Aggregate Demand Spillovers Aren’t Coherent
Dec18
Money & Macro

Aggregate Demand Spillovers Aren’t Coherent

A number of models of increasing returns and path dependence in international trade and development involve the idea of aggregate demand spillovers (e.g. Shleifer & Vishny 1988) or externalities (e.g. Blanchard & Kiyotaki 1987). Murphy, Shleifer, & Vishny (1989), for example, take the Shleifer-Vishny model and conclude that “big push industrialization” – i.e. the coordination of investment in manufacturing technology and infrastructure in an industry by the government – can break an economy out of an agricultural equilibrium and into an industrial equilibrium. Sachs and Yang (2005) build off of it to model increases in the division of labor resulting from demand externalities. A number of other models also use it as a starting point.

The influence of this class of model does not appear to be due to any empirical success, which is not attempted in any of the aforementioned papers. Indeed it is unclear how the model could be operationalized into a regression specification. It is only through careful attention to what the models silently pass over that their real-world relevance can be ascertained.

This paper evaluates two classes of models which demonstrate an aggregate demand externality: the Shleifer-Vishny model, and the Blanchard-Kiyotaki model. For each model, after a brief outline of the logic, this paper identifies the mismatch between economic theory, the real world, and the model at hand. For the Shleifer-Vishny model, the first section argues that the model does not “add up”, and that accounting identities provide a strong prima facie case that adjustment happens elsewhere than in the level of aggregate demand. The next section argues that the model mischaracterizes the economic import of productivity shocks. There is no reason to preclude the usual avenues of economic adjustment to a productivity shock, and a basic AS/AD framework shows that including them eliminates entirely the exotic features of the model. Finally, the representative consumer assumption is relaxed in order to salvage some of the model’s intuition regarding wage effects arising from the complementarity between heterogeneous factors of production. Next the paper argues that the Blanchard-Kiyotaki model, though far more sophisticated than the former, ultimately misinterprets the meaning of a crucial accounting identity, and derives the aggregate demand externality from the “missing half” of aggregate demand which it segregates into its own set of variables.

The Shleifer-Vishny Model

The Shleifer-Vishny AD spillover model begins with a representative consumer, to whom is disbursed wages plus all profits from production. There exists a continuum of goods, each produced in a sector of the economy. Each sector is characterized by a perfectly competitive “fringe” of firms producing with a constant-returns-to-scale technology. In addition, each sector also has a single “monopolist” firm which has the opportunity to invest in an increasing-returns technology, and which must decide whether or not to enter the market and adopt a productivity-enhancing technology.

To install this technology requires an outlay of some amount of labor F. This outlay bids up wages, which increases aggregate demand. Since each firm’s revenue is basically a fixed portion of the total, any benefit from increased aggregate spending accrues to all firms, including the competitive fringe, rather than just the investing firm. This is the pecuniary externality. For this reason, no monopolist will find it worthwhile to adopt this superior technology, unless it can be guaranteed aggregate demand will increase sufficiently to make the investment worth it – a shift which requires a coordinated investment by all the monopolist firms.

The model is far more remarkable for what it does not say than for what it does. First, for a model to which aggregate demand is central, there are two variables which surprisingly never make an appearance: the price level, and the money supply – indeed, prices are fixed, and there is no separate money commodity. One would expect a model of aggregate demand to be a general equilibrium model, but in fact the model is an unusual hybrid of partial and general equilibrium features that closes off all usual avenues for economic adjustment in order to conclude that aggregate demand spillovers are a serious theoretical issue. In particular, though a monopolist enters each sector with more productive technology, it competes neither on price nor quantity, but simply enters the market and collects (and distributes) quasi-rents arising from its sole possession in the sector of the increasing returns technology.

The ramifications of this modeling decision will be discussed in the next several sections. For the next two, in order to consider the model’s implications as a proper general equilibrium model, we will need a conception of aggregate demand and aggregate supply – the latter of which is omitted entirely from the original model. For the purpose, we summarize a basic quantity-theory-derived aggregate supply/aggregate demand model, highlighting along the way the subtle and unusual ways in which the Shleifer-Vishny model diverges from it.

