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Market Pessimism, Involuntary Unemployment and Fiscal Policy

Joël Hellier

EQUIPPE, Univ. of Lille 1 and LEMNA, Univ. of Nantes

Abstract: We analyse the impact of market pessimism on employment, and the influence of fiscal policies when this creates involuntary unemployment. In this purpose, we build a model of monopolistic competition with entrepreneur heterogeneity and subjective demand functions. A clear distinction is made between market pessimism and general activity pessimism, the former being characterised by an under-valuation of their market shares by the entrepreneurs on average. We show that market pessimism always results in involuntary unemployment. In such a case, public orders (fiscal policy) have a stabilising impact when they are financed by an income tax and make it possible to re-attain full employment when financed by money creation.

Key Words: Expected demand, Fiscal policy, Pessimism, Unemployment.

JEL Classification: E24, E62.

Corresponding author:

Joel Hellier

EQUIPPE, Univ. of Lille 1 and LEMNA, Univ. of Nantes Pers. address: 28 rue de Sévigné 75004 Paris FRANCE

Tel. +33 142775740 / Fax. +33 320436768 [email protected]

1 Introduction

The central role of expected demand in determining macroeconomic performances is one of the key elements of Keynes’ General Theory. However, in the early Keynesian models with fixed prices, firms’ expectations were to a large extent ignored. In line with Phelps (1967), the following Keynesian models incorporated expectations, but these were originally limited to the setting of prices. These early approaches have been questioned for their lack of sound micro-foundations. The disequilibrium theory (Benassy, 1975) attempted to lay such foundations by showing that under-employment equilibria with non Walrasian prices could emerge, but this failed to explain why unemployment does not result in lowering real wages, thereby restoring the full employment equilibrium.

Since the late seventies, the ‘new Keynesians’ have proposed a wide range of micro-founded models that integrate expectations and in which under-employment has derived from nominal and/or real rigidities¹. Information asymmetries, transaction and adjustment costs, imperfect competition, multiple equilibria with coordination failures etc. have been utilised to explain the emergence and persistence of under-employment. These approaches were however not based on demand expectations and the market failures they put forward could typically not be treated by the traditional Keynesian remedies. Active fiscal intervention, a key tool in Keynesian policies, is useless in most of these situations, with a few exceptions however (Hart, 1982; Blanchard & Kyiotaki, 1987; Cooper & John, 1988).

From the mid-eighties, a series of theoretical models has displayed involuntary unemployment based on imperfect competition in the market for goods (d’Aspremont et al., 1984; Dehez, 1985; d’Aspremont et al., 1990, 1991; Kaas, 1998; see Lasselle and Svizzero, 2002, for a review). In this class of model the demand met by firms in imperfect competition is the main explanation for involuntary unemployment because this results in a marginal revenue that is negative for the full employment output. These explanations are however based on certain characteristics of the ‘true’ demand functions, and the likelihood of the related conditions may be regarded as questionable.

Finally, if ‘animal spirits’ (market psychology) and expectations in great uncertainty have always been deemed by post-Keynesians to be key elements in market imperfection, they have not proposed firm micro-foundations of these elements that they considered as realistic

1 A selection of new Keynesian articles is proposed by Mankiw and Romer (1993). Gordon (1990), Greenwald and Stiglitz (1991), Romer (1993) and Benassi et al. (1994) provide surveys of new Keynesian contributions, and Lindbeck (1998) an assessment of their analyses of aggregate economic activity and unemployment.

and heuristic hypotheses. In contrast, within a two-period monopolistic competition model with self fulfilling rational expectations on future total demand, Kiyotaki (1988) generates optimistic and pessimistic equilibria that provide micro-foundations to the Keynesian animal spirits, but pessimism does not come with unemployment in this approach.

In the model developed here, we insert entrepreneurial heterogeneity and subjective demand functions into a simple monopolistic competition approach à la Dixit-Stiglitz-Krugman (DSK) so as to analyse the impact of expected demand upon production and employment.

Initiated by the seminal works of Chamberlin (1933), Joan Robinson (1933) and Triffin (1940), monopolistic competition theory has experienced a substantial revival following Dixit and Stiglitz (1977) model². The Dixit-Stiglitz approach has subsequently been discussed, extended and utilised in several ways, particularly to lay the micro foundations to certain Keynesian results (Benassy, 1976; Blanchard and Kyiotaki, 1987). Krugman (1980) has proposed a simplified version of the model so as to analyse intra-industry trade. Like the initial Dixit-Stiglitz model and most of its subsequent extensions, Krugman’s approach draws on pure horizontal differentiation (varieties symmetrically enter in the utility function), on free entry, and on the hypothesis that firms know their true demand functions. Such an approach does not account (i) for differences in quality, such that differentiated goods at same price may be differently demanded, and (ii) for the fact that the monopolists rarely know their true demand function and more often use subjective demand functions in their calculations.

