consumption, saving, and...

ChChapter 4

Consumption, Saving, and Investment

Copyright © 2009 Pearson Education Canada

This ChapterI Ch 3 h h l f d i In Chapter 3 we saw how the supply of goods is determined. In this chapter we will turn to factors that determine the demand for those goods and gservices.Output supply was determined by firms’ ND and HH’s NSHH’s NS

In the labour market, the equilibrium is reached through changes in w

Output demand determined by firms’ investment and HH’s consumption/savings decisions.

In the goods market the equilibrium is reached through In the goods market, the equilibrium is reached through changes in r

Copyright © 2009 Pearson Education Canada 4-2

This ChapterIn particular, this chapter will focus on the goods market:

The determinants of consumption and savingB l d ( )Borrowers vs. lenders (savers)Role of government in savingInvestmentInvestmentGoods market equilibrium


This Chapterll f h d hRecall from the Expenditure Approach:

Y = C + I + G + NXG is determined by non economic factors and by the political system (ignore it for now)(ignore it for now)Consider a closed economy (i.e. NX=0)F h i C d I Y C IFocus here is on C and I; Y = C + I

Natural issue: what goods and services to consume today and what to leave for consume today, and what to leave for tomorrow (savings)?


Consumption and SavingChanges in consumers’ willingness to spend have major implications for the b h i f th behaviour of the economy.

Consumption accounts for about 60% of total spending.The decision to consume and to save are closely linkedy

Define: aggregate desired consumption (Cd) as the aggregate quantity of goods and services that household want to consume given income and other factors


consume, given income and other factors.

Consumption and Saving (continued)Desired national saving (Sd) is the level of national saving that occurs when

t ti i t it d i d aggregate consumption is at its desired level.Note: superscript d desiredNote: superscript d = desired

C: consumption goods produced, i.e. ACTUAL amounts availableamounts availableCd: spending on consumption goods i.e. amounts that individuals want/DESIRE


C ‐ Cd = undesired inventories of consumption goods

Consumption and Saving (continued)

With no international economic relationships, NX=0 but also NFP=0When NFP=0, national saving is:e 0, at o a sa g s

S=Y-C-GThen desired national saving is:Then, desired national saving is:

Sd=Y-Cd-G


The Consumption and Saving Decision

l d ( d b )A lender earns (and a borrower pays) a real interest rate of r per year.1 d ll th f ti t d i 1 dollar worth of consumption today is equivalent to 1+r dollar’s worth of consumption in the next time periodconsumption in the next time period.So, 1+r is the price of current consumption in terms of future consumption in terms of future consumptionHow do people decide when to consume?


How do people decide when to consume?

The Consumption and Saving Decision (continued)The consumption-smoothing motiveis the desire to have a relatively even pattern of consumption over time.

This seems to be consistent with observed behaviour.A good part of a one-time income bonus is A good part of a one-time income bonus is likely to be saved, and the income earned on that saving likely to be spread over time.


Changes in Current IncomeMarginal propensity to consume (MPC) is the fraction of additional current income that is consumed in the current period.

MPC is a number between 0 and 1When Y rises by 1:When Y rises by 1:

Cd rises by less than 1;Sd rises by the fraction of 1 not spent


S rises by the fraction of 1 not spent on consumption.

A Formal Model of Consumption and SavingThis part of the lecture follows closely Appendix 4.A (on the course website).Start by considering the choice of a single individual (micro foundations) in i l a simple economy:Two periods (the present and future)I di id l k i i ili b Individual seeks to maximize utility by choosing between present and future consumptionconsumption.


A Formal Model of Consumption and Saving

l d l f dTo analyze a model of consumption and saving, we need to know two things:

What people can afford to consume What people can afford to consume How people rank the different options they are facing.g

We need to consider the budget constraint.We need to consider preferences (utility) over consumption today and tomorrow.


