes that, for a constant level of government expenditure, a cut in

current taxation followed by an increase in future taxes will have the same discounted present

value as the tax cut. Ricardo argued that both bond and tax financing of government

expenditure are equivalent; therefore a deficit financed cut in current taxes would have no

effect in either the short- or long-run. This means that governments shouldn’t worry about the

size of their deficit as it reflects the size of their spending. This arises because the present

value of taxes can only change if the government changes the present value of its spending,

which under Ricardian equivalence is assumed constant.

A fall in taxes which is financed by government bond issue will increase the current

disposable income for the population, however there is an increase in future tax liability to

cover both the interest payments on the new bonds and to pay the principal back from bonds

which have reached maturity. Because the discounted present value of the higher future tax is

equal to the tax cut, households are therefore no better or worse off by the reduction in

current taxation over the course of their life. This implication means that households will not

change their spending; however households will increase their saving by the full magnitude

of the reduction in taxes. Since the increase in household saving is exactly equal to the

increase in government bond issue (borrowing), the interest rate which clears the bond market

is unchanged as both the supply and demand for loanable funds schedules shift in equal and

opposite direction.

To illustrate that a bond financed tax reduction has no effect on private sector consumption

because private sector saving increases by the full extent of the bond issue; we can consider

households saving function which is given as

Where S1 is household saving, Y1 is household income for each period (given exogenously),

T1 is the initial level of taxation, and is household consumption. This is a standard savings

function which shows that households save what is left of their disposable income (

after consumption. Because the decrease in taxation is equal to the value of the bond issue

Where shows the post-cut tax level and B is bond issue. This gives the new savings

function post tax reduction, as

.

Using the previous formula to find the change to household saving then gives

.

This final equation shows that the value of the bond issue is equal to the increase in savings;

therefore household consumption, C1, does not change. This finding isn’t consistent with the


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Keynesian viewpoint which would expect consumption to rise.

In multi-generational models where households have the opportunity for capital accumulation

over the generations, the above situation continues. Ricardian equivalence assumes that each

generation’s utility also depends on the utility of the next generation. This means that given

reduction in current taxes for generation 1, generation 1 will save the full amount of the

reduction in taxes which will be passed on to the next generation as gross bequest, which is

assumed to not be negative. The higher level of gross bequest, because of the higher savings,

means that the next generation can continue to consume at the same level as before the tax

cut. Therefore, there is no capital accumulation as the savings from the previous periods are

used up in next period consumption.

Question B

A liquidity constraint restricts a household’s ability to borrow against their period two

income to increase their period one consumption. The liquidity constraint can either

bebinding (which means that the household would like to borrow in period one but is unable

to due to the constraint) or it can be non-binding(which means that the constraint does not

affect the household’s consumption in either period).

Ahousehold which is subject to a binding liquidity constraint in period one by the constraint

will choose to consume all their disposable income of in period one.

The household’s budget constraint is given by the equation

Considering the graph below; without a liquidity constraint the household would use their

endowment income, E, to consume at point B which is where their utility is maximised on

utility curve U’.The individual would choose to consume at point B because that is where

their indifference curve is tangential to the non-liquidity constrained budget line YEBX.

Therefore because point B is to the right of the initial endowment point, the household would

choose to borrow if there is no liquidity constraint

However the liquidity constraint stops the household from borrowing against their period two

income which will kink the budget line from YEBX to YEC1. This occurs at point E because

the individual cannot borrow to increase their period one consumption and as such they

cannot have any more disposable income in period one. The highest possible indifference

curve that the household could reach is curve U1 which is tangential to the budget constraint

at point E. They cannot be made any better off as they cannot borrow to reach a higher

indifference curve, and if they saved their period one income they would be worse off as they

would be on a lower indifference curve. Therefore the household has chosen to consume at

point E, which means that they will be consuming all of their period one disposable income

in period one.


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From looking at the two consumption points B and E, it is clear to see that the liquidity

constraint is making the household worse off as they are now consuming on a lower

indifference curve U1<U’.

If the government decided to implement a bond-financed reduction in period one taxation

which would be followed by an increase in period two taxation such that the taxes are now

and

The new intertemporal budget constraint is given by

This new budget constraint is exactly the same as the original before tax reduction budget

constraint as the B’s cancel out. Therefore the budget constraint does not move or shift.

However, the endowment point shifts down and to the right along the budget line as period

one income increases whilst period two income reduces.

We can see the effects of this bond financed tax reduction on the next graph and we will

consider two separate situations (1) a small reduction in taxation, and (2) a larger reduction in

taxation.

C2

C1 C1=Y1-T1

C2=Y2-T2

C2’

C1’

E

X

U’

U1

B

Y


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First we can examine the effects of a small reduction in period one taxation.The original

endowment point E is now shifted to the right to point E’, which has a higher period one

income and lower period two income than the original endowment point. This household

would still prefer to borrow in period one if there was no liquidity constraint, however

because of this constraint they will use all of their period one income to consume at the new

endowment point E’, on utility curve U*. Because the individual has a preference towards

period one consumption, this situation yields a higher level of utility than before since

U*>U1. Again, to reach a higher indifference curve would mean violation of the liquidity

constraint and they could not save any of their period one income as it would make them

worse off. Therefore the liquidity constraint is still binding in this situation and their

consumption function is and .

The situation is quite different when the government makes a larger tax cut. If the cut is large

enough to shift the endowment point further to the right such that it is to the right of point B,

such as point E’’. In fact any point to the right of the optimum point if there is no liquidity

constraint (point B here), will end up with the household being a saver once there is a

liquidity constraint imposed. From this initial endowment point, the household would

actually save some of their period one income such that they would shift back along the

budget line until point B which is where the utility curve U’ is tangential to the budget

constraint. Therefore, the liquidity constraint is not binding in this situation, as the household

has been able to increase their utility regardless of the liquidity constraint.

The consequences of these findings for Ricardian equivalence are that it is not realistic. In

real life a household is not concerned with the value of their lifetime income; instead they are

most concerned with their current consumption. As such a household who needs to consume

C2

C1 C1

C2*=Y2-T2*

X

U’ U*

E’

B

Y

C1*

E

E’’

C2’

’

C1’

’

U1


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more than their current income must borrow in order to sustain this consumption. If they are

impaired from borrowing to supplement their current income, the household’s current income

is the only thing which determines their consumption, irrespective of their future income.

We can see how Ricardian Equivalence could breakdown because of liquidity constraints if

we consider a young student who is currently at university with a part time job but who has a

job lined up for when he leaves university which will have a significantly higher income than

he currently earns. This individual may want to borrow against his expected higher future

income in order to smooth his consumption or pay for a holiday. However because of

liquidity constraints, such as imperfect financial markets or asymmetry in the information

between people looking to borrow or lend; this individual cannot secure a loan. Once the

government carries out the bond-financed tax reduction followed by a future tax increase, he

is not likely to increase how much he saves by the same value as the tax cut because instead it

will be a relief from his liquidity constraint so that he can consume more this period. This

would be against Ricardian Equivalence which expects that savings increase by the same

amount as the tax cut, but it will favour the Keynesian viewpoint which expects consumption

to increase. Consequently national savings and the government’s current account would

decline in value because of both government savings reducing and no change in private

saving.

Therefore when a bond financed tax reduction is implemented, households will have higher

current income and current consumption even though their future income will be reduced.

This means that the government is essentially giving the household a loan because of the

lower current tax and higher future taxes.

richardian equivalence

Economy & Finance