Chapter IV Consumption, Saving, and Investment
Assumption in this chapter:
Because the political process determines the level of government purchase, we
will consider it a constant.
What is left in the equation?
When is the goods market at equilibrium?
When the quantity of Goods producers want to supply equal the quantity of Gs demanded
4.1 Consumption and Saving
What happens to the economy if the willingness of households to consume changes?
What happens to savings?
Desire Consumption (Cd) is defined as the aggregate quantity of goods that households
want to consume, given income and other factors that determine households’ economic
What happens if there is a change in income or interest rates?
Cd is obtained by adding all the desired household consumptions in the economy.
Any factors that reduce individual households’ desired consumptions will reduce
Any factors that increase individual households’ desired consumptions will
From Chapter two we derive the following:
S ≡ Y + NFP – C (Y – t) – G
But since our assumption is a close economy
S ≡ Y – C (Y – t) – G
If we notice we are now looking at the desire consumption, thus
Sd ≡ Y – Cd (Y – t) – G
We can determine using the budget line: Future consumption
Its slope is (1 + r).
X-axis is present C. Budget line (1+r)
Y-axis is future C. Present consumption
I. The Consumption and Saving Decision of an Individual
Given our budget constraint we face the following trade-offs:
1. Consume 100% of income
2. Consume less than 100% and save the rest for future consumption
3. Consume more than 100% and borrow the rest, which reduces future
The rate at which you trade off current and future consumption depends on the real
interest rate prevailing in the economy.
What is my Yearly Salary?
What is the prevailing r?
What happens if I borrow $10,000?
What about the indifference curve how is it affected?
Important to notice in this example… is ceteris paribus.
Given our trade offs most rational people will neither go on a buying spree or save every
We will try to maximize our indifference curve.
The consumption-smoothing motive is the desire to have a relatively even pattern of
consumption over time. The rational people will avoid high borrowing or high savings.
II. Effect of Changes in Current Income
What would you do:
1. If you receive a raise in your salary?
2. If you get laid off and you go on unemployment?
If you use the entire income raise in consumption, you will not have anything when you
get laid off!!!
If you save it all, your wealth will increase and so will your future income.
The marginal propensity to consume (MPC) is defined as the fraction of additional
current income that one consumes in the current period.
If I receive the $10,000 and I only consume $4,000, what is MPC?
If I am laid off and I my MPC is the same as above, plus my salary decrease by $10,000,
how much will I consume?
Give me a guess of what the MPC of the US is?
If we aggregate this affects from one person to the entire economy we see the affects on
Y, Cd, and Sd.
III. Effect of Changes in Expected Future Income
If you have a contract out of college to play professional sport, but you are currently
unemployed, how much do you think this person will consume?
Using the example:
What happens if the future salary is expected to increase (assuming it is legally
If one’s decisions are guided by a consumption-smoothing motive, one will prefer to use
the bonus to increase the current consumption as well as the future consumption.
To summarize, an increase in an individual’s expected future income is likely to lead that
person to increase current consumption and decrease current saving.
Lets assume you do not use up the entire expected raise, then in essence what we do is
increasing the income in both T 1 and 2 by a fraction of the raise (and some goes to the
Economist can not measure expected future income directly, so economist do survey to
obtain the labor’s perceptions.
IV. Effect of Changes in Wealth
Suppose you have 10,000 of stocks of company XYZ and each is worth $10. What
happened to your current income if the stock increases to $15?
Your consumption will increase by about $50,000 times the MPC.
V. Effect of Changes in the Real Interest Rate
What is the slope of the budget line?
If interest increases:
1. One should save more, and
2. Spend less
The reason is because each real dollar of saving in the current year grows to 1+r real
dollars next year, and increase in the real interest rate means that each dollar of current
saving will have a greater payoff in terms of increased future consumption. In other
words you will be compensated at a high rate!!
A higher real interest means that one could achieve any future saving goals with a smaller
amount of current saving. This allows for more consumption today if preferred.
The two opposing effects are:
The substitution effect of the real interest rate on saving reflects the tendency to reduce
current consumption and increase future consumption as the price of current consumption
1+r increases (i.e. substitute today for tomorrow).
The income effect of the real interest rate on saving reflects the change in current
consumption that results when a higher real interest rate makes a consumer richer or
poorer (Ex: saving accounts interest payments).
What happens if you owe money?
Taxes and the Real Return to Savings.
Expected after-tax real interest rate is the after tax nominal interest rate minus the
expected inflation rate. Defined as:
rat 1 t i e
It is used to measure the returns received by the saver after taxes and it should be the one
used when making consumption and saving decisions because it measures the increase in
the purchasing power of their savings after payment of taxes.