The importance of subjective or ‘perceived’ demand functions in imperfect competition has been underscored by a number of authors, including Chamberlin (1933), Kaldor (1934, 1935), Sweezy (1939), Triffin (1940), Bushaw and Clower (1957), and Negishi (1961)³. With a few exceptions, the literature that followed Negishi’s seminal article has emphasized the tâtonnement process by which equilibrium is restored (Benassy, 1976). The consistency of the different ex ante subjective market shares and their impact on total production and employment has to a large extent been neglected.

The model developed here modifies the basic DSK approach in three ways. Entrepreneurs are heterogeneous in that they supply goods that match consumer tastes in different ways, which results in different demand functions across firms and creates profit as a return to the entrepreneur’s ability. In addition, entrepreneurs do not know their true demand function when deciding for production. They thereby draw their calculations on ex ante subjective market shares that may turn out to be misleading. Finally, new entrepreneurs join the market

2 See Keppler (1994) for a general exposition.

3 See the discussion by Negishi (1979), chapter 6, and the presentation in Bonanno’s survey article (1990).

and former entrepreneurs quit the market at each period of time, which prevent the firms from learning their true demand function. From this framework, we uncover ‘pessimistic’ and

‘optimistic’ situations, the former being always characterised by involuntary unemployment.

We also establish that fiscal policies may be efficient tools to fight against unemployment or economic overheating.

The model is constructed in Section 2. Its results in terms of ‘market psychology’ (optimism versus pessimism) and employment are presented in Section 3. Section 4 analyses the impact of fiscal policies. The discussion of the model results and the conclusion are provided in Section 6.

2 The model

2.1. General framework

The traditional DSK monopolistic competition approach is extended by assuming entrepreneur heterogeneity and subjective demand functions.

Entrepreneur heterogeneity and demand

There are different entrepreneurs who have different abilities so that the goods they produce are attractive in varying degrees, and thereby differently demanded from households. This takes the form of different coefficients a in the households’ utility function: _i

( 1) / 1

n i i i

u a x ^{ε− ε}

=

=

∑

Entrepreneur i manages firm i that produces good i with quality a . Coefficient _i a indicates _i the quality the market allocates to good i, and it is thereby an ex post value. Coefficient a _i also measures entrepreneur i’s ability as revealed by the market.

The maximisation of the utility function results in the total demand for good i:

1

d i

i

i j j j

y a I

p a p

ε

ε ε −ε

=

∑

where I is total income and p_k the price if good k.

Given that all goods are produced with the same technology whatever their quality (see below), such a framework generates pure profit for the firms, this profit being the entrepreneur’s return to ability.

Labour and Incomes

Workers supply one unit of labour that is paid at the wage rate w. In contrast, entrepreneurs’

income comprises two elements, a wage component that remunerates her working time (the entrepreneur’s labour participates in the production function) and a pure profit component that pays for her ability. Note that the model outcomes would be identical by assuming that pure profit is the only income for entrepreneurs. This would however make the analysis slightly more complex because (i) the condition for an individual to choose to be an entrepreneur would shift from a positive profit condition to a profit higher than the unit wage, and (ii) total labour supply should then be cut by the number of entrepreneurs.

Firms and the subjective demand functions

At each period of time, a number of former entrepreneurs (qualities) disappear and a number of new entrepreneurs (qualities) join the market. As a consequence, the vector of the a_i significantly changes from one period to another and the demand functions that enter the entrepreneurs’ calculations are highly subjective.

Ex ante, entrepreneur i assigns a certain quality level ˆa_ii to her own product and certain quality levels ˆa_ji, j≠i, to each of her competitors product. As shown hereafter, this is equivalent to saying that each entrepreneur allocates a certain market share to her own good.

It is important to note that the different ˆa_ii, ˆa_ji, and the related market shares, are expected values that may well turn out to be false ex post. Equalities ˆa_ii =a_i and ˆa_ji =a_j, ∀i j, , are typically not met because a large number of entrepreneurs and goods are newcomers to the market, and there is thus no way for entrepreneurs to accurately quantify the attractiveness of each good.

It is assumed that there is no uncertainty about the elasticity of substitution ε so as to concentrate on the analysis of market shares. Finally, firms are wage takers on the labour market, wage w is perfectly known by all entrepreneurs, as well as the economy endowment of labour L .

As in Krugman (1980), all goods are produced with the same technology:

i i/

l = y λ+ f ,

where l is the quantity of labour used in production _i y of good i, _i λ the marginal productivity of labour and f the fixed cost of production.

The fact that the technology is the same for all goods is known by all entrepreneurs.