A Formal Model of Consumption and SavingS b d fi i h f ll iStart by defining the following:

y = current real incomeyf = future real incomey future real incomea = real wealth at the beginning of the current periodc = current real consumption

f fcf = future real consumptionr = real interest rate (for both borrowing and lending)

ld l k b b d fWe would like to obtain a budget constraint: for any level of current consumption (c), how much future consumption (cf ) can I afford based on future consumption (c ) can I afford based on my current and future income and initial wealth


A Digression: The Concept of Present Value

h b dWe can represent the budget constraint using the concept of present value which measures the value of payments to be made measures the value of payments to be made in the future in terms of today’s dollarsSuppose I’ll have a future income (Yf) of Suppose I ll have a future income (Y ) of $13 200 (one year from now) but I would like to to spend it all now.pI can get a bank loan but how much can I borrow given that Yf?g


A Digression: The Concept of P t V l ( ti d)Present Value (continued)The loan (L) at 10% current interest rate The loan (L) at 10% current interest rate satisfies:

L(1+0 10) = $13 200L(1+0.10) = $13 200L = $13 200/1.1 = $12 000

If I as a sa e and anted to ha e $13 If I was a saver and wanted to have $13 200 in the future, I would need to invest only $12 000 today to achieve that goalonly $12 000 today to achieve that goal.Economically, at an interest rate of 10%, having $13 200 one year from now is having $13 200 one year from now is equivalent to having $12 000 today.


A Digression: Present Value and the Budget ConstraintIn our two period model we can define the In our two period model, we can define the present value of lifetime resources (PVLR)as the present value of current income and as the present value of current income and expected future income plus initial wealth:

PVLR = y + yf/(1+r) + aPVLR y + y /(1+r) + aNext, divide both sides of the budget constraint by (1+r) and then add c to both y ( )sides:

c + cf/(1+r) = y + yf/(1+r) + a( ) y y ( )PVLC = PVLR


A Digression: Present Value

PVLC is the present value of lifetime

and the Budget ConstraintPVLC is the present value of lifetime consumption. The budget constraint shows that the PV The budget constraint shows that the PV of lifetime consumption equals the PV of lifetime resources.lifetime resources.If we choose to consume all the resources today (set cf = 0), then we get:y ( ), g

c = y + yf/(1+r) + aThis is the horizontal intercept on the budget p gconstraint graph.


Consumer PreferencesTo graphically represent consumer preferences To graphically represent consumer preferences for current and future consumption, we introduce indifference curves which represent all pcombinations of current and future consumption that yield the same level of utilityIndifference curves have three important properties:1 Slope downward from left to right1. Slope downward from left to right.2. Further away from origin represents more utility.3. Are bowed towards the origin because we assume

consumption smoothing (a preference for smooth changes to consumption smoothing (a preference for smooth changes to consumption).


The Optimal Level of Consumption

We can combine the budget line and indifference curves and find the optimal level of current consumption and savingGraphically, the optimum level of c is the point where the budget line is gtangent to an indifference curve (i.e. It just touches the highest indifference curve it can reach)


Effect of a Change in Income or Wealth

h ff ll d d h hThe effect will depend on how the PVLR is changed when either y, yf or a is changed.All three changes move the PVLR line without All three changes move the PVLR line without changing its slope -(1+r). It is an income effect.

An increase in y raises both c and current saving (y-c).An increase in yf or a raise c but lower current saving since current income (y) is not affectedsince current income (y) is not affected.

The consumer moves from point D to point J (not H or K because of consumption ( psmoothing).


The Permanent Income Theory

f h d l hIn terms of the model, a temporary change in income is represented by a change in ywith yf held constantwith yf held constant.A permanent change would assume both components (y and yf) changecomponents (y and y ) change.

This would have a larger effect on PVLR and so on both c and cf since the increase in income lasts for a longer duration.

The theory is known as the permanent i h (Mil F i d 1950 )income theory (Milton Friedman, 1950s)


The Life-Cycle Modelh i d d l b li dThe two period model can be generalised to many

periods which capture real world phenomena.Income tends to follow a pattern over the life of the Income tends to follow a pattern over the life of the economic agent, rising from early years and then peaking between ages 50 to 60. After retirement, income falls sharply.After retirement, income falls sharply.Consumption patterns tend to be smoother (which is consistent with consumption smoothing) than patterns of income over time.income over time.Saving as a result is first negative, then positive and then negative.