What happens if taxes decrease or increase?
VI. Fiscal Policy
In general, fiscal policy affects desired consumption, Cd, primarily by affecting
households’ current and expected future income.
Change in t on the private sector, by either raising expectation or raising it, will cause
people to consume less.
How do we explain it by using rat 1 t i e ?
How does the government fiscal policies affect desired national saving, Sd?
Sd ≡ Y – Cd (Y – t) – G
1. For any level of Y and G, and increase in Cd (through tax or tax expectation) by
one dollar will lower the Sd by one dollar.
2. For any level of Y and Cd, and increase in G will directly lowers Sd.
Government Purchases (G)
Assume that this increase or decrease is a temporary change in the fiscal policy.
Given; consumers respond to decline in their current income by reducing C, but by less
than the decline in current income because of MPC.
What happens if G increase w/o changes in taxes?
An increase in G (through borrowing because we did not increase taxes)
means higher taxes in the future.
Higher future taxes will reduce rat 1 t i e and Cd (Y – T)
Important thing to notice that the increase in G is higher than decrease in C because of
MPC, which means that savings have to make up for it (Sd ≡ Y – Cd (Y – t) – G).
Assume G is constant.
Ricardian equivalence proposition is the idea that tax cuts do not affect desire
consumption and also do not affect desired national savings.
According to David Ricardo, taxes and G are a zero sum. If you spend today without
raising taxes, your taxes will raise in the future to pay for pass expenditures.
Problem with a reduction in taxes without reducing without reducing G, leads to a
increase in C.
If we look at “Sd ≡ Y – Cd (Y – t) – G”, we can see that Savings must decrease.
In the short run a tax cut will lead to Cd increase lowering Sd.
In the long run, a cut in t will not have an affect on Sd due to the expected increase in t.
4.2 Investment (I)
This is the spending by firms.
In making capital investment, a firm commits its current resources to increasing its
capacity to produce and earn profits in the future.
Reason for to study I:
1. Investment spending fluctuates sharply over the business cycle.
2. Investment plays a crucial role in determining the L-R productive capacity of the
I. The Desired Capital Stock
A firm’s desired capital stock is the amount of capital that allows the firm to earn the
largest expected profit.
This is done using a cost benefit analysis. If the benefits out weight the costs, then we do
it. Otherwise, we do not do or continue the program.
Example: we want to build a new factory.
x x x x
1 2 3 4
1 1 r n
We do the project if z A
1 1 r n
We reject the project if z A
As mentioned before, in real terms, the benefit to a firm of having an additional unit of K
is the MPK.
Because of lags with obtaining K, then we must obtain the expected MPKe.
MPKe is the benefit from increasing investment today by one unit of K.
Denoted as: dI dK
a. The User const of Capital
The user must know:
1. The cost of product in real terms ($, €, ₤…). This includes maintenance, yearly,
2. Production output and depreciation overtime.
3. Interest rate.
4. Salvage price.
The user cost of capital is the expected real cost of using a unit of capital for a specified
period of time.
This includes the opportunity cost of borrowing or using retained earnings. Denoted
uc rpk dpk r d Pk
Where p is the price of the capital good,
d is the rate of depreciation
r is the expected real interest rate
b. Determining the Desired Capital Stock
A firm’s desired capital stock is the capital stock at which the expected future marginal
product of capital equals the user cost of capital.
What happens if K is below K*?
When the capital stock is K* the MKPf is equal to uc*. This means that the cost of an
additional unit is the same as the benefit.
II. Changes in the Desire Capital Stock
Any factor that shifts the MPKf curve or changes the user cost of capital changes the
firm’s desired capital stock.
If r decreases, then uc rpk dpk will also decrease.
This will shift the curve down
Increases the desired capital stock rises.
A fall in the real interest rate lowers the user cost of capital.
Play with Tobin’s q
Taxes and the Desired Capital Stock
What are the two things we know for sure in live?
Now we have to relax the assumption and take into account the affects of taxes on
business decision making process.
The desired capital stock is the one for which the after-tax MPKf equals the user cost,
1 MPK f uc
uc rp dpk
MPK f k
This is the tax-adjusted user cost of capital and it shows how large the before-tax MPKf
must be for a firm to willingly add another unit of capital.
We must recall that τ is taxes minus depreciation, debt deductions…and all the fun things
that we could think about.
Effective tax rate is the summery of the many provisions of the tax code affecting
Basically it is the affect of taxes after we take in consideration all the provisions in the
If a change in the tax code increases the effective tax rate, it will lower the desire
for capital stock.