Firm i maximises its profit ˆπ_i = p yˆ_{ii i}−w y( _i/λ+ f) under the subjective demand constraint

1

ˆ ˆ

ˆ ˆ ˆ ˆ

d ii i

i

ii j ji ji

y a I

p a p

ε

ε ε −ε

=

∑

, where the circumflex denotes expected values⁴. ˆ

Ii is entrepreneur i’s expectation of total income, and ˆp and ˆ_ii p the respective prices of good i and j as expected _ji by entrepreneur i. The price ˆp determined by the maximisation programme is proposed by _ii the firm in order to sell its production. However, as prices will ex post depend on supply and demand, and since the ex post market share may differ from its value expected by the firm, the ex post price may turn out to be fairly different from the price ˆp initially proposed by the _ii firm.

As the number of goods is large, each producer considers as negligible the impact of her own decision on both the price index

( ^∑

^{jaˆjiεpˆji1−ε}

)

^1/(1−ε)and total income and demand (no ‘Ford effect’⁵).

Money

We assume a demand for credit driven money supply that takes the following shape. Firms borrow money from a bank at the outset of the relevant period so as to pay the labour force they utilise for production. At the end of the period, they reimburse the bank without interest.

This very simple way to model money ignores the interest rate, which can be seen as acceptable since we suppose that there is no capital, no risk aversion, and no intertemporal choice. Assuming that the bank applies an interest rate to the loans it attributes (for instance to pay its staff), it would nevertheless not change the model outcomes provided that the related interests are spent over the current period. In addition, when pure profit is generated, money velocity adapts to allow both the demand for production and the repayment to the bank. In fact, once the price of the quality they produce is determined by the market, entrepreneurs

4 The circumflex denotes exogenous as well as endogenous expected values.

5 d'Aspremont et al. (1990)

know the value of the profit their firm will generate and they thereby spend this money to buy goods in the market as and when they receive money from their sales. As a consequence, if the profit accounts for, say, 20% of the total wage bill wL , then the borrowed money

M =wL is used 1.2 times and the money velocity is 1.2. At the end of this process, all firms possess the exact amount of money they borrowed and they can pay the bank back.

These assumptions concerning money make it possible to simplify the model and to concentrate on the production decisions. In addition, this is in line with certain features of the traditional Keynesian view for which money is demand-driven and ‘money or credit must precede production. This is because money is used to pay factors of production in the current period’ (Hewitson, 1995, p.286).

2.2. Production, employment and ex ante prices and profits

The firm’s maximisation programme provides the following results⁶:

ˆ /

ii 1

p ε w λ

=ε

− (1)

ˆ 1 ˆ /

i i i

y α ε λI w

ε

= − (2)

ˆ 1 ˆ /

i i i

l α ε I w f

ε

= − + (3)

1 ˆ ˆ ˆ_{i i i}I wf

π α

=ε − (4)

1 ˆ_{i i}ˆ

i

Y I

w

ε λ α

ε

= −

∑

⁽⁵⁾

1 ˆ_{i i}ˆ /

i

L ε α I w nf

ε

= −

∑

+ ⁽⁶⁾

with: ˆ

ˆ ˆ

ii i

ji j

a a

ε

α ≡ ε

∑

^{, Y =}

∑

^iyi the total production, and L=

∑

_il_i the total employment.

Production (y and Y) and employment (_i l and L) are ex post values when condition L_i ≤L is fulfilled, i.e., when the firms’ production plans are consistent with labour endowment.

6 Equation (2) is obtained by assuming pˆ_ii = pˆ_ji since all entrepreneurs know that all the firms share the same technology.

Conversely, prices and profits are expected values that are typically not met ex post. Since ˆ ˆ

ˆ_{ii i i i}

p y =α I (Relations 1 and 2), coefficient ˆα_i is the subjective market share entrepreneur i assigns to her product.

Firm i’s expected profit is given by Relation (4). For a firm to produce, its profit must be positive, i.e. α εˆ_i > wf I/ ˆ_i. Arranging the firms in decreasing order of expected profitability, it is thus possible to determine the number n of firms on the market which is such that

ˆ_n wf I/ ˆ_n

α ≥ε ^and αˆ_n+1<εwf I/ ˆ_n+1^.

We can also express relations (2)-(5) in terms of expected total employment. Let ˆ

Li and ˆ Πi

be respectively total employment and total profit as expected by firm i. Expected income ˆ Ii is equal to ˆ ˆ

i i

wL + Π . It can be shown (see Appendix 1) that ˆ (ˆ )

i 1 i

I ε w L nf

=ε −

− . Inserting this

equality into relations (2)-(6) yields:

(

^ˆ

)

i ˆi i

y =α λ L −nf (7)

(

^ˆ

)

i ˆi i

l =α L −nf + f (8)

( )

1 ˆ

ˆ

ˆ_{i i}( 1) w L_i nf wf

π α ε= − ⁻ − − (9)

ˆ_iˆ_i ˆ_i

i i

Y =λ α

∑

L −λnf

∑

α ⁽¹⁰⁾

( )

ˆ_iˆ_i 1 ˆ

i

L=

∑

α L + −α nf ⁽¹¹⁾

As already specified, y , _i l , Y and L are ex post values (if L_i ≤L) whereas ˆπ_i is the profit expected by firm i.