The Life Cycle theory is attributable to Franco The Life-Cycle theory is attributable to Franco Modigliani.


Excess Sensitivity and Borrowing Constraints Studies confirm that y yf and a all affect Studies confirm that y, yf and a all affect consumption and that permanent income changes have larger effects on changes have larger effects on consumption than temporary changes.Other studies point out that consumption Other studies point out that consumption responds to current income more strongly than theory predicts: excess sensitivity Possible reasons:

People are short sighted.p gBorrowing constraints may be binding


The Real Interest Rate and the C-S DecisionWhat happens to the budget line when the What happens to the budget line when the real interest rate changes?It rotates around a point (E in the figure) It rotates around a point (E in the figure) where there is neither borrowing or lending (c=y+a and cf=yf ).(c y+a and c y ).Since such a point involves neither borrowing or lending; it remains on the g g;budget line no matter what the interest rate.Since an increase in r causes the line to become steeper, it must rotate around E.


The Substitution Effectll h hRecall that an increase in r raises the price

of c in terms of cf.St ti f b i /l di i t Starting from a no-borrowing/lending point, the increase in r will cause consumers to lower c and increase s This increase in lower c and increase s. This increase in saving reflects the substitution effect of the interest rate on savinggThe increase in saving is measured along the horizontal axis as a drop in c.p


The Substitution Effect and Income Effect Together

Assume the consumer is initially a lenderAssume the consumer is initially a lender.We can use the graphical model to separate the two effects: (board)the two effects: (board)

Let the budget constraint pivot around the initial position (D). The drop in c (equivalent to a rise in p ( ) p ( qs) from going from D to P is the substitution effect.Th i ff t i d b th t The income effect is measured by the movement from P to Q.

Note that if the initial position was one of Note that if the initial position was one of dissaving, saving would unambiguously rise.


Changes in the Real Interest Rate

For a lender an increase in r has two opposite effects:

increase in current saving (substitution effect);decrease in current saving (income effect).

F littl d l i From our little model saving seems to rise nonetheless.


Changes in the Real Interest Rate (continued)

For a borrower when r increases the substitution and income effects both result in increased s.The empirical evidence is that an increase in r reduces c and increases s, but the effect is not very strong.


Taxes and the Real Return to SavingInterest earning (and other returns on savings) are often taxed

The real return earned by savers is actually less than the difference between i and πe

The expected after tax real interest rateThe expected after-tax real interest rate( ) is the after-tax nominal interest rate minus the expected inflation rate.

tar −minus the expected inflation rate.

eta πt)i(1r −−=−


Taxes and the Real Return to Saving (continued)

By reducing the tax rate on interest the government can increase the real rate of return for savers and (possibly) increase the rate of saving in the economy.

This is one motivation behind RRSPs (Registered Retirement Savings Plans)


Fiscal PolicyL ’ k i h h Let’s make an assumption that the economy’s aggregate output is i it i t ff t d b th given, it is not affected by the

changes in fiscal policy.In gene al fiscal polic affects Cd b In general, fiscal policy affects Cd by affecting households’ current and expected future incomes

The government fiscal policy has two major components:


government purchases and taxes.

Government PurchasesGovernment purchases increase temporarily:Government purchases increase temporarily:Indirect effects:

Cd f ll b hi h t b d ( d l Cd falls, because higher taxes burden (and lower income) is expected, but by less than the rise in taxes (MPC). Therefore, Sd increases.

Direct effect:Sd falls, because G increases: Sd = Y – Cd – G

Total effect is a reduction in Sd (the direct effect of the rise in G outweighs the indirect

d


effect), and a fall in Cd

TaxesA t t t (l h A government tax cut (lump sum, so each taxpayer gets the same amount) without a reduction in current government spending reduction in current government spending should:

Increase income and, therefore, Cd increases by a fraction of the tax cut.But expectations of higher taxes in the future (lower future after-tax income) would cause (lower future after tax income) would cause people to consume less today, offsetting the positive effect of the increased current income.

ld h /l d


A current tax cut could either raise/lower Cd

Taxes (continued)According to the Ricardian equivalence proposition the positive and the negative effects of the tax cut without reduction of effects of the tax cut without reduction of the current spending should exactly cancel.

