ECON 314: MACROECONOMICS II CONSUMPTION

ECON 314: MACROECONOMICS II CONSUMPTION

Consumption is a key component of aggregate demand in any modern economy. Previously we considered consumption in a simple way: consumption was conjectured to be a function of current income (more appropriately disposable income).

This was largely attributed to the work of John Maynard Keynes (based on his work from the mid-1930s) The consumption function was stated as follows: C = c(y T), where C, Y and T are as previously defined.

In its linear form, it is written as: C = c 0 + c 1 (Y T), where c 1 is the MPC. This is what is termed the Keynesian consumption function, with c 0 > 0 and 0 < c 1 < 1, that is: 0 < C [Y T] < 1

As previously noted, consumption is important in any modern economy, and therefore has important consequences regarding the behaviour of the economy over the long-run (e.g., on long-run growth via savings decisions) and the short-run (volatility in GDP).

Based on the Keynesian consumption function, three conjectures emerge: 0 < MPC < 1 Average propensity to consume (APC ) falls as income rises: (APC = C/Y ) Income is the main determinant of consumption.

C As income rises, consumers save a bigger fraction of their income, so APC falls. C C cy C C APC c Y Y slope = APC Y

How do we test these conjectures? We look at cross-sectional data and also at short-time series data. Initially these conclusions looked good for the Keynesian consumption function.

Another aspect of the Keynesian consumption function had to do with its prediction regarding the rate of saving as a country gets richer. The savings rate, s, is defined below: s = [(Y T) C] [Y T] = 1 C Y T = 1 c 0 Y T c 1

Where C Y T CONSUMPTION is APC. Thus, given the definition for the savings rate, we can see why the Keynesian prediction that as a country gets richer the saving rate should rise. This resulted in what Alvin Hansen termed the secular stagnation theory/hypothesis.

The basic idea was that an economy will slow down in the long-run because of high saving and little investment (and under consumption). But this did not turn out to be so over time. It was observed that the saving rate remained constant over long periods of time.

Using data on consumption and income for long periods of time, Simon Kuznets found that consumption was stable in spite of rising income in these periods. He also found that the APC was also relatively constant over long periods of time. This raised concerns regarding the Keynesian consumption function.

To summarise, these were the findings from Kuznets study: Cross-sectional budget studies show s/y increasing and c/y decreasing as y rises, so that in cross-sections of the population, MPC < APC.

Business cycle or short-run data show that that c/y ratio is smaller than average during boom periods and greater than average during slumps, so that in the short run, as income fluctuates, MPC < APC.

Long-run trend data show no tendency for the c/y ratio to change over the long-run, so that as income grows long trend, MPC = APC. Saving also played an important part in consumption decision.

To address these issues, new theories were developed to explain how the observed phenomena could be reconciled with the Keynesian view. All these theories have basic foundations in the microeconomic theory of consumer choice.

The theories that explain consumption include: The Permanent Income Hypothesis by Milton Friedman. The Life-Cycle Hypothesis by Franco Modigliani, Albert Ando and Richard Brumberg

The Random-Walk Hypothesis by Richard Hall. Pull of Instant Gratification by David Laibson. The first two rely on Irving Fisher s Intertemporal Utility Maximization Model.

The first two give rise to what may be termed the neoclassical consumption model, in that individuals choose the time path of the consumption to maximize utility. This results in a solution in which consumption is proportional to an individuals total wealth, including current financial wealth and the present value of current and future labour income.

Irving Fisher and Intertemporal Choice: The basis for much subsequent work on consumption. Assumes consumer is forward-looking and chooses consumption for the present and future to maximize lifetime satisfaction.

Irving Fisher and Intertemporal Choice: Consumer s choices are subject to an intertemporal budget constraint, which is a measure of the total resources available for present and future consumption. The consumption model then has two main elements: an intertemporal budget constraint and a utility function.

Irving Fisher and Intertemporal Choice: Utility: the consumer chooses his/her consumption today and in the future in order to maximize utility. Consumption yields utility through a utility function. Thus, when the consumer consumes some amount c in a given period, we assume s/he receives u(c) units of utility.

Irving Fisher and Intertemporal Choice: Utility: the consumer receives more utility whenever consumption is higher, but consumption runs into diminishing returns, or what is termed diminishing marginal utility. Consumption is over different periods of time. How then do we add up utility across time?

Irving Fisher and Intertemporal Choice: Utility: to do that, we simply take the sum of individual utilities. So over two periods, the total utility following lifetime utility function, U, is: U = u c today + βu(c future ) The parameter β is some number (β 0) that captures the weight the individual places on the future relative to today.

Irving Fisher and Intertemporal Choice: Utility: this suggests that if β = 1, the individual treats utility flows today and in the future equally. If however, β < 1, then a given flow of utility is more when it occurs today. In this analysis we ignore the notion of discounting, and assume that the individual treats as equal utility flows today and in the future.

Irving Fisher and Intertemporal Choice: Intertemporal Budget Constraint: suppose the individual is faced with two periods today and future and that s/he has income today (y today ) and income in the future (y future ).