Finally, as all firms know the economy endowment of labour L , then Lˆ_i ≤L, ∀i^.

3 Market psychology and employment

We denote ˆ ˆ_i

α ≡

∑

iα the sum of the subjective market shares of the firms.

As entrepreneurs’ expectations are not coordinated, there is no reason for the expected market shares to be consistent with each other, and thus ˆα is typically different from 1. Two cases may thus be distinguished, namely ˆα <1 and ˆα >1.

3.1. Market pessimism versus market optimism

Definition 1: The market is pessimistic when ˆα <1, and it is optimistic when ˆα >1.

Market pessimism occurs when firms on average underestimate their market share.

Conversely, market optimism corresponds to situations in which firms on average overestimate their market share. It must be noted that pessimism and optimism are totally defined in terms of market shares whereas production and employment depend on both expected market shares ( ˆα_i) and expected total income ( ˆ

Ii).

Definition 2: Activity pessimism is a situation in which the expected total income (and production) results in unemployment when the ex post market shares α_i are perfectly forecasted by all entrepreneurs.

Activity pessimism occurs when ˆ

iαi iI <I

∑

, with I being the full employment total income

(it can easily be shown that ( ) I w ε 1 L nf

= ε −

− ). Assuming rational entrepreneurs, no entrepreneur forecasts a total income higher than the full employment income (Iˆ_i ≤ ∀I, i^).

Hence, it is sufficient that one entrepreneur only expects a total income lower than I to create activity pessimism. Obviously, for activity pessimism to be effective in terms of production and employment, it is necessary that a number of entrepreneurs expect under- employment total income.

There is thus a clear difference between market pessimism and activity pessimism. Le latter has been analysed by several authors (e.g., Kiyotaki, 1988; Abel, 2002; Jouini and Napp, 2008⁷). In this article, we only draw attention to market pessimism/optimism. The impact of market pessimism upon activity pessimism is however discussed in Subsection 5.2.

Involuntary unemployment is defined as a situation in which unemployment persists whatever the (positive) level of the real wage. On the other hand, over-employment is defined as a

7 Abel (2002) and Jouini and Napp (2008) draw attention to the impact of the stochastic distribution of aggregate consumption expectations. Our definition of activity pessimism is thus somewhat different from their.

situation in which the firms’ production plans result in a total demand for labour that is higher than the endowment of labour of the economy L .

Proposition 1: When the market is pessimistic, this always generates involuntary unemployment.

Proof: Total employment is L=

∑

iα^ˆiL^ˆi + −

(

¹ α^ˆ

)

nf (Relation 11). Since Lˆ_i ≤L, ∀i^, then L≤αˆL+ −(1 αˆ)nf . Expression ˆαL+ −(1 αˆ)nf is increasing in ˆα ^{for L}>^nf (which is always true since L>nf by construction and L≤L), and ˆαL+ −(1 αˆ)nf =L for ˆα =1. Thus, L<L for ˆα <1.

Proposition 1 shows that involuntary unemployment is a regular situation that emerges every time the market is pessimistic.

In the case of optimism, no general result in terms of employment can be stated. In fact, employment ^ˆiˆi

(

^{1 ˆ}

)

i

L=

∑

αL + −α nf depends on both vectors

{ }

^{αˆi and}

{ }

^{L (or ˆi}

{ }

^{I ). The ˆi}

overvaluation of market shares ( ˆα >1) may then be offset by employment expectations lower than full employment ( ˆ

Li <L in average). Two cases may then be distinguished. In the first

( )

ˆ_iˆ_i 1 ˆ

i

L=

∑

α L + −α nf ≤L, which indicates that the firms decisions about production and employment are consistent with labour endowment L . In this situation, the firms’ production plans are carried out and this results, either in underemployment ( L<L), or in full employment ( L=L). The second case is when L=

∑

iα^ˆiL^ˆi+ −

(

¹ α^ˆ

)

nf >L^{. Then,} employment as defined by Relation (11) cannot be achieved because labour endowment is too low to meet the firm’s production plans (see Subsection 3.3 for a discussion).

Finally note that, when firms anticipate full employment (Lˆ_i =L, ∀i), market pessimism generates involuntary unemployment and market optimism over-employment.