If there’s no change in G, tax cuts don’t affect Cd If there s no change in G, tax cuts don t affect Cand therefore don’t affect Sd

Will not hold if: P l ’t th t f d l kiPeople aren’t that forward-lookingPeople are credit constrained (so spend it)People don’t understand how today’s T, G affect

’ T


tomorrow’s T

Ricardian Equivalence in it’s Strict Formh d l f b h dIn the model of consumer behaviour, Ricardian

equivalence would suggest that a change in current taxes does not affect the PVLR and thus current taxes does not affect the PVLR and thus shouldn’t affect Cd or Sd (board)

If the government cuts taxes today then y rises, If the government cuts taxes today then y rises, which should raise c, all else being equal.Assuming unchanged spending, the government

ffmust borrow the difference.But taxpayers are ultimately responsible for the government’s debt so yf will be lowergovernment s debt, so y will be lower.Under certain conditions one offsets the other.


InvestmentNow consider a second major component of spending: investment spending

Like C-S decisions, there is a trade-off between the present and future. e.g. A firm commits its current resources to increasing its capacity to produce and earn profits in the f t e


future.

Investment (continued)Investment spending fluctuates sharply over the business cycle and typically contributes half of the total decline in spending.Investment plays a crucial role in determining the long-run d g o g uproductive capacity of the economy.


y

The Desired Capital StockDesired capital stock is the amount of capital that allows a firm to earn the l t t d fitlargest expected profit.Recall, MPK is the increase in output from adding a unit of capital (other from adding a unit of capital (other factors held constant).Since lags occur in obtaining capital we Since lags occur in obtaining capital, we can define MPKf as the expected future MPK (i.e. Benefit from increasing


MPK (i.e. Benefit from increasing investment today by one unit of capital)

The User Cost of Capitalh d f b fCompare the expected future benefit to

the expected cost U t f it l i th t d l User cost of capital is the expected real cost of using a unit of capital for a specified period of timespecified period of time.

KKK d)p(rdprpuc +=+=uc is the user cost of capitalr is the expected real rate of interestd is the rate at which capital depreciates


d is the rate at which capital depreciatespK is the real price of capital goods

Determining the Desired Capital StockThe desired capital stock is the capital stock at which MPKf = uc.

This is where expected profit is maximized.If MPKf > uc, add K; If MPKf < uc, sell K.

The MPKf curve (slopes down) falls as Ki (di i i hi i l d ti it )rises (diminishing marginal productivity)

The uc curve does not depend in the amount capital and is a horizontal line


amount capital and is a horizontal line

Changes in the Desired Capital Stock

Any factor that shifts the MFKf

curve or changes uc, changes KIf r falls (other factors held constant), the uc line falls (shifts co sta t), t e uc e a s (s tsdownward), then MFKf>uc, and Krises.

The same is true when d or pK fall (other factors held constant).


( )

Changes in the Desired Capital Stock (continued)

When technology improves (other factors held constant) the MFKf

curve shifts upward, then MFKf>uc, and K rises.


Taxes and the Desired Capital Stock

Let’s incorporate taxes into the investment decisionThe after-tax MPKf is (1-τ)MPKf.

d)p(ruc +τ1d)p(r

τ1ucMPK kf

−+

=−

=

uc/(1-τ) is tax-adjusted user costof capital


of capital.

Taxes and the Desired Capital Stock (continued)

An increase in the tax rate τ raises the tax-adjusted user cost and so reduces the desired stock of capitalthe desired stock of capital.The effective tax rate is a single measure of the tax burden on capitalmeasure of the tax burden on capital.

This is the tax rate or a firm’s revenue that has the same effect on the desired stock of

i l ld l i i f h capital as would actual provisions of the tax code.


