back start next


[start] [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12] [13] [14] [15] [16] [17] [18] [19] [20] [21] [22] [23] [24] [25] [26] [27] [28] [29] [30] [31] [32] [33] [34] [35] [36] [37] [38] [39] [40] [41] [42] [43] [44] [45] [46] [47] [48] [49] [50] [51] [52] [53] [54] [55] [56] [57] [58] [59] [60] [61] [62] [63] [64] [65] [66] [67] [68] [69] [70] [71] [72] [73] [74] [75] [76] [77] [78] [79] [80] [81] [82] [83] [84] [85] [86] [87] [88] [89] [90] [91] [92] [93] [94] [95] [96] [97] [98] [99] [100] [101] [102] [103] [104] [105] [ 106 ] [107] [108] [109] [110] [111] [112] [113] [114] [115] [116] [117] [118] [119] [120] [121] [122] [123] [124] [125] [126] [127] [128] [129] [130] [131] [132] [133] [134] [135] [136] [137] [138] [139] [140] [141] [142] [143] [144] [145] [146] [147] [148] [149] [150] [151] [152] [153] [154] [155] [156] [157] [158] [159] [160] [161] [162] [163] [164] [165] [166] [167] [168] [169] [170] [171] [172] [173] [174] [175] [176] [177] [178] [179] [180] [181] [182] [183]


106

Chapter 7

CONSUMPTION

This chapter and the next investigate households consumption choices and firms investment decisions in more detail. Consumption and investment are important to both growth and fluctuations. With regard to growth, the division of societys resources between current consumption and various types of investment-in physical capital, human capital, and research and development-is central to standards of living in the long run. That division is determined by the interaction of households allocation of their incomes between consumption and saving given the rates of return and other constraints they face, and firms investment demand given the interest rates and other constraints they face. With regard to fluctuations, consumption and investment make up the vast majority of the demand for goods. Thus if we wish to understand how such forces as government purchases, technology, and monetary policy affect aggregate output, we must understand how consumption and investment are determined.

There are two other reasons for studying consumption and investment. First, they introduce some important issues involving financial markets. Financial markets affect the macroeconomy mainly through their impact on consumption and investment. In addition, consumption and investment have important feedback effects on financial markets. We will investigate the interaction between financial markets and consumption and investment both in cases where financial markets function perfectly and in cases where they do not.

Second, much of the most insightful empirical work in macroeconomics over the past twenty years has been concerned with consumption and investment. These two chapters therefore have an unusually intensive empirical focus.



Behavior

Since the marginal utility of consumption is always positive, the individual satisfies the budget constraint with equality. The Lagrangian for his or her maximization problem is therefore

/ t \

\ t=i f=i /

(7.3)

The first-order condition for Q is

u(Cf) = A. (7.4)

Note that we have also assumed that the individuals discount rate is zero (see [7.1]). Assuming that the interest rate and the discount rate are equal but not necessarily zero would have almost no effect on the analysis in this section and the next. And assuming that they need not be equal would have only modest effects.

7.1 Consumption under Certainty: The Life-Cycle/Permanent-lncome Hypothesis

Assumptions

Although we have aheady examined aspects of individuals consumption decisions in our investigations of the Ramsey and Diamond models in Chapter 2 and of real-business-cycle theory in Chapter 4, here we start with a simple case. Consider an individual who lives for T periods whose lifetime utility is

U=X "(Cf), Wi-) > 0, < 0, (7.1)

where u(«) is the instantaneous utility function and Q is consumption in period . The individual has initial wealth of Ao and labor incomes of Yl, Y2,...,Yt in the T periods of his or her life; the individual takes these as given. The individual can save or borrow at an exogenous interest rate, subject only to the constraint that any outstanding debt must be repaid at the end of his or her life. For simplicity, this interest rate is set to zero. Thus the individuals budget constraint is

X Q < Ao + X Yt. (7.2)

f=i f=i



1 /

for aU t. (7.5)

The term in parentheses is the individuals total lifetime resources. Thus (7.5) states that the individual divides his or her lifetime resources equally among each period of life.

Implications

This analysis imphes that the individuals consumption in a given period is determined not by income that period, but by income over his or her entire lifetime. In the terminology of Friedman (1957), the right-hand side of (7.5) is permanent income, and the difference between current and permanent income is transitory income. Equation (7.5) implies that consumption is determined by permanent income.

To see the importance of the distinction between permanent and transitory income, consider the effect of a windfall gain of amount Z in the first period of life. Although this windfaU raises current income by Z, it raises permanent income by only Z/T. Thus if the individuals horizon is fairly long, the windfaUs impact on current consumption is smaU. One implication is that a temporary tax cut may have little impact on consumption; as described in Chapter 6, this appears to be the case in practice.

Our analysis also implies that although the time pattern of income is not important to consumption, it is critical to saving. The individuals saving in period t is the difference between income and consumption:

St = Yt- Q

I , \ (7.6)

where the second line uses (7.5) to substitute for Cf. Thus saving is high when income is high relative to its average-that is, when transitory income is high. Similarly, when current income is less than permanent income, saving is negative. Thus the individual uses saving and borrowing to smooth the path of consumption. This is the key idea of the life-cycle/permanent-income hypothesis of Modigliani and Brumberg (1954) and Friedman (1957).

Since (7.4) holds in every period, the marginal utility of consumption is constant. And since the level of consumption uniquely determines its marginal utility, this means that consumption must be constant. Thus Ci = Cz = = Ct- Substituting this fact into the budget constraint yields



[start] [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12] [13] [14] [15] [16] [17] [18] [19] [20] [21] [22] [23] [24] [25] [26] [27] [28] [29] [30] [31] [32] [33] [34] [35] [36] [37] [38] [39] [40] [41] [42] [43] [44] [45] [46] [47] [48] [49] [50] [51] [52] [53] [54] [55] [56] [57] [58] [59] [60] [61] [62] [63] [64] [65] [66] [67] [68] [69] [70] [71] [72] [73] [74] [75] [76] [77] [78] [79] [80] [81] [82] [83] [84] [85] [86] [87] [88] [89] [90] [91] [92] [93] [94] [95] [96] [97] [98] [99] [100] [101] [102] [103] [104] [105] [ 106 ] [107] [108] [109] [110] [111] [112] [113] [114] [115] [116] [117] [118] [119] [120] [121] [122] [123] [124] [125] [126] [127] [128] [129] [130] [131] [132] [133] [134] [135] [136] [137] [138] [139] [140] [141] [142] [143] [144] [145] [146] [147] [148] [149] [150] [151] [152] [153] [154] [155] [156] [157] [158] [159] [160] [161] [162] [163] [164] [165] [166] [167] [168] [169] [170] [171] [172] [173] [174] [175] [176] [177] [178] [179] [180] [181] [182] [183]