3.2. Expectations

So as to concentrate on market shares expectations, we shall suppose henceforth that all entrepreneurs have the same expectation of total income: Iˆ_i =Iˆ, ∀i, and similarly Lˆ_i =Lˆ, ∀i^.

Assuming this, total production Y and total employment L are fully determined by the couple of expected values

( )

^{αˆ , Iˆ :}

1 ˆ

Y ˆ I

w ε λ α ε

= − (12)

1 ˆ

ˆ I

L nf

w αε

ε

= − + (13)

In the traditional DSK approach, expectations of total activity are self-fulfilling. The same result may easily be established by assuming entrepreneurial heterogeneity with true demand functions. Conversely, expectations are no longer self-fulfilling when entrepreneurial heterogeneity is combined with subjective demand functions. Assuming that all firms hold the same employment expectations (Lˆ=Lˆ , _i ∀i), Relation (11) becomes ^{L=αˆLˆ+ −}

(

^{1 αˆ}

)

^{nf . This}

shows that firms’ expectations are not self-fulfilling, except for ˆα =1.

3.3. Ex post equilibrium

We now briefly explore the determination of the ex post equilibrium, i.e., the mechanism by which ex post demand adjusts to production. This point has been the main concern in a sizeable literature that followed Negishi’s seminal article (1961). We also mention certain issues that remain open to analysis.

The model is based on the assumption that the ex post market shares may significantly differ from their values anticipated by entrepreneurs. The true demand function for good i is

i 1

d i

i j j j

y a I

p a p

ε

ε ε −ε

=

∑

(see Section 2) with typically a_i ≠aˆ_ii and a_j ≠aˆ_ji.

Market pessimism

In the case of market pessimism, the production of each good is equal to the values given by Relations (2) and (7). Let us suppose that good i is sold at price p that allows firm i to sell _i the total of its production.

Proposition 2: There is one unique ex post equilibrium that allows all firms to sell their production, and this is characterised by the following relative prices (p_i/p ) and _j market shares (α_i^):

ˆ 1 /

ˆ

i i j

j j i

p a

p a

α ε

α

 

=  

  (14)

1

1

ˆ ˆ

i i

i

j j

j

a a

ε ε

ε ε

α α

α

−

= −

∑

(15)

Proof: See Appendix 2.

Proposition 2 shows that an ex post equilibrium can always be achieved in the case of market pessimism. This equilibrium is characterised by a vector of relative prices (Relation 14) and a vector of market shares (Relation 15). Note that this equilibrium may however result in insolvency for certain firms when the ex post price is too low to guarantee that the firm’s revenue covers its production costs.

Market optimism

In the case of market optimism, we have mentioned that two situations were possible (Section 3.1). When ^{L=αˆLˆ+ −}

(

^{1 αˆ}

)

^{nf ≤L} the model outcome is similar to pessimism and Proposition 2 applies. When ^{L=αˆLˆ+ −}

(

^{1 αˆ}

)

^{nf >L}, the firms’ production plans cannot be carried out. In addition, a rise in the nominal wage may typically not level the firms’

production with the full employment production because a higher unit wage causes a rise in ex ante prices (Relation 1) and in the firms’ expectations of total income (since

ˆ (ˆ )

i 1 i

I ε w L nf

=ε −

− ). In this case, the unit wage and expected prices tend to infinity before the firms begin to produce, and the production plans can never be consistent with labour endowment. This may lead to a disequilibrium analysis (Benassy, 1976): the production is carried out before the setting of an equilibrium wage, and certain firms will thereby be unable to implement their production plans. This rationale also provides a sound foundation for disequilibrium because an increase in the nominal wage cannot restore the full employment equilibrium. In fact, if we assume that price equilibrium is not immediate, then optimism leads to a succession of disequilibrium situations with lasting inflation (rise in both nominal wage and prices).

There exists however a means by which the firms’ production decisions can be made effective even when these result in a demand for labour that is higher than the initial labour endowment. If we consider the post World War II period, almost all advanced countries (Western Europe, Canada and the US, Japan) experienced full employment from the fifties up to the first oil shock. Full employment has also been achieved in a number of countries from the mid-90s up to the late 2000s financial crisis (North America, Scandinavian countries, the UK etc.). This seems to contradict our main result, i.e., that full employment is a rather unlikely state, under and over-employment being the normal situations. In actual fact, to a large extent these periods were characterised by over-employment rather than full employment. This can easily be deduced given that the relevant countries experienced substantial immigration flows that made labour supply meet labour demand throughout these

‘full-employment’ periods. As a consequence, firms typically utilised immigration as a means to attaining their production goals in the situations of optimism characterised by insufficient labour endowment (see Chusseau et al., 2005, for the case of Western Europe in the sixties).

4 Efficient fiscal policies

In this Section we analyse the impact of several patterns of fiscal policy on production and employment when the market is pessimistic.

