Consumption
1
Consumption data
2
The Keynesian Consumption Function
3
Goods Market Equilibrium
4
Review and to Do
Keynes proposed that on average, consumption was closely related to current income, but would not move 1 for 1 will current income:
\[C=C(Y_D)\]
Often specified as:
\[ C = c_0 + c_1Y_D\] where:
\(c_1\) is the average propensity to consume out of current income
\(c_0\) is the portion of consumption NOT attributable to current income
Total demand in the economy is:
\[Z= C + \bar{I} + \bar{G} + \bar{NX}\]
We assume that producers make predictions about demand and have a target inventory
These two considerations help them determine the amount to produce
However, they could be wrong, in which case inventories will either be drawn down or pile up
If inventories pile up because \(Y>Z\), we can assume producers will decrease production next period
If inventories are drawn down because \(Y<Z\), we can assume producers will increase production next period
If inventories are at target because \(Y=Z\) producers will not change production (equilibrium)
\[ Y = Z \]
\[Y = c_c + c_1(Y-T) + \bar{I} +\bar{G} + \bar{NX}\]
\[Y - c_1Y = c_0 -c_1T + \bar{I} + \bar{NX}\]
\[Y = \frac{1}{1-c_1}(c_0 - c_1T + \bar{I} + \bar{G} + \bar{NX})\]
\[Y = \frac{1}{1-c_1}(c_0 - c_1T + \bar{I} + \bar{G} + \bar{NX})\]
We call \((c_0 - c_1T + \bar{I} + \bar{G} + \bar{NX})\) autonomous spending
We call \(\frac{1}{1-c_1}\) the multiplier
The multiplier implies that a change in autonomous spending will cause an even larger change in equilibrium GDP
Spending creates income which then induces further spending
This principle is at the core of a lot of macroeconomic policy making
You can think of autonomous spending as a splash, and the multiplier as ripples
Suppose the consumption equation is represented by the following: \[C = 250 + .8Y_D\] Assume that investment, govenment spending, and net exports can be described as: \[I = 100\]
\[G = 50\]
\[T = 100\]
\[NX = 0\]
The adjustment of output over time is called the dynamics of adjustment.
How long the adjustment takes depends on how and when firms revise their production schedule.
In other words, the full multiplier effect won’t happen immediately.
\[\Delta C \rightarrow \Delta Y\]
\[c_1(\Delta Y)\]
\[c_1(c_1 \Delta Y)\]
\[c_1(c_1 (c_1 (\Delta Y)))\]
\[\Delta Y + c_1(\Delta Y) + c_1^2 (\Delta Y) + c_1^3 (\Delta Y) + \ldots + c_1^n(\Delta Y)\] Extracting Y \[\Delta Y (1 + c_1 + c_1^2 + \ldots + c_1^n)\]
As the series approaches its limit:
\[\Delta Y (\frac{1}{1-c_1})\]
\[ \frac{C}{Y_d} = \frac{c_0 + c_1Y_d}{Y_d} \]
So that as income rises, consumption becomes a declining share of total income
But as you have seen in your homeworks, consumption is a roughly constant (and recently increasing!) share of total income
As we saw earlier, the classical theorists thought that interest rates played a big role in decisions to save and therefore consume.
But the interest rate plays no role in the Keynesian story
People save because they think they will need money in the future
Macroeconomists often think of the decision to save as a decision to consume later
though there are some issues with this
Some economists have thus argued that consumption should in general depend on a consumers vision of the future
In a series of papers in the 1950s Franco Modigliani argued for a life cycle style consumption function
Saving allows consumers to move income from those times in life when income is high to those times when it is low.
Most people plan to stop working at about age 65, and they expect their incomes to fall when they retire. To maintain consumption, people must save during their working years.
Suppose a consumer expects to live another T years, has wealth of W, and expects to earn income Y per year until he retires R years from now.
lifetime resources are composed of initial wealth \(W\) and lifetime earnings \(R \times Y\)
\[ C = \frac{W+RY}{T}\]
\[ C = (1/T)W + (R/T)Y \]
If all consumers do this, aggregate income looks like:
\[ C = \alpha W + \beta Y \] in other words, wealth is now our \(C_0\)
While income increases in the short run, sure higher income corresponds to a lower average propensity to consumer
Over the long run though, income grows wealth, which shifts the consumption function up
\[ Y = Y^P + Y^T \]
Where \(Y^P\) is permanent income, and \(Y^T\) are transitory fluctuations in income
Friedman argued that permanent income will have much larger influence than transitory
According to the permanent-income hypothesis, the average propensity to consume depends on the ratio of permanent income to current income.
When current income temporarily rises above permanent income, the average propensity to consume temporarily falls; when current income temporarily falls below permanent income, the average propensity to consume temporarily rises.
Future oriented theories of consumption imply that government stimulus may not be as effective as the Keynesians suggested
In particular, if a tax cut or increase in government spending is a short term even (like stimulus checks), it will be primarily saved because it does not increase lifetime income
But it does imply that financial markets could play a big role in consumption
In practice consumption seems to be more volatile and more closely related to short term changes in income than future oriented theories predict.
Why?
Durable goods tend to be very very volatile and closely realted to short term income.
Three kinds of considerations:
Real interest rate
Credit availability
Uncertainty about future income
But even non-durables are more sensitive than we would expect.
One reason is that households must have large prior wealth, or access to credit to smooth consumption
Many households do not have stocks of wealth, and even more importantly, credit is often rationed
In part this is because of imperfect information
We can say:
Consumers try to smooth consumption
Wealth matters
Access to credit matters
Consumption is still pretty closely related to current income.