Wages Are Not A Determinant of Aggregate Demand

Aggregate demand is typically defined in Keynesian-inspired models by the accounting identity Y=C+I+G+X, the variables representing nominal income,1 consumption, imports, government spending, and net exports, respectively, all in nominal terms. In this sense, it seems obvious that an increase in C – as occasioned, perhaps, by a general increase in wages – would increase aggregate demand, ceteris paribus.

However, a number of additional theoretical constraints are brought to light by another accounting identity: the equation of exchange, MV=Py, the variables representing the money stock, the velocity of money, the price level, and real income, respectively (we follow the convention of indicating real magnitudes with a lowercase variable and nominal with an uppercase variable). By the definition of real income, y=Y/P, we can substitute to get an alternative (but formally equivalent) definition of aggregate demand:

MV = C+I+G+X

In other words, as a matter of logical necessity, the sum of the nominal values of our four “buckets” for aggregate demand can never exceed the money stock times the velocity of money. Consider the implications of this accounting identity for the usual assumption that an increase in government spending represents a stimulus to output. An increase in government spending out of accumulated surplus, without an adjustment of the money stock, must be interpreted on the left hand side as a rise in velocity; or in other words as a dishoarding of cash balances. If the government instead should spend out of a monetized deficit, the effect is exactly equivalent, except M rather than V has risen on the left to account for the rise on the right hand side. If it spends on the basis of new taxes, G increases at the expense of C (and if the government is more likely to spend that money than the consumers it taxed, V also rises). And finally, if it spends out of money borrowed on the open market, I falls as a result of funds bid away from private investment. The former two cases represent an aggregate demand stimulus (Y increases); the latter two, however, do not.

As this example shows, we must be scrupulous in taking stock of the effects of an exogenous change in order to avoid running afoul of the accounting identity. If it is true that accounting identities “add nothing to our knowledge”, strictly speaking, it is equally true that they are invaluable in ruling out otherwise plausible arguments that simply don’t add up, and directing our attention toward equilibrating forces that might otherwise be overlooked. No doubt the assumption in Shleifer-Vishny is that bidding up wages constitutes an exogenous increase in C, which raises aggregate demand. But as our accounting identity shows, and as James Buchanan argued as far back as 1958, there can be no such thing as a ceteris paribus rise in nominal consumption. It must either be accounted for by a rise in M or V, or offset by a decline in one or more of the other three right-hand buckets.

An increase in nominal wages must, therefore, come from somewhere. It is here that the model equivocates between a general and a partial equilibrium setting. It is legitimate in a partial equilibrium setting to hold the price level constant and allow total within-model spending to increase, presumably drawn from other sectors outside the model. But in a general equilibrium setting, the spending must “add up”. It cannot, after all, be drawn from markets on the moon – and if it could, the moon would be included in the model. If the sectors described in the model constitute the entire economy, unless we also assume an accommodative central bank, the monopolist firms can only increase spending on wages at the expense of spending by the competitive fringe, as a matter of mathematical necessity.

In order that we may properly consider the model’s mechanisms as ceteris paribus as possible, let us assume that neither the money supply (which we assume to be a function of monetary policy) nor the velocity of money (the determination of which we assume to be exogenous to the model) change. If this is the case, any increase in wages leading to higher consumer spending must come out of money otherwise destined for corporate spending or investment.2 Stated more strongly: the money supply and the velocity of money are jointly exhaustive of the determinants of the height of aggregate demand. If neither of these change, then no other factor can alter the height of aggregate demand.

If it seems that this claim will force us to tell a story involving crowding out or something similarly circuitous, we may also assume that consumption, investment, government spending, and net exports are all determined exogenously to the model as well – at least in real terms. As each of our buckets is expressed in nominal terms, we can just as easily express the right hand side in real terms, factoring out the P:

MV = P(c+i+g+x)

with all lowercase variables representing real magnitudes. If M, V, c, i, g, and x are all exogenously determined, then an exogenous increase in consumption can only be accounted for by a fall in P – which, of course, lowers the nominal values I, G, and X.