If a change in the tax code decreases the effective tax rate, it will raise the desire
for capital stock.
III. From the Desired Capital Stock to Investment
Now we link desire of capital and investment.
In general K changes over time through opposing channels.
1. Gross investment increases the capital stock.
2. The capital stock depreciates or wears out which reduces the K
Gross investment is the total purchase or construction of new capital goods that takes
place each year “investment”. (It)
Net investment is the change in the K over a period of time. Denoted:
Net investment = K t 1 K t
The relationship between net and gross investment is:
K t 1 K t I t dK t
The difference between Gross and net is the depreciation.
The amount of depreciation that occurs during the year is determined by the depreciation
rate and the initial capital stock.
To illustrate the relationship between K and I we use the following:
1. K* is the desired amount of capital that the firm would like to have at the end of
the year (for whatever reason).
2. K is easily obtainable.
I t K t 1 K t dK t , which states that Gross investment equals net investment
Sub Kt-1 by K* and we get
I t K * Kt dKt
Basically Gross investment has two parts
1. The desire net increase in the capital stock over the year (K* – Kt).
2. The investment need to replace worn out or depreciated capital (dKt).
The desired net increase in the capital stock over the year depends on the factors that
affect the desired capital stock.
Lags and Investment
In practice a firm’s desire to increase capital stock may not occur in one year. In other
words if you want a factory it may take some year.
All things aside, factors that increase firm’s desired capital stock also tend to
increase the current rate of investment.
IV. Investment in Inventories and Housing
Investments are composed of:
1. Business fix investment
2. Inventory investment (change in inventory over a year)
3. Residential investment (construction of new housing)
Using the same process; if the MPK of having extra amount of inventory increase sales,
will lead to more inventory.
4.3 Goods Market Equilibrium
At this point we are constructing the goods market where:
AS = AD
This could be written algebraically as such
Y = Cd + Id + G
Where Y is the AS, and
AD is the right hand side.
Thus, we say that the quantity of goods demanded is equal to:
The desired investment
And government purchases
The market where aggregate demand and aggregate supply interact is the goods market
Labor Market Function
Y ≡ Cd + Id + G ≠ Y ≡ C + I + G
The right hand side of this inequality shows actual income and actual expenditure.
By definition this identity is always satisfied.
The left hand side of this inequality shows the goods market.
By definition (since we are looking at desired not actual) this identity is not
Why would this not be satisfied?
The goods market identity may not be at equilibrium, but market forces will bring it back
to equilibrium fairly quick.
A way to write the goods market is by emphasizing the relationship between the desire
savings and desired investment.
Y ≡ Cd + Id + G
Put investment on one side and the rest on the other
Id ≡ Y – Cd – G
Substitute the left hand side by the desired national savings.
Id ≡ Sd
This condition says that the goods market is at equilibrium when the desired savings is
equal to the desired savings.
The Saving–Investment Diagram
For the goods market to be at equilibrium the AD must equal the AS (at a given price) or
the Id must equal the Sd (at a given real interest rate).
The upward sloping of the saving curve tells us what?
The downward sloping of the Investment curve tells us what?
What happens if the real interest rate is higher or lower that the actual?
a. Shift in the Saving Curve
For any real interest rate, a change that increases or decreases the national savings (ΔG,
ΔY, ΔYe, Δre or ΔW) will shift the savings curve.
b. Shift in the Investment Curve
For any real interest rate, a change that increases or decreases the desired investment
(ΔMPK, Δr and Δτ) will shift the investment curve.
Budget line shows the combination of current and future consumption available to an
individual or economy. It is sloped as – (1 + r).
o Measures the relative price of good X in terms of good Y
o How much of Y you have to give up in order to acquire an additional unit
o Usually negative, as consuming more of one good involves the sacrifice of
Indifference curve (IC) represents consumption combination that yield the same level of
They have four important properties:
They are downward sloping
o marginal rate of substitution - the maximum amount of Y you are willing to
sacrifice to get an extra unit of X, remaining indifferent or keep the same utility
IC Can not intercept
Monotonicity: More is better. Consumers prefer more of any quantity to less.
(note: this assumption will not hold if one or both goods in the bundle cause
Convex (bowed towards the origin)
The Consumer's Problem: how to optimize one's utility with a constrained budget. The
consumer's problem is a typical maximization problem, in that it has both aims and
Aims: achieving the highest possible level of satisfaction - shown through
Constraints: limited budget, limited time, limited available information - shown
through the budget line.
What happens if income or wealth?