We consider three types of public funding, respectively an income tax, a consumer tax, and a money creation by seigniorage. In addition, we analyse two types of public expenditure. The first consists of direct orders of the public planner to the firms, these orders being placed before the firms’ production decisions. The firms will thereby incorporate these orders into their production plan. The second consists of public transfers to households.

We shall assume that the fiscal policy decided by the public planner does not modify the number n of firms in the market. In this case, the total production at full employment is

( )

Y =λ L−nf .

We firstly analyse the impact of each type of public funding by assuming that public expenditure consists of direct orders to the firms. We subsequently study the case of transfers to households.

4.1. Public orders financed by an income tax and automatic stabilisation

The public planner places orders with the different firms. Total public expenditure is thus

i i

G=

∑

ip g ^{, with} g being the public order to firm i, and i p the price of good i. The _i demand function of the public planner is assumed to be _{i i 1}

i j j j

g G

p p

ε

ε ε ε

γ γ ⁻

=

∑

, and this is

known by firms. This signifies that the firms perfectly know the public orders before producing. We also allow for the pursuit of goals by the public planner which differ from those of private agents (when γ_i ≠a_i). Finally, the firms perfectly know the amount of public expenditure (G) and the fact that this is totally financed by an income tax.

As ˆI is the total income expected by firms without public intervention, and since public expenditure is totally financed by an income tax, the post-tax value of expected income becomes Iˆ−G.The maximisation programme of firm i that produces g is: _i

,

, ,

ˆ , ,

ˆ ˆ

max ( ) /

ii p i i

i ii i ii p i i p i

p y gπ = p g + p y −w g + y λ−wf ,

s.t.: _, ˆ ₁

ˆ ˆ ˆ ˆ

p i ii

ii j ji ji

I G

y a

p a p

ε

ε ε −ε

= −

∑

^{and i i ˆ}ii j j ^ˆji¹

g G

p p

ε

ε ε ε

γ γ ⁻

=

∑

Where y_{p i,} denotes the production for the private market.

This programme results in the following optimal values:

ˆ /

ii 1

p ε w λ

=ε

−

,

1 ˆ

ˆ ( ) /

p i i

y α ε λ I G w

ε

= − −

1 /

i i

g β ε λG w

ε

= −

(

^{ˆ (ˆ )}

)

^{1 /}

i i i

y α I G βG ε λ w

ε

= − + −

Where y_i = y_{p i,} +g_i is the total production of firm i, ˆα_i the (expected) share of total private demand met by firm i, and _{i i j}

j

ε ε

β γ=

∑

γ the (perfectly known) share of total public orders provided by firm i.

In addition, since the public demand is perfectly known to the firms, we have: _i 1

i

β =

∑

^.

Proposition 3: When the market is pessimistic (optimistic), direct public orders financed by an income tax increase (decrease) production and employment.

Proof: Since _i 1

i

β =

∑

, the total production that corresponds to the public expenditure

G financed by an income tax is: ^{Y G( )=ε}_ε⁻¹_w^{λ α}

(

^{ˆIˆ+ −}

(

^{1 αˆ}

)

^G

)

. The total production ( )Y G thus increases with G for ˆα <1, and decreases for ˆα >1, as well as total employment

( )

ˆˆ 1 ˆ

( ) 1 I G

L G nf

w

α α

ε ε

+ −

= − × + (equation (6) with public expenditure G).

Proposition 3 shows that fiscal policy plays its traditional role as an automatic stabiliser. If τ is the income tax rate, balanced budget implies G=τpY, and by inserting this equality into

( )

( )

1 ˆˆ 1 ˆ

Y I G

w

ε λ α α

ε

= − + − , we obtain:

(

^ˆ

)

1 ˆ

1 1 ˆ

Y I

w

ε λ α

ε τ α

= − ×

− − . Consequently, for a given tax rate τ , fiscal policy raises production and employment in cases of low activity ( ˆα <1), and it causes these to decrease in the event of overheating (αˆ Iˆ> pY ).

This result stems from the fact that pessimism (optimism) applies to the expected private spending, but not to public expense that is known with certainty. Then, by cutting G from ˆI and by spending it, the social planner diminishes production by ˆGα and raises it by G, which increases (decreases) production and employment when ˆα <1 ( ˆα >1).

However, there is a situation in which such a policy has an impact that is contrary to what is expected. This is when unemployment occurs despite optimism because the expected total income ˆI is low. In this case, the fiscal policy decreases total production because ˆα >1, and this raises unemployment.

It must finally be noted that:

(i) The same results can be obtained by assuming a corporate tax on the firms’ profits because this also reduces the total income expected by firms by the amount of the levies.

(ii) If public orders financed by an income tax have a stabilising impact, this shape of fiscal policy can however not be used to reach full employment. In fact, when unemployment results from market pessimism only (then ˆL=L), a 100% income tax rate is required to restore full employment, which is obviously impossible.