Thus, without embarking on any economic theory beyond simple accounting identities, a plausible set of constraints on which variables are exogenously determined 1) tells us that the Shleifer-Vishny model doesn’t add up without the additional assumption of accommodative monetary policy or irrational “hoarding” of cash balances on the part of employers, and 2) gives us a strong prima facie case that a consumption-increasing productivity shock such as the model contemplates must be accounted for in the price level rather than in aggregate demand. And in fact, basic economic theory does gives strong reasons to believe, contra the model’s assumption of fixed prices, that price level adjustment is the most plausible path to equilibrium following a productivity shock.

Productivity is an Aggregate Supply Phenomenon

One of the more striking omissions of the Shleifer-Vishny model is any mention of aggregate supply. In order to adequately treat aggregate supply in the context of the model, we must introduce some economic theory in addition to the accounting identities which sufficed for aggregate demand.

Aggregate supply will be defined as the sum of the money values of products offered for sale. Long-run aggregate supply we consider to be determined exogenously to the model in the long run, and so the long-run aggregate supply curve is vertical in y-P space. In the traditional exposition, aggregate supply does slope upward to the extent that prices are sticky in the face of stimulated aggregate demand, but y returns to its “natural” level in the long-run. While stickiness may be a useful assumption in certain macroeconomic contexts, it is by no means permissible to assume that prices never adjust. Indeed, the long run is defined as that time following the adjustment of prices to new data. Thus, even apart from the failure of adding up, by proscribing price changes, the Shleifer-Vishny model – without admitting as much – limits its relevance at the outset to the description of very short run effects at best.

As we have seen, a productivity increase cannot be expected to appreciably shift aggregate demand. If it did, we would find that productivity increases were inflationary, as the economy moved up the aggregate supply curve. In fact, productivity increases are better considered as a shift in aggregate supply.3 The long-run curve shifts outward reflecting a productivity shock, and prices in fact fall along the downward-sloping aggregate demand curve.

To make the same point on a microeconomic level, consider a firm entering an industry with a productivity advantage over incumbent rivals. If its good is undifferentiated from those of other firms, it competes on price. It bids away buyers by offering its wares for cheaper, and thus drives out newly inframarginal firms. Or alternatively, in Cournot terms, the firm is able to profitably produce such a quantity of its wares as to drive down the price of the good, which – again – drives out inframarginal firms. In both cases, the effect is a rise in quantity and a fall in price, which are both magnified to the extent that competition forces the new firm’s competitors to also employ the more productive technology. In the aggregate, this implies that – all else equal – increases in total factor productivity lower the price level (Selgin 1997), as indeed the traditional AS/AD model shows.4 5

In fact, this hypothetical firm is identical to the monopolist in each sector of the Shleifer-Vishny economy. No doubt in order to avoid specifying a demand function for each good,6 the model holds both the price and quantity of the good in each sector fixed. The monopolist suffers the firms in the competitive fringe to continue as before, content with collecting a stream of quasi-rents which it disburses to the representative consumer.7 But this assumption is tantamount to a denial of the entire corpus of the microeconomics of competition. In fact, price competition will be of crucial importance in the monopolist’s decision to adopt the increasing-returns technology. These adjustments affect the aggregate price level P sufficiently to account for the increase in consumption occasioned by the bidding up of (real) wages, and obviate entirely the accounting necessity of an aggregate demand spillover.

Factor Complementarity Drives Wage Effects

All the analysis so far has been on the assumption of an undifferentiated labor force: an increase in the demand for labor anywhere bids up wages everywhere. If any inframarginal firms were driven out of business by the introduction of the increasing returns technology, the resulting slack in labor demand was more than taken up – almost by construction – by the monopolist firm. Capital, in this case, is a pure complement to an undifferentiated labor factor.

