Knowledge that Transforms

THE graphic method of determining the level of income which is consistent with a consumption function and given investment is familiar to most students.1 The method is that of plotting the aggregate demand function (consumption demand function with investment superimposed vertically) against national income; the intersection of this line with a forty-five degree line through the origin indicates the level of income at which income equals assumed investment plus derived consumption. But this forty-five degree line method suffers from the disadvantage that consumption must explicitly be related to the national income or gross national product. It is common nowadays to assume that consumption is related to disposable income, and to assume as well that taxes, government transfer payments, and corporate savings are themselves related to gross national product, so that the consumption-gross national product relationship is a derived one. In the graphic solution as ordinarily presented, a change in the tax structure cannot be assumed without having the shape of the derived consumption-GNP relationship affected. So, where graphic methods are desired, an elaboration that allows separate manipulation of the tax function and the consumption function is of some advantage. This paper will present a graphic method which goes one step further than the forty-five degree line method, that is, one which portrays the solution when consumption is explicitly related to disposable income, the latter being explicitly related to the gross national product.2 The method is simple. We have two relationships, here assumed linear for convenience. One is the consumption-disposable income relationship, in the form C a + bDI, in which the parameter b measures the marginal propensity to consume. The other is the disposable income-gross national product relationship, in the form DI = c + dGNP, where the parameter d measures the marginal ratio of DI to GNP.3 Both these relationships are plotted on Chart i. Measuring GNP along the horizontal

IT is quite common to discuss interest theory and influence of a controlled rate of interest on economy in terms of rate of interest, assuming some definite, and often fixed, relationship among various types of rates. Lord Keynes, for example, referred to the complex of rates of interest on loans of various maturities and risks. 1 Dr. J. R. Hicks, in a later work,2 also speaks of rate; thus, he states that rates will differ some sort of 'normal' risk-premium, whose size will depend upon estimate put upon gain in security (p. I50I). Yet, even most superficial inspection of interest rate data will show that various complexes do not move together. Particularly is this true of various risks within same time (or maturity) category. Moreover, there is no logical reason for concordant movement to rule all time. Borrowing from Hicks, we may say that variations in rate of interest among loans of same duration are caused by differences in risk of default by borrower, I or, rate for each loan of a given duration is pure rate of interest plus a risk-premium. To a great extent, this risk element is a subjective valuation of lender; that is, it is a measure of how certain he feels that loan will be repaid.4 Hence, if lender feels cheerful, he is likely to believe risk element less than if in a more disagreeable frame of mind. fairly well established fact is that community in general, and lenders in particular, feel more optimistic in prosperity than in a depression.5 Applying this statement to risk premium, we would expect it to decrease in prosperity and increase in a depression. In other words, spread between safest investments and riskier ones would tend to narrow as boom proceeds, and widen as times become worse. Thus, complex of interest rates is highly unstable, and we must be careful in regard to rates we are discussing. Rates on safe investments will fall in depression, particularly after passing of panic phase, but rates on risky investments may well rise. Hence, to state that rate of interest falls in this case is erroneous; some rates fall, while others rise, or fall less. Implied in preceding paragraph is difficulty of government manipulation of rate of interest, particularly current cheapmoney policy. All that may result from such interference is a low rate of return of triple A securities, but an increase in risk-premium on riskier securities, notably those representing new investment, whose revival may be chief aim of such a policy. If this interference creates fears among investing class, either as to future interest rates being higher after cheap-money policy is ended, thus depressing capital value of older securities, or simply a reluctance to invest because of political opposition to such governmental policy, then risk premium will almost certainly rise pari passu with fall in yields of safe investments.

i. in his recent book Keynesian Revolution, a significant contribution to current literature, Lawrence Klein says (p. 91 ) that there are two Keyneses in the matter of the savingsinvestment equation. This statement has frequently been made before and while much has been written about it, perhaps something useful can still be added. In Klein's exposition, savings and investment as observables are always equal, being the point of intersection of the schedules of savings and investment. There is, of course, as Klein points out, no inconsistency between (i) the definition which makes actual or observable savings and investment always equal, and (2) the concept of savings and investment as intersecting schedules. Nevertheless the question remains whether these schedules are to be regarded as (a) very short run schedules which might at times shift about violently and capriciously in response to temporary conditions, or (b) longerrun schedules determined by fairly stable factors involving the behavior pattern of a community with respect to the ratio of savings to income at different income levels. 2. A related, but distinct, terminological matter should be mentioned. While the Keynesian theory of income determination can indeed be formulated in terms of savings and investment schedules, I am increasingly convinced that the presentation as given in the General Theory is more useful. In the General Theory, Keynes, in fact, did not explicitly work with savings and investment schedules,' even though it is perfectly true that his analysis can be put in these terms. General Theory, however, makes (i) actual investment and (2) the consumption function, the determinants of income. The propensity to consume and the rate of new investment determine between them the volume of employment. . (General Theory