From the Desired Capital pStock to Investment

In general, K changes over time through two opposing channels:

Gross investment is the total purchase or construction of new capital goodscapital goods.Depreciation is the capital wearing out.out.

K increases or decreases over the year depending on which is greater.


year depending on which is greater.

Investment (continued)N t i t t i th diff b t Net investment is the difference between gross investment and depreciation.

ttt1t

dKKKIdKIKK

+−=−+

It is gross investment during year t.

tt1tt dKKKI +−= +

Kt and Kt+1 is capital stock at the beginning of year t and t+1.dKt is the amount of depreciation during year t

This says that gross investment is equal to changes


This says that gross investment is equal to changes in the capital stock plus depreciation.

y


Investment (continued)The firm’s gross investment during the year has The firm’s gross investment during the year has two parts:

The desired net increase in capital stock over the e des ed et c ease cap ta stoc o e t eyear (K*-Kt), (K* is the desired capital stock)• Depends on factors like taxes, interest rates, and MPKf

The investment needed to replace worn out or The investment needed to replace worn-out or depreciated capital (dKt).

* dKKKI +−=Typically there are lags in achieving K*.These concepts also apply to investment in

ttt dKKKI +−=


These concepts also apply to investment in inventories and housing

Goods Market Equilibrium( ) d d lJust as prices (w) adjusted to clear L

market, now r (real interest rate) adjusts to clear goods market, i.e. to adjusts to clear goods market, i.e. to equate quantities of goods demanded and supplied.P i di t d i i f HH’ Prices coordinate decisions of: HH’s demand for Cd and Sd, and firm’s demand for Id

In equilibrium, firm’s desired production equals the economy’s desired purchases


Goods Market Equilibrium (continued)The goods market equilibrium condition is when the aggregate quantity of goods supplied equals the aggregate quantity of supplied equals the aggregate quantity of goods demanded:

GICY dd ++=We can also write this condition to

h i th S I l ti hi b

GICY ++=

emphasize the S-I relationship by subtracting Cd + G from both sides:

Id = Y Cd G Sd = Id


Id = Y – Cd – G Sd = Id

The Saving-Investment DiagramThe saving curve, S, is upward sloping (empirically supported). A higher real interest rate raises desired national interest rate raises desired national savings.

Drawn for given levels of Y, Yf, wealth, G, T Drawn for given levels of Y, Y , wealth, G, T The investment curve, I, is downward sloping. A higher interest rate increases the user cost of capital and, thus, reduces investment.

D f i l l f th ff ti t t


Drawn for given levels of the effective tax rate and MPKf

The Saving-Investment Diagram (continued)Adjustments of the real interest rate, in response to excess supply or demand for saving, bring the goods market into equilibrium.

If ‘t l ’ Sd Id t t If r ‘too low’, Sd < Id, return to savings bid up by firms, r increases until the equilibrium is reachedqIf r ‘too high’, Sd > Id, return to savings falls, r decreases until the equilibrium is reached


equilibrium is reached

of


The Saving-Investment Diagram (Continued)

Goods market equilibrium can also be expressed as Y (supply of goods) equal t Cd + Id + G (d d f d )to Cd + Id + G (demand for goods):

Cd depends on r because a higher r raises SdS .Id depends on r because a higher r raises uc, which lowers Id.

In the same way, adjustments of reliminate excess supply or demand for

iCopyright © 2009 Pearson Education Canada 4-65

saving.

Shifts of theSaving CurveThe saving curve shifters are all factors, excluding the real interest rate, which affect national savingaffect national saving.E.g. The crowding out of investment by government purchases:government purchases:

increase in G causes a decrease Sd;

Sd curve shifts to the left;th ilib i the equilibrium r goes up;Id falls because of higher uc.This occurs because the government is using more real

hi h th i ld h i t


resources which otherwise would have gone into private investment.

Shifts of theInvestment Curve

The investment curve shifters are all the factors which affect investment, excluding the real interest rate (it determines the movement along the curve).


Shifts of theInvestment Curve

Example:An innovation or economic reform raises MPKf.The increase in Id shifts the investment curve to the right.r rises to a new equilibrium level.S increases.


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