In fact, we can take the analysis even further by relaxing the assumption of a representative consumer, and show that whatever “stress” may be laid on the price system in the event of a productivity shock is an upper bound, relieved by some degree of specialization. We will continue to assume that the entire labor force is equally productive working with the competitive fringe’s constant returns to scale technology. But in addition, we now assume that some “skilled” fraction of the labor force has a substantial productivity advantage over the rest in working with the monopolists’ increasing returns technology.

As Hayek (1937) notes, any addition to an economy’s capital stock will raise the demand for factors of production which complement it, and lower the demand for factors of production which substitute for it. This does not mean that the return to capital falls and the return to labor rises, as in a model with homogenous factors of production. Rather, in general, both categories will contain both capital and labor of different sorts. In our model, skilled labor (being complementary to the increasing returns technology) rises in value, and the constant returns technology (being a substitute) falls in value, along with the unskilled labor primarily complementary to it.

This change in the pattern of wages does in fact constitute an externality on other firms – albeit a far narrower (and Pareto-irrelevant) externality than the all-encompassing “aggregate demand spillover”. It is a specific example of the general maxim that any economic change will produce winners and losers. Stated in this way the point might seem trivial. And yet, it is entirely glossed over by treating the effect as pertaining to aggregate demand. And again, as we have assumed that neither the supply nor the velocity of money are changing, the nominal increases in spending from one group must be exactly offset by nominal decreases from the other. In real terms, however, the loss of the unskilled labor force is somewhat ameliorated by an increase in purchasing power due to falling prices, and the economy as a whole is wealthier. In the very long run, the accumulation of new human capital will adjust to the new situation until the returns to both groups (inclusive of the cost of training) are equalized.

Formulating the problem in terms of the pattern of wages and spending makes it clear that, far from being beneficiaries of an aggregate demand externality, the firms in the competitive fringe are likely to be victims of a shift in demand away from their goods! The model casts the firm’s decision as whether the additional revenue from investment is sufficient to justify that investment – a familiar decision to any businessman. However, by holding price and revenue fixed, the implicit assumption is that 1) the firm fails to bid away demand to its own resources from others beyond what it could expect if consumers were completely indiscriminate, and therefore that 2) any revenue benefit to the firm is mediated entirely through a general increase in consumer spending.

Consider what corporate behavior would look like in a world accurately described by the assumptions in the Shleifer-Vishny model. If productivity is a public good in some sense, a firm would compete to be the least efficient, and continually beggar its competitors to invest in productivity-enhancing technology. If other firms’ investments bid up the first firm’s wage bill, at least they also increase its revenue. The absurdity of a firm reasoning this way, even in a developing country, suggests that aggregate demand externalities are unlikely to be a major impediment to development. An industrial policy predicated on the assumption of their importance must ultimately fail to pay for itself.

Empirical Relevance: Industrial Policy and the Classical Dichotomy

All this being granted, big-push-style industrial policies do still appear to have had some success. Though the paper has no empirical section, its followup (Murphy, Shleifer, & Vishny 1989) is explicitly concerned with explaining demand-led growth under a coordinated industrial policy in the “Asian tiger” economies, and with bringing that success to other developing countries. A country opening its markets to foreign demand, and coordinating investment in the capacity to produce things that foreigners will demand, seems clearly to constitute an increase in aggregate demand.8 It seems apparent that this increase is the crucial factor in explaining the takeoff of these economies. However unsatisfying the model is on its own terms, it retains some plausibility as an explanation of export-led industrialization unless an alternative is available.

In this respect, the Shleifer-Vishny model can be read more charitably: there is indeed a need for coordination in investment, though this is due to the necessity of matching the pattern of demand from the richer foreign country, rather than from a supposed aggregate demand externality. Industrial policy, in this case, coordinated investment in those sectors corresponding to foreign demand, leading to a long-run boost in aggregate demand through which the country was able to develop. However, in order to justify industrial policy, it would need to be proved that its capacity to direct investment to its most valued uses not only matches that of the price system, but is sufficiently far above that of the price system so as to justify the administrative cost. In light of the above criticisms, we consider this far from proved.