4.2. Inefficiency of public expenditures financed by a consumer tax

When the public expenditure (orders to the firms) is financed by a consumer tax, it can be easily shown (see Appendix 3) that production and employment remain the same as when there is no fiscal policy. This result is logical because such a policy simply consists in increasing the public expenditure by the same amount as the reduction in private spending brought about by the consumption tax.

4.3. Public orders financed by money creation, multiplier and full employment

We now assume that the public orders are totally financed by money creation (seigniorage), so that fiscal policy causes no cut in total income. In this case, the firm does not remove public spending G from its expected total income ˆI in the private demand function.

The public spending firstly increases the demand for, and the production of good i by the

amount 1

i i

g G

w ε λ β ε

= − , and thus total production by 1 wG ε λ

ε

− . However, this is not the

only occurrence. The increase in production to meet public demand causes an increase in the total wage bill due to higher employment, and thereby an increase in demand that stems from these newly employed workers. This means that the wages received by workers to produce those goods ordered by the public planner will be spent to buy new goods. In addition, as prices are typically higher than production costs, the new demand creates new profits that will equally be spent on new goods. All together, the G money units spent by public authorities increase the expected demand by (1+αˆ)G: G because of public orders to the firms, and ˆGα because the income created by this new production is spent by individuals (workers and entrepreneurs), the sum of the expected market shares ˆα then applying to this additional expense because entrepreneurs account for this in their calculations. Total production is then increased by 1

(1 ˆ)G w

ε λ α

ε

− + , which establishes the following proposition:

Proposition 4: Multiplier (1+αˆ) applies to public orders when these are financed by money creation.

With nominal public expense G, firm i’s optimal production is ^{yi =ε}_ε⁻¹_w^{λ α β α}

(

^{ˆiIˆ+ i(1+ ˆi)G}

)

^,

and total production ^{Y G( )=ε}_ε⁻¹_w^{λ α}

(

^{ˆIˆ+ +(1 αˆ)G}

)

. The public planner may now choose her spending G so as to make ( )Y G ensure full employment Y =λ(L−nf). In contrast with the case of public spending financed by an income tax, the financing through money creation provides a tool to restore full employment.

Proposition 5: For any couple of macro-expectations

( )

^{αˆ , Iˆ} , there is one level of public spending financed by money creation that permits to reach full employment.

Proof: Total employment is ^{1 ˆˆ}

(

^{1 ˆ}

)

( ) I G

L G nf

w

α α

ε ε

+ +

= − × + (equation (6) with

public expense G and multiplier

(

^1+αˆ

)

). Then, the amount of public orders G consistent with full employment L is: ^G=_ε^ε_{−1 1}^× ₊^w_αˆ

(

^L−nf

)

⁻₁₊^αˆ_αˆ ^Iˆ.

Proposition 5 applies to situations of under employment for which G must be positive, as well as situations of overheating for which G must be negative (i.e., a budget surplus).

Finally, since the ex post price p may well differ from the ex ante (expected) price ˆ_i p , and _i since public orders are placed with price ˆp , the prices paid by the public planner can differ _i from those subsequently paid by private agents.

4.4. Public transfers to households

If public expenditure means public transfers to households, its impact on production and employment is always lessened compared to direct public orders to the firms. This is because the public transfers are spent by households, which signifies that the different ˆα_i apply to them in the entrepreneurs' calculations, so that they are affected by pessimism or optimism.

More precisely, public transfers to households produce the following impact on production and employment⁸:

1. No impact when they are financed by an income and/or a consumption tax. In both cases, the cut in income due to levies is just equal to the increase in income resulting from the transfer.

8 These results are rather straightforward. Formal proofs are available from the author upon request.

2. A positive impact when they are financed by money creation, albeit with a reduced efficiency compared to direct orders to the firms. In particular, the multiplier is now ˆα <1 compared to (1+αˆ) in the case of public orders.

As a consequence, public transfers must primarily be regarded as a means for income redistribution, and it is a rather inefficient stabiliser.

6 Discussion and conclusion

We have proposed a model of monopolistic competition with entrepreneurial heterogeneity and subjective demand functions that produces Keynesian outcomes: market pessimism and optimism, the crucial impact of expected demand on production and employment, the regularity of under-employment or over-employment equilibria in market economies, and the efficiency of fiscal policies. In addition, the model reveals a number of habitual outcomes of market economies such as firms’ insolvency and differences in profitability. Situations of market pessimism are always characterised by involuntary unemployment. Fiscal policy displays its usual Keynesian stabilising impact and it provides a tool to restore full employment.

