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B. Monetary policy and the classical aggregate supply curve
2.1 Introduction
The consumption function is important because of a number of reasons. Consumption is part of the aggregate demand. If income is not spent on consumption, then the saving rate rises. Consumption is an integral part of day-to-day life.
Most of the traditional and modern theories have explained the consumption function. The life cycle theory is associated with Franco Modigliani of MIT, who was a Nobel Prize winner in economic science.
The permanent income theory is associated primarily with Milton Friedman of the University of Chicago.
He won the Nobel prize for economics in 1976. Both theories are similar in nature and pay attention to a foundation in microeconomics. The classical theory of consumption known as the Ando-Modigliani approach proposes that people make consumption decisions according to the stage of life they are in as well as the resources available to them during their lifetime. It was developed in 1950 and is also known as the life cycle hypothesis. This approach was criticized by Friedman in 1956. He developed a new approach known as the Friedman’s approach of permanent income advocating that consumer choices for consumption are determined primarily by a change in their permanent income as compared to their temporary income. This approach was later replaced by the Duesenberry approach, which was further replaced by the relative income approach in 1960.
The Friedman and Modigliani Approach
Friedman and Modigliani begin with the explicit common assumption that observed consumer behavior is a result of an attempt by rational expectation. Consumers maximize utility by allocating a lifetime stream of earnings to an optimum lifetime pattern of consumption.
Consumption and present value of income:
We assume that there is a single consumer and the utility function of this consumer is defined as
U = u (c0……c1……cT) (2.1)
The lifetime utility is a function of his real consumption c in all time periods up to ‘T’, the instant before he dies. The consumer will try to maximize his utility, that is, obtain the highest level of utility subject to the constraints that the present value (PV) of his total consumption in life exceeds the present value (PV) of his total income in life.
0 (1 ) 0 (1 )
T T
t t
Yt Ct
r = r
+ +
∑ ∑
(2.2)Advanced Macroeconomics
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The Consumption Function This constraint states that the consumer can allocate his income stream to a consumption stream by borrowing and lending, but the present value of consumption is limited by the present value of income.
Let us consider a two-period case in which the individual has an income stream Y0,Y1 and wants to maximize U(C0,C1) subject to borrowing and lending constraints as
1 1
0 (1 ) 0 (1 )
C Y
C Y
r r
+ = +
+ + (2.3)
In Figure 2.1, the income streams Y0 and Y1, intersect at point A. This point shows the amount of income the individual will earn in period 0, Y0 and the amount of income he will earn in period 1, Y1.
<U<
< $VORSH U
< <
U
LQSHULRG <
Figure 2.1 The income of an individual in two periods
If his income in period 0 is greater than the value of goods and services he wants to consume in that period, then he can lend, that is, save his unspent income.
0 0 0
S Y C= − = money lent in period 0
By lending this amount, he will receive in period 1 an amount equal to S0 (1+r)
1 (1 ) 0 1 1
S = − +r s Y C= − (2.4)
The negative sign enters equation (2.4) because the dissaving in period 1 is opposite to the saving in period 0 and C1 > Y1
By dividing the expression for S1 by t S0, the equation yields the tradeoff between present and future consumption.
0
1 1 1
0 0 0 0
S (1 )r
S Y C
S S Y C−−
= + = (2.5)
By cancelling the S0 in equation (2.5) and multiplying through by (Y0-C0), we obtain
1 1
(1 )(
0 0)
Y C − = − + r Y C −
(2.6)Advanced Macroeconomics
54
The Consumption Function The above equation explains that by reducing consumption in period 0 below income by the amount S0=Y0-C0, the consumer can enjoy in period 1, consumption in excess of income C1-Y1 by the amount of – (1+r)sb.
From the individual utility function U = u(C0,C1), we can obtain a set of difference curves that show the point at which the individual is indifferent between additional consumption period 1 or period 0 at each level of utility. These curves U0,U1 to U2 raises the individual’s level of utility.
0D[8WLOLW\ $
< % 8
& 8 8
<&LQSHULRG
Figure 2.2 The individual utility function
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Advanced Macroeconomics
55
The Consumption Function At point B, the individual’s consumption pattern is C0,C1. The position of the budget line is determined by two variables, namely: income period and interest rates. The relationship between the present value of the income stream and current consumption from the above figure gives us the first general formulation of the consumption function
Ct = f (PV1) and f > 0 (2.7)
where PV1 is the present value of current and future income at time t is (1 )t t
Y
∑ r +
Thus, it can be simply stated that an individual’s consumption in time t is an increasing function of the present value of his income in time t.
Both Ando-Modigliani and Friedman began their analysis of the consumption function with the general form of the function given in equation (2.8).