Nevertheless, the fact remains that the Shleifer-Vishny model is, by itself, concerned purely with the domestic economy. The charitable reading depends on an implicit analogy between a boost to aggregate demand arising from trade leads to economic growth and development and a boost to aggregate demand cajoled out of the domestic economy.

In order to evaluate the analogy, we will have to distinguish between nominal aggregate demand (Y – the traditional definition, per above) and real aggregate demand (y – divided by the price level). As argued above, boosts to nominal AD that operate through wage effects are mitigated through price adjustments. Likewise, a general expansion of AD through, say, expansion of the money supply, are – with due allowance for short-run effects – mitigated through adjustments in the general level of prices; i.e. through inflation. This much has been established so far: any real boost in aggregate demand depends on an excess supply of real balances, which vanish as prices adjust. The classical dichotomy holds: in the long run, real variables are determined by real factors, and changes to nominal variables are dissipated into prices.

The crucial difference between the two types of AD boost is that an increase in aggregate demand arising from new export markets does not consist in an excess supply of real balances. Such demand is an exogenous real factor, and is thus entirely consistent with a permanent boost to real income without being dissipated into prices. For this reason, a too-self-contained model whose aggregate demand shock originates within the domestic economy has no bearing on the viability of export-led industrialization. There is no such thing as “big push in one country” – the exports must, after all, go somewhere.

The Blanchard-Kiyotaki Model

Carefully separating real and nominal aggregate demand presents a challenge to a theory of aggregate demand spillovers. Blanchard and Kiyotaki (1987) rise to the challenge with a much more sophisticated account of AD externalities arising from monopolistic competition that remedies most of the major oversights of the Shleifer-Vishny model. In particular, they explicitly introduce a separate money commodity, a price index composed of a weighted average of the prices in the economy (and similarly for a wage index), and limit permanent welfare effects to changes in real aggregate demand.

The upshot of this inclusion is that the model is at once more complex and less ambitious than the Shleifer-Vishny model. Functional forms must be specified for consumer utility, labor supply, and product demand, the latter to of which are derived from the former. At the same time, the paper manages to avoid many of the pitfalls of the Shleifer-Vishny model and is thus somewhat more circumscribed in its conclusions. Their aggregate demand externality depends, they argue, on the assumption of monopolistic competition and sticky prices (specifically menu costs). The price level, in their model, is “too high”, and efficiency can be improved by a boost in aggregate demand which does not exceed the cost of adjusting prices. Monopolistic competition, in their model, means that more real balances can in fact be eked out of the domestic economy, leading to higher AD, and menu costs prevent the boost from being dissipated into prices, at least below some threshold.

They do, of course, recognize the tenuousness of hanging the Nash equilibrium of an entire economy’s pricing decisions on something so practically heterogeneous and in many cases unmeasurable as menu costs (cf. Caplin & Spulber 1987), and heavily qualify the applicability of their model in the conclusion. If aggregate demand increases beyond the threshold where firms find it worthwhile to adjust their own prices, the equilibrium falls apart and firms again “defect” to higher prices, dissipating the welfare effects.

The policy implications are thus naturally limited, though it does seem to suggest continual low-level inflation. There will be less to say about this model for the simple reason that there is less wrong with it. Still, the model does make a strong case for the existence of an aggregate demand externality, even if it does not make a convincing case for its exploitability through the multiple equilibria created by menu costs. It will therefore be worthwhile to consider the commensurability of the model’s parameters with their real-world and theoretical analogues.

The Volume of Spending Includes Wages

The Shleifer-Vishny model could not capture the tradeoff between corporate and consumer spending: without the ability to track changes in money and velocity, it is unable to trace the forces that keep the aggregates in line with the accounting identities. The Blanchard-Kiyotaki model is an improvement in this regard in that it explicitly assumes (because, as they admit in the first section, of a “need to avoid Say’s Law”) that agents have the option of hoarding money balances – i.e. that there could be an endogenous relationship between wages and velocity. This would let us relax the earlier assumption of exogenous supply and velocity of money. And indeed one might argue for a positive relationship between wage and velocity: the consumer’s higher marginal propensity to spend (relative to his employer’s) results in a rise in velocity when his wages rise.

