Journal Article A Model of Economic Growth with Induced Bias in Technical Progress Get access Winston W. Chang Winston W. Chang State University of New York at Buffalo Search for other works by this author on: Oxford Academic Google Scholar The Review of Economic Studies, Volume 39, Issue 2, April 1972, Pages 205–212, https://doi.org/10.2307/2296872 Published: 01 April 1972

I. Introduction and summary of main conclusions, 491. — II. The structure of an aggregate economy, 493. — III. The general saving function and the existence of the steady-state growth path, 494. — IV. Uniqueness and stability of the steady-state growth path, 498.

This paper examines various theorems of trade and general equilibrium in a generalized framework involving arbitrary numbers of goods and factors. It develops structural relations among the changes in outputs, commodity prices, factor rewards, and factor endowments. By finding a way of inverting a bordered matrix with a singular Hessian, the paper derives explicit expressions for the following matrices: the Stolper-Samuelson matrix; the Rybczynski matrix; the matrix which measures the effect of a change in factor endowments upon factor rewards at constant commodity prices; and the matrix which measures the effect of a change in commodity prices upon outputs at constant factor endowments. Various properties of these matrices are used to obtain, among other results, the reciprocity relations and general results on factor-price equalization. The paper also ey.amines the problem of indeterminacy in production when the number of commodities exceeds the rank of the input-coefficient matrix and presents the correct specifications of the supply functions of outputs. Finally a new theorem on the degree of flatness of the production transformation surface is derived.

T HE theory of induced invention along Kennedy-Weizsacker lines has recently been incorporated into growth models with factor-augmenting technical progress by Samuelson [9], Drandakis and Phelps [4], Amano [1] and Fellner [5]. In these models they have shown that under the assumption of a proportional saving function, the condition that the elasticity of substitution (C-) be less than unity is sufficient for global stability of the long-run equilibrium. In this paper we attempt to generalize their results by employing a more general saving function and to examine the role of saving in a growth model of this type. We assume that the marginal propensity to save out of profits (s1) and out of wages (s2) are two different constant proportions. It turns out that, in the presence of a C-ambridge saving function, the condition C< 1 is not always sufficient to assure global stability of Kennedy's economy. The stability of the system, in general, depends upon not only the elasticity of substitution, but also the saving propensities. Furthermore, the position of the invention possibility frontier as well as its shape is an important element in stability analysis. This is due to an important feature of the generalization in which changes in income distribution between profits and wages resulting from factor substitution along the isoquants, and technological substitution along the invention possibility frontier, are taken into account in determining the changes of the rate of growth of capital. In section I we set up the model and derive the required dynamic equations. In section II we analyze the existence and global stability of the steady-state growth path. In particular, a local stability condition will be derived. Finally, in section III, after summarizing the principal findings, we interpret our stability condition and compare it with the condition which we found elsewhere in a model with exogenous Harrod-neutral technical change [2].

[In this paper, we focus on capital aggregation in a general equilibrium model of production. Various potential aggregates involving intrasectoral and intersectoral, as well as full aggregation are discussed in connection with the various aggregation procedures. It will be shown that the satisfaction of the Gorman conditions allows for full aggregation within a general equilibrium model of production. We shall derive new conditions for aggregation using a composite commodity approach that appears to be somewhat weaker than the conditions associated with restrictions-on-functional-form theorems. Our main conditions relate to the equality of sectoral labor shares. The data for testing those conditions appear to be readily available. It is shown that the equal labor share condition can be applied to models with joint and nonjoint products. In addition, the conditions for aggregation are derived for a model with many primary inputs and also for a model with unequal rates of depreciation. Two sections are devoted to the main correspondences between certain aggregation procedures in the literature from the point of view of a general equilibrium model. The implications of our analysis for the form of the unit cost function and of the aggregate production function are discussed. In particular, if our aggregation condition holds, then the aggregate production function can be Cobb-Douglas, if one of the sectoral forms is also Cobb-Douglas, irrespective of the forms of the other sectoral production functions.]

Edwin Burmeister, Winston W. Chang, Rodney Dobell, The Role of Saving in a Growth Model with Induced Inventions: A Correction, The Review of Economics and Statistics, Vol. 52, No. 4 (Nov., 1970), pp. 446-447

In 1958, James Tobin generalized the Keynesian theory of liquidity preference by means of his famous portfolio model in which the demand for money (narrowly defined) is treated as behavior towards [interest] risk. Whatever merit this theory may have had then has long since been questionable. The reason is the existence of a large set of substitutes for money, typically short-term money market instruments, which can be regarded as riskless, or virtually so, and which pay substantial interest. The availability of these instruments would appear to make Tobin's theory that money is held to cope with interest risk resemble a scenario without a recognizable cast of actors. In the literature on monetary theory, other authors have also expressed misgivings about the Tobin theory by noting that savings and (nontransferable) time deposits have the same risk properties as money but pay interest (see, for example, Robert Barro and Stanley Fischer, 1976). Although correct, the allusion to these deposits is simplistic. It is true that while both types mimic money's freedom from interest risk in the conventional sense of capital loss, time deposits are still exposed to a kind of interest risk, because they can be liquidated before maturity only with interest penalty. More important, business firms are either denied access to savings deposits or, as in the United States, can hold a maximum of $150,000 (per account) at commercial banks, thereby effectively eliminating large firms as holders. Furthermore, although business firms can own most time deposits, they typically do not (except for negotiable CDs, a money market instrument); they are loath to tie up funds in long-term maturities, and they can usually obtain the same or higher yields on other types of short-term debt instruments that are also negotiable. In the United States, households have long accounted for about one-third of demand deposits, business firms owning most of the rest. Therefore any effort to rest a case against the Tobin theory of money demand on the existence of savings and time deposits gets at only a small part of the problem. This stricture extends to so-called NOW and ATS accounts. These interest-bearing demand deposits (disguised under other names) are also denied to business firms. For them, the short-term instruments of the money market are the principal alternative to money in asset portfolios.