In the model, the definition of market pessimism / optimism is based on both assumptions of heterogeneous entrepreneurs and subjective ex ante demand functions. Entrepreneurs are heterogeneous in the sense that they provide goods of different quality that are thereby differently demanded on the market. Subjective demand functions are linked to entrepreneur heterogeneity because it is assumed that a number of new entrepreneurs join, and a number of former entrepreneur leave, the market at each period of time, which means that entrepreneurs cannot know and learn their true demand function. Finally heterogeneity and subjective demand functions lead to non-coordinated expected markets shares, thereby creating situations of pessimism and optimism. This mechanism is fairly different from the coordination failure as exposed by Cooper and John (1988). Here, non-coordination does not stem from strategic complementarity since the expected market share of each firm is not its optimal response to the market shares expected by other firms. The lack of coordination is inherent to fundamental uncertainty concerning the quality of each good in relation to others;

it does not result from multiple Nash equilibria.

One crucial element of this mechanism is that the firms’ decisions regarding their production are taken before the materialization of the true market demand. This is based on the sequence

‘production decisions
production
ex post equilibrium’, with the ex ante equilibrium (that determines production decisions) being typically not achieved ex post.

The model developed here is rather well tailored to represent a number of sectors such as the car industry, durable consumer goods, computer industry, communications equipment etc. In these industries, the World market is divided among a rather large number of firms and a very large number of varieties of different quality whose market shares are changing over time.

New designs and qualities are continuously coming in, and old ones continuously disappearing from the market, and firms display rather different returns that depend on their ability to meet demand. It should also be noted that both globalisation and technical progress, which are some of the mainstays of economic development over the last twenty years, tend to speed up the rhythm of entry of new firms and new goods, and the related changes in the firms’ market shares.

The model is based upon a simplified static approach with one factor of production (labour), no investment and no technical progress. The release of these simplifying assumptions provides several opportunities for further researches. Capital and investment may firstly be introduced in such a way that production cannot fully adjust to demand ex post, which can be achieved by assuming a putty-clay production function. In a dynamic perspective, technical change can also be introduced and this can take different forms. It can firstly consist in allowing a proportion of total income for knowledge accumulation, which increases productivity λ. In this case, lasting pessimism that reduces total income could hamper technological change as well. Technological change can also consist in allocating resources to improve the quality level of the differentiated goods. This generates a quality growth model whose results in terms of (un)employment are similar to those of the static model provided that entrepreneurs differ in their ability to improve the quality of goods. In this case, pessimism also hinders quality growth.

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Appendix 1

. Equilibrium in terms of expected total employment

We denote ˆ_ji ˆ_ji / ˆ_ki

k

a ^ε a ^ε

α ≡

∑

good j’ s market share as expected by firm i. Then ˆ_ji 1

j

α =

∑

^,

which signifies that each entrepreneur anticipates that the market will be totally distributed among the existing firms. We respectively denote ˆ

Li and ˆ

Πitotal employment and total profit as expected by firm i.

Firm i’s expected profit is πˆ_i 1αˆ_{i i}Iˆ wf

=ε − (Relation 4). Inserting ˆ ˆ ˆ

i i i

I =wL + Π into this relation yields: ^{π α εˆi = ˆi −1}

(

^{wLˆi + Π −ˆi}

)

^wf . And, since ˆ_i ˆ_ji

j

π

Π =

∑

^{, with ˆ}πji being firm j’

profit as expected by firm i: ^{ˆi ˆji 1}

(

^{ˆi ˆi}

)

j

wL wf

α ε⁻

 

Π =

∑

 + Π − ^{. As ˆ}ji ¹ j

α =

∑

^{, we}

have ^{Π =ˆi ε−1}

(

^{wLˆi + Π −ˆi}

)

^wnf , and thus: ˆ 1 ˆ

1 1

i wLi ε wnf

ε ε

Π = −

− − .

By inserting the preceding equality into ˆ ˆ ˆ

i i

I =wL + Π and ^{π α εˆi = ˆi −1}

(

^{wLˆi+ Π −ˆi}

)

^{wf , we}

obtain :

ˆ (ˆ )

1 ⁱ

I ε w L nf

=ε −

− π α εˆ_i = ˆ_iw( −1)⁻¹w L(ˆ_i −nf)−wf

Appendix 2.

Proof of Proposition 2

The true demand for good i is d / i ₁

i i

j j

j

y a I p

a p

ε ε

ε −ε

=

∑

, which yields:

1 / ^d

i j j i i

j

p^ε

∑

a p^{ε −ε}=a I y^{ε (a1)}

Good i’s production isy_i ⁼αˆ_iεε⁻1 ˆλI_i/w. Ex post total income is equal to the sum of the nominal productions of the n goods, i.e. _{j j} 1 _jˆ_jˆ_j

j j

I p y p I

w

ε λ α

ε

=

∑

= −

∑

^.