But phrased in this way, it is easier to see that the model implies an enormous difference between the employer’s and the employee’s MPS in order for a transfer from the former to the latter to stimulate aggregate demand appreciably. The volume of spending is not increased one-for-one with the increase in wages, but is offset to a large degree by the diminished spending power of those paying the wages.

For all the sophistication of the Blanchard-Kiyotaki model, it overlooks this offset due to its complete segregation consumer and corporate spending. Aggregate demand is defined only as (real) consumer spending. The price level, likewise, is defined as an index of goods prices, exclusive of wages, which have their own index. Because money enters the model by putting real balances in the utility function, firms themselves have no demand for money balances.

This being the case, “aggregate demand” in the model is completely incommensurate with aggregate demand in monetary theory. In the latter it does not matter for velocity whether a dollar passes from a consumer to a firm, a firm to an employee, or a firm to another firm. All such transactions must – at least in theory – be subsumed into aggregate demand. For the purposes of tabulating the volume of spending, there is nothing special about consumer spending as opposed to spending by any other group.

Unfortunately, by segregating firm spending from consumer spending and defining aggregate demand solely as the latter, a transfer of spending power from consumers to firms falls outside the view of the model, and thus appears like an aggregate demand externality. If AD is defined as total consumer spending, then it is trivial that an increase in wages increases AD. If, however, AD is properly defined as the sum total of all spending in an economy, we must make additional assumptions about relative propensities to spend. The model does not attempt to argue that consumers are substantially more prone to spend the marginal dollar than their employers; rather, similarly to the Shleifer-Vishny model, the increase in wages is assumed to simply represent an increase in spending.9

Firms Are More Likely to Spend the Marginal Dollar than Consumers

It is clear from a moment’s reflection that firms demand real balances for exactly the same reason as consumers – namely to facilitate transactions and to provide a cushion against losses in the uncertain future. We will therefore not expect the marginal dollar to be completely hoarded. Even if we assume that the marginal propensity to consume falls with the level of wealth, and that corporations (having more wealth than individual consumers) should be less likely to consume their marginal dollar, the shift to consumer spending – as argued above – is offset by some decline in corporate spending.

However, it must be remembered that the marginal propensity to consume is not the same as the marginal propensity to spend. Consumption spending is merely a subset of spending, and not even the largest (Skousen 2010): the aforementioned traditional definition of AD as Y=C+I+G+X includes three buckets besides consumption. Just as it does not matter for AD who is doing the spending, it similarly does not matter what the spending is done on10 – that is, which bucket it falls into. Thus, though it is reasonable to assume that the marginal propensity to consume falls with the level of wealth, MPC is – by itself – entirely irrelevant to the level of aggregate demand.

Indeed, it may be more reasonable to assume that the marginal propensity to spend rises as the firm becomes more and more capable of investing – if not in his own productive capacity, then in someone else’s through interest-bearing assets. Though consumer savings also largely get translated into investment through bank holdings, he will tend to hold more cash for convenience’s sake than a firm – which, in modern economies, is base money, and whose holding thus properly counts as “hoarding”. A firm, on the other hand, because (by presumption) it can take advantage of economies of scale in real balance holding, is able to hold them in the form interest-bearing assets, which – being investments – do not properly count as hoarding.

If, therefore, a profit-maximizing firm’s optimal holdings of base money are far lower as a proportion of total real balances than a consumer’s, it is entirely illegitimate to derive aggregate demand effects as if the entire balances of the former consisted of hoarding. Indeed, the opposite is more likely to be the case: if we are concerned about the level of aggregate demand, a transfer from firms to consumers through an increase in wages is likely to be contractionary, if perhaps not significantly so.