Irving Fisher and Intertemporal Choice: Intertemporal Budget Constraint: the individual thus faces two budget constraints: c today = y today saving today c future = y future + 1 + r saving today

Irving Fisher and Intertemporal Choice: Intertemporal Budget Constraint: if we denote today and the future by 1 and 2 respectively, then in the future: From c 2 = y 2 + 1 + r (y 1 c 1 )

Irving Fisher and Intertemporal Choice: Intertemporal Budget Constraint: this yields the following conclusion: c 1 + c 2 (1 + r) = y 1 + y 2 (1 + r)

Irving Fisher and Intertemporal Choice: Intertemporal Budget Constraint: the intertemporal budget constraint indicates that the individual can borrow or save in each period at the prevailing interest rate.

Irving Fisher and Intertemporal Choice: Intertemporal Budget Constraint: This means that the individual s present discounted value of lifetime consumption must equal its present discounted value of lifetime income.

Irving Fisher and Intertemporal Choice: Intertemporal Budget Constraint: if we generalise over the lifetime of the individual to point T, which is the instant before the consumer dies, the objective of the individual is to maximize utility over the lifetime.

Irving Fisher and Intertemporal Choice: Intertemporal Budget Constraint: in order to obtain the highest level of utility, subject to the budget constraint, the present value of his/her total consumption in life cannot exceed the present value of his/her total income in life.

Irving Fisher and Intertemporal Choice: Intertemporal Budget Constraint: symbolically this constraint can be written as: T y t 1 (1+r) t = T c t 1, where T is (1+r) t the individual s expected lifetime.

Irving Fisher and Intertemporal Choice: Intertemporal Budget Constraint: This intertemporal budget constraint says that the individual can allocate his/her income stream by borrowing and lending, nevertheless the present value of consumption is limited by the present value of income.

Irving Fisher and Intertemporal Choice: We can simplify matters by sticking to the two-period case, which give us the following: c 1 + c 2 (1+r) = y 1 + y 2 (1+r) Present value of lifetime consumption Present value of lifetime income

Irving Fisher and Intertemporal Choice C 2 C C Y Y 1 r 1 r 2 2 1 1 (1 r ) Y Y 1 2 The budget constraint shows all combinations of C 1 and C 2 that just exhaust the consumer s resources. C 1 Y 2 Saving Consumption = income in both periods Borrowing Y 1 Y Y (1 r ) 1 2

Irving Fisher and Intertemporal Choice C 2 C C Y Y 1 r 1 r 2 2 1 1 The slope of the budget line equals -(1+r ) Y 2 1 (1+r ) Y 1 C 1

Irving Fisher and Intertemporal Choice Consumer Preferences An indifference curve shows all combinations of C 1 and C 2 that make the consumer C 2 Higher indifference curves represent higher levels of happiness. IC 2 IC 1 equally happy. C 1

Irving Fisher and Intertemporal Choice - Consumer preferences Marginal rate of substitution (MRS ): the amount of C 2 the consumer would be willing to substitute for one unit of C 1. C 2 1 MRS The slope of an indifference curve at any point equals the MRS at that point. IC 1 C 1

Irving Fisher and Intertemporal Choice - Optimization The optimal (C 1,C 2 ) is where the budget line just touches the highest indifference curve. C 2 O At the optimal point, MRS = 1+r C 1

Irving Fisher and Intertemporal Choice: How C responds to changes in Y Results: Provided they are both normal goods, C 1 and C 2 both increase, C 2 An increase in Y 1 or Y 2 shifts the budget line outward. regardless of whether the income increase occurs in period 1 or period 2. C 1

Irving Fisher and Intertemporal Choice: How C responds to changes in r As depicted here, C 1 falls and C 2 rises. However, it could turn out differently Y 2 C 2 B A An increase in r pivots the budget line around the point (Y 1,Y 2 ). Y 1 C 1

Irving Fisher and Intertemporal Choice: How C responds to changes in r Income effect: If the consumer is a saver, the rise in r makes him better off, which tends to increase consumption in both periods. Substitution effect: The rise in r increases the opportunity cost of current consumption, which tends to reduce C 1 and increase C 2.

Irving Fisher and Intertemporal Choice: How C responds to changes in r Both effects C 2. Whether C 1 rises or falls depends on the relative size of the income & substitution effects.

Irving Fisher and Intertemporal Choice: Implications One implication of the forgoing analysis is that current period consumption will vary less than does income. Thus, in the two-period case, an increase in present income would be spread across an increase in both present and future consumption.

Irving Fisher and Intertemporal Choice: Implications Hence, if we extend the analysis to many periods, say 25 years, then spreading an increase in present income over 25 years of consumption increments would give a present consumption increase that is very small relative to the increase in present income.

Irving Fisher and Intertemporal Choice: Implications The relationship between the present value of the income stream and current consumption gives us the first general formulation of the consumption function C f ( PV ); f 1 1 ' 0

Irving Fisher and Intertemporal Choice: Implications This simply states that the individual consumer s consumption in time 1 (present period) is an increasing function of the present value of his/her income in time 1 (present period).

Irving Fisher and Intertemporal Choice: Implications Where PV 1 is formulated as: PV 1 T y (1 1 t r ) t

Keynes vs. Fisher Keynes: Current consumption depends only on current income. Fisher: Current consumption depends only on the present value of lifetime income. The timing of income is irrelevant because the consumer can borrow or lend between periods.