Answer to Question #191940 in Macroeconomics for justin matengu

Question

Question 2 [18 marks]

(a)   Explain how Life-Cycle Hypothesis and the Permanent Income Hypothesis, explain the difference between long run APC and short run APC.                                                                                               (6)

With a help of a diagram discuss how the permanent income theory of consumption explains the difference between the cross-section and time-series estimates of the Keynesian aggregate consumption function.

Answer 1

(a)

Life Cycle Hypothesis

The key explanation for a person's income fluctuation is retirement. Most people save a portion of their income per year because they do not want their current living standard (as calculated by consumption) to decline after retirement. This saving motivation has significant implications for a person's consumption habits.

Assume that a representative customer plans to live for another T years, has a net worth of W, and earns an annual income of Y until he or she retires in R years. Initial capital W and lifetime earnings RY comprise the consumer's lifetime endowments. If we conclude that the buyer divides his total wealth W + RY evenly over the T years and wishes to consume evenly over his life, then consumption will be,

C = (W + RY)/T

The consumption function of this individual can now be expressed as

C=(1/T)W + (R/T)Y

The aggregate consumption function is a copy of our representative consumer's consumption function if everyone plans their consumption in the same way. To be more precise, aggregate consumption is influenced by both income and capital. The aggregate consumption function, in other words, is

C = αW + βY

where the MPC out of wealth is the α parameter, and the MPC out of income is the β parameter.

The APC, according to this theory, is:

C/Y = α(W/Y) + β

Cross-section data (which show inter-individual variations in income and consumption over short periods) reveal that high income correlates to a low APC because wealth does not vary proportionately with income from person to person or year to year. However, wealth and income rise in lockstep over time, resulting in a constant W/Y and APC (as time-series show). As wealth is stable, as it is in the short run, the life cycle consumption function resembles the Keynesian consumption function, the consumption function moves upward as seen in the figure below. As income rises, the APC does not fall.

 

Permanent Income Hypothesis

Friedman divides an individual's total calculated income Ym into two parts: permanent income Y_p and transitory income$Yt. ( Ym – Yp + Yt )$ , to be precise.

Permanent income is the portion of a person's earnings that they hope to receive during their working life. The part of people's income that they don't plan to last is called transitory income. To put it another way, while permanent income is the average, transitory income is the random deviation from the average. The longevity of various sources of income varies. Although adequate human capital investment (training and education expenditure) results in a permanent increase in income, good weather only results in a temporary increase.

According to the PIH, current consumption is determined not only by current disposable income, but also by whether that income is supposed to be permanent or temporary. According to the PIH, income and consumption are divided into two categories: permanent and transitory. 

This feature of the consumption function is clearly in line with the observed long run constancy of the consumption income ratio, as permanent income should be compared to long run average income.

Let Y reflect the calculated income of a consumer unit over a given time span, such as a year. This is the number of two elements, according to Friedman: a permanent component (Y_p) and a transitory component (Y_t) or,

$Y = Y_p + Y_t$

The effect of such factors that the unit considers to be deciding its capital value or income, such as the non-human wealth it owns, the personal attributes of the unit's earners, such as their training, skill, and personality, and the attributes of the earners' economic activity, such as the occupation pursued, the position of the economic activity, and so on, is reflected in the permanent part. 

A random variable is transitory revenue. The distinction between the two is determined by the duration of the salary. To put it another way, the difference between the two is determined by persistence. Consider the case of a daily wage earner who becomes ill and is unable to work for a day or two. As a result, his short-term earnings are nil.

Let C reflect the expenses of a customer unit over a given period of time. It's also the product of a permanent (C_p) and a transitory (C_t) portion, resulting in 

$C = Cp + Ct$

As a result, the total consumption of units with a measured income Y₀ equals the average permanent consumption. This is k times their total permanent salary, according to Friedman's hypotheses. Their mean consumption would be Y₀ or Y₀E if Y₀ was not only their measured income but also their permanent income. Their average intake, Y₀F, is less than Y₀E since their mean permanent income is less than their measured income.

The average transitory variable of income and consumption is zero for consumer units with an income equal to the mean of the group as a whole, or Y, so the ordinate of the regression line is equal to the ordinate of the line 0E that gives the relationship between Y_p and C_p.

The average transitory portion of income is negative for units with incomes below the mean, so average calculated consumption exceeds the ordinate of 0E (BC'). As a result, the regression line (C = a + bY) intersects 0E at D, is above it on the left, and below it on the right. Permanent consumption is often less than permanent income if k is less than unity. However, calculated consumption does not always imply lower income. C = Y along the OH axis, which is a 45° line.

The average measured savings are represented by the vertical distance between this line and IF. The 'break-even' point, where average measured savings are zero, is designated as J. Average measured savings are negative to the left of J and positive to the right; as estimated income rises, the ratio of average measured savings to estimated income rises as well.

As a result, Friedman's hypothesis generates a relationship between defined consumption and calculated income that propagates the broadest aspects of the associated regressions calculated from results obtained. The argument is that, in the long run, spending expenses seem to be proportional to disposable income. 

In comparison to the short run non-proportional consumption-income relationship, the long run consumption function has a = 0 and APC does not adjust over time and MPC = APC at all levels of income. The consumption-to-income ratio varies a lot in the short term. To summarize, current spending is linked to some long-run measure of income (e.g., permanent income), while short-run income fluctuations tend to influence the level of saving the most.

APC is defined as C_p/Y_m = kY_p in Friedman's model. As a result, APC is determined by the ratio of permanent to existing wages. When current income temporarily exceeds permanent income, the average propensity to consume momentarily increases; when current income temporarily falls below permanent income, the average propensity to consume temporarily rises.

 

(b)

Permanent income theory of consumption states that people spend money at a level consistent with their expected long term average income.

The permanent income theory of consumption explains the difference between the cross-section and time-series estimates of the Keynesian aggregate consumption function in the following ways.

1:In cross-section it considers concepts of propensity to consume such as average propensity to consume and other marginal propensity to consume. It states that consumption changes as income changes. In addition, how the consumption changes in response to change in income depends on the average and marginal propensity to consume.

2:In time-series the theory argues that consumption depends on level of income and how it changes over period of time.