Conclusions and Future Research

The aggregate demand externality, whether in a crude or a sophisticated model, appears to depend in general on assuming away the coordinating mechanisms of price adjustments. The exercise is not, of course, without use. In conjunction with the arguments in this paper, they may be read as a kind of demonstration by contradiction. If such assumptions as characterize the Shleifer-Vishny model, or such an artificially segregated definition of aggregate demand as characterizes the Blanchard-Kiyotaki model, are necessary to result in pervasive aggregate demand externalities, their practical relevance is prima facie negligible.

Still, a prima facie theoretical case is not an open and shut case. While the difference in corporate and consumer marginal propensities to spend would have to be large and opposite the expected sign in order for a wage boost to result in a significant dishoarding, as would be necessary for either model to be consistent with accounting identities, there is no a priori reason why it might not be so, perhaps for tax reasons. To my knowledge there are no estimates of these magnitudes. Future empirical research will therefore be needed in order to fully evaluate the applicability of the Blanchard-Kiyotaki model.

In addition, the criticisms in this paper are contingent, model-internal criticisms. A model which purported to demonstrate an aggregate demand externality arising from an increase in foreign demand, for example, would have a much better claim to empirical relevance, and would have to be evaluated on its own terms. The specific problems laid forth in this paper could – at least in principle – be avoided, though it is unclear how much room their solution would leave for the emergence of a spillover. A theoretical model demonstrating or refuting the plausibility of aggregate demand spillovers in principle has yet to be articulated.

Footnotes

  1. However, the Blanchard-Kiyotaki model defines aggregate demand as real income in terms of real money balances (see their equation 6, and the section below). The conclusions which follow regarding aggregate demand, and especially spillovers or externalities, must be duly modified before they can be compared to the conclusions of the Shleifer-Vishny model.
  2. However, see below on the Blanchard-Kiyotaki model for discussion of an endogenous relationship between wages and velocity.
  3. One might also interpret the fixity of prices in the model as an assumption that productivity shocks shift aggregate demand and aggregate supply pari passu.
  4. This is obscured in practice because overlaid by a general expansionary tendency since the second World War, but appears in our exposition due to our assumption of a constant money supply. The general logic is as follows: from the equation of exchange MV=Py, we take growth rates and rearrange to get gP = gM + gV – gy. If productivity growth is accounted primarily as a positive growth rate of real income gy, then it enters our expression for inflation with a negative sign. Similarly, for a constant M and V, an increase in y can be accounted only by a fall in P.
  5. A different supposed aggregate demand externality obtains when firms face the prospect of adjusting prices to an inflation or deflation: Yeager (1982) argues that price adjustment in this setting is akin to a public good. However, as Selgin (1997) points out, this applies only to monetary inflation and deflation. For productivity-induced changes in the price level, the benefits of cutting prices are fully internalized through competitive pressures, and we need fear no downward stickiness.
  6. Yamada (1999), in a modest extension of the Shleifer-Vishny model to include intermediate goods, does in fact specify a unit-elastic demand curve for each good. The Blanchard-Kiyotaki model also specifies a constant-elasticity demand curve.
  7. These profits are disbursed to the consumer in his capacity as stockholder, not as wage-earner – note that Π and WL are separate terms in the consumer’s budget constraint.
  8. However, in the spirit of the section on accounting identities earlier, we must be careful about positing an exogenous increase in X. To the extent that the country runs a trade surplus, the majority of the new X most likely comes at the expense of C in the short run. V will also likely fall due to an increase in foreign demand for the domestic currency. The effect on prices is therefore ambiguous.
  9. Though to their credit, unlike Shleifer-Vishny, they do recognize that an increase in spending produces upward pressure on prices, hence the importance of menu costs for blocking that pressure.
  10. Which is not, of course, to deny that what the spending is done on matters a great deal for other questions. This suggests that those critics of aggregation who would agree with the conclusions here ought not properly be against aggregation as such, for total aggregation (keeping in mind the proper accounting identities) results in similar conclusions to total disaggregation. It is only the use of arbitrary semi-aggregates – like consumption spending as opposed to the total volume of spending – which is liable to lead the argument astray.

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General Equilibrium, Increasing Returns, James Buchanan

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