Effective demand in a stylised Keynesian model of growth

Abstract

This paper models an economy which suffers from a coordination failure and lack of effective demand in the long run. Specifically, it shows that an input–output economy, with or without credit rationing, converges to a long-period growth path, but that this path is generally Pareto sub-optimal. Yet, although Keynesian problems extend to the long run, typical Keynesian solutions do not: the government seems generally incapable of sustaining growth by demand management measures. The question as to what the government can do to sustain growth is an open one.

Acknowledgments

Thanks go to Nicholas Dimsdale, Geoffrey Harcourt, Sean Hargreaves Heap, Peter Docherty, Tony Aspromourgos and two referees who read draft copies and suggested a number of improvements. The errors and infelicities that remain, however, are the author's responsibility. I also wish to thank the Cambridge Commonwealth Trust and the Cambridge Political Economy Society for their financial assistance.

Notes

¹For surveys of this material, see Cooper & John (1988), Benassy (1993), Dixon & Rankin (1994), Solow (1998) and Cooper (1999).

²For a full discussion of the existence and uniqueness conditions for the kind of minimisation problem given in (1) see Kurz & Salvadori (1995, ch.2). We assume existence and uniqueness throughout.

³These two functions of the financial intermediary correspond to the two decisions made by ‘the centre’ in the analysis of Duménil & Lévy (1987, Section 3). As with their analysis, a single financial agent is posited here to simplify the discussion and to focus attention on potential coordination failures elsewhere in the economy.

⁴The simplification of the financial sector adopted here allows us to concentrate on the dysfunction of the economy that arises from the diversified nature of the production process. A diverse financial sector is likely to be a source of further coordination failures, and so will tend, if anything, to reinforce the broadly negative conclusions drawn here about the operation of laissez faire economies.

⁵This assumption is equivalent to assumption (v. 6) of Pasinetti (1974, p. 106); and it seems to be a realistic one to make.

⁶The relationship between investment, savings, and retained earnings can be represented schematically as: I _t  → S _t  → δ _t . The manner in which I _t is determined is analysed in Section 4.

⁷It might be thought that the given pricing rule allows firms to manipulate the price of the sector's output by restricting its own output levels, but this is ruled out under assumption that firms are price takers. The assumption that firms treat prices parametrically can be warranted in the following way. Suppose that each of the J productive units (firms) is itself composed of representative sub-units whose outputs add up to give the total supply of each unit j; and each of these sub-units conjectures that it is so small relative to the market demand of the jth sector that it cannot affect the market price. Since these sub-units are representative, we do not need to model their behaviour individually but can model their aggregate behaviour in the form of firm j as we have done in the text.

⁸In this stylised framework, we are abstracting from any adjustments of capacity utilisation or inventories that might moderate the adjustments of the prices needed to bring about short-run equilibrium. Allowing for varying utilisation rates in the short run does not alter the proposition that industries that have initially over- (under-)produced see profits fall (rise); nor does it alter the basic qualitative analyses described below. In fact, if y _jt is interpreted as the ‘normal’ capacity level of output, and p _jt is interpreted as a ‘stretching parameter’ – representing increases or decreases in actual output relative to normal-capacity output delivered at constant prices – then the propositions given below all hold, but bear the different interpretation just given. Which is to say that if prices are fixed over time, so that p _jt  ≠ 1 ⇒ actual output ≠ normal-capacity output, then adjustments in investment and production result in the system converging to the point where p _jt  = 1 ∀j ∀t, i.e. to a state where all firms are producing at normal capacity, at which point r _jt  = r ∀j ∀t.

⁹ is the rate of profits that would obtain for the chosen technique at t were w = 0. The relationship in equation (10) is obtained by comparing the price equation (1) with the price equation given by: a · (1 + r _j )+w ·  = μ/y _j .

¹⁰This fact, which is readily accounted for here, has proved to be somewhat problematical for neoclassical theory; see the discussion in Taylor (1999).

¹¹We are assuming throughout this passage that the rate of growth of the economy is below the full employment growth rate, g _n .

¹²That γ∘ | _r=0 = σ · (1 − a)/a is the minimum of the maximum rates of growth of savings follows straightforwardly from equations (1) and (5).

¹³None of this is intended to diminish the practical and theoretical importance of supply side policy measures in facilitating growth; nor is it even to deny that these are the most important issues. All that is being asserted is that effective demand issues, which are largely assumed away in orthodox growth models, might also be important, and so government policy might consider these matters too.