Study of government policies for promotion of green technology in the framework of real business cycle model Текст научной статьи по специальности «Экономика и бизнес»

Study of Government Policies for Promotion of green Technology in the Framework of Real Business Cycle Model*

Elena STEPANOVA

Santa Anna School of Advanced Studies, Pisa, Italy [email protected]

Abstract. This paper analyzes possible impact of government reduction in market entry costs for firms that are using green technologies. Government may promote use of green technologies by facilitating market entry for such companies. Or government may impose restrictions to enter the market if firms are not using the green technology, which will result in increase of sunk costs of entering the market. We study cases of reduction and increase in market entry costs using Real Business Cycle model (RBC) with endogenous entry and different forms of market competition. We compare impact from supply shock in the form of reduction (or increase) in entry costs to standard form of supply shock, i. e. improvement in technology.

Аннотация. Статья рассматривает влияние государственной политики снижения затрат на вход на рынок для фирм, использующих зеленые технологии. Государство может стимулировать использование зеленых технологий, упрощая возможности входа на рынок для таких компаний. Государство также может наложить запреты и ограничения на вход в отрасль, если фирма не использует зеленые технологии, что вызовет рост необходимых капиталовложений для входа на рынок. Мы изучаем случаи уменьшения и увеличения необходимых капиталовложений для входа на рынок, используя модель реального бизнес-цикла с эндогенным входом фирм на рынок и различными формами конкуренции. Мы сравниваем влияние шока-предложения, а именно уменьшения (увеличения) необходимых капиталовложений для входа на рынок, и стандартного шока-предложения, а именно улучшения технологий производства.

Key words: Real Business Cycle, endogenous entry.

introduction

It is reasonable to study the problem of facilitating market access for green technology firms in the framework of RBC models with endogenous number of producers. These models were proposed in Ghironi and Melitz (2005), Bilbiie, Ghironi and Melitz (BGM, 2007) and Etro (2009). Moreover, as we want to see impact of market competition on business cycle properties of the model, we impose imperfect competition, as it is done in Etro and Colciago (EC, 2010) and Colciago and Etro (2010). In this manner the model departs from the RBC model assumption of homogenous goods and considers goods that can be imperfectly substitutable. We will not focus on the general equilibrium properties of the model as they are extensively studied in the above-mentioned literature. What we aim to show in the paper are possible consequences for the economy business cycle of government’s efforts to facilitate market entry for green technology firms, or to restrict access to the market for firms that are not using green technologies. In BGM (2008) it

was shown that in RBC model with endogenous entry government subsidy to firm entry financed by lump-sum taxes on profits is optimal in a sense that economy first best allocation is reached. Here we will study the case of government lowering entry barriers to the firms. This can be done also in the form of subsidies, which will bring us close to BGM (2008) case. The policy can be applied when government wants to promote use of green technologies by facilitating access to the market for such firms, and we want to study economic consequences of such policy. The model also allows to study the opposite policy, when the government forbids market entry if the firm is not using green technology, which will increase sunk costs of entry to the market, and we are interested in impact of such policy on the whole economy.

The paper is organized as follows. In the first section we introduce notions and explain the model dynamics. In the second section we study transmission of economic fluctuations due to shock to the entry cost by means of computing impulse response functions. We perform comparison between classical supply shock

* Изучение государственной политики стимулирования зеленых технологий в рамках модели реального бизнес-цикла

and entry cost shock. We are interested in economic implications of government policy aimed to support and protection of green technology companies. Last section provides some conclusions and possible directions for further research.

1 MODEL SETUP

1.1 HOUSEHOLD PREFERENCES

The number of households in the economy is normalized to unity. Let us assume that contracts and prices are indicated in nominal terms with prices being flexible. Thus, it is sufficient to solve model only for real variables. Money does not have any role in the economy; it is introduced only as convenient unit of account for contracts. Composition of the consumption basket changes over time due to firm entry affecting the definition of the consumption-based price index.

The representative household supplies L units of labor inelastically in each period at the nominal wage rate W . The household maximizes expected intertemporal utility from consumption (C ):

E b "'U (c, )

where b ^(P,!) is the subjective discount factor and U (C) is a period utility function with the standard properties. At time t, the household consumes the basket of goods Q , defined over a continuum of goods W. At any given time t, only a subset of goods Ot cO is available.

Let pt (w) denote the nominal price of a good w E&,t.

For any symmetric homothetic preferences, there exists a well-defined consumption index Ct and an associated welfare-based price index p.

The demand for an individual variety, ct (w), is then defined as

( W ^ dPt

ct (w)dw = Ct

dpt (w)

where, by the conventional notation, quantities with a continuum of goods are flow values. The relative price p describes the benefit of additional product variety:

_ Pt M

, for any symmetric variety w ,

(1.1)

or, in elasticity form it is expresses as:

e(N) = P (N)N

)- p(n) N

where Nt is the number of producers.

The model considers C.E.S. preferences (constant elasticity of substitution between goods) as initially proposed in Dixit and Stiglitz (1977). Therefore the consumption aggregator is

J ct (uf 1 du

e

e-1

where q > 1 is the symmetric elasticity of substitution across goods or we will also call it the degree of substitutability between goods.

The consumption-based price index is then

Pt =

(1.2)

s='

and the household’s demand for each individual good w is

Proof of 1.3

ct M=Ct

Pt (M)

(1.3)

Let us denote expenditure in each sector of economy as EXPt = CtPt

In each time period the households maximize consumption in this time period by choosing bundle of goods w under the time period budget constraint. Demand for each individual good is delivered by solution of the following optimization problem:

max C

{c, (w)}

subject to J pt (w) ct (w) dw

= EXP,

Lagrangian for this problem is: L =

uGO

6_

6-1

/0— 1/ r

ct (u) /<6 du — X I pt (u)ct (u)du

> — EXP

uGO

First order conditions with respect to ct(w) - f-1/ ct (u) 1 du

1

0-1

0-1 ( N— - / N

—c (^)0 = Xpt ^

-1

c (w) 6 = \pt (w)

J ct (w)6 1 dw

-1

6-1

C (w) = A-0pt (w)- Ct

(1.3.1)

First order conditions with respect to l : J pt (w)ct (w) dw = EXPt, where we plug (1.3.1) and get

wGO

f p H*-' 9p, (u) - C,du = EXP, , th en we used formula for expenditure and get

/1 0 C* 1 0

pt (u) du = PtCt ; or after simplification A 0 I pt (u) du = Pt

here we use formula of the price index (1.2) Pt =

J pt (u)1 - du

1

1-0

and we get that:

X 6 J pt (u)1 6 du = J pt (u)1 6 du

1-6

A =

J Pt M1'

-1

I-«

6

1

Plugging A back to (1.3.1) we get the result ç (u>) = Ct

Pt

1.2 FIRMS

The economy is populated by a continuum of firms, each producing a different variety/good w efi. For simplicity, the model equates a producer with a production line for an individual variety/good (while empirically, a firm may comprise more than one production line). Model does not address the determination of product variety within firms. So process of producer entry and exit should be seen in broad sense, i. e. as also incorporating product creation and destruction by existing firms within them.

Production depends on only one factor, which is labor. Aggregate labor productivity is indexed by At, which represents the effectiveness of one unit of labor. A is exogenous variable of the model. Output supplied by firm w is

yt (w) = Atlt (w),

where lt (w) denotes the firm’s labor demand for production purpose. The unit cost of production, in units

^ W -wt

of the consumption good Ct, is , where wt = is the real wage.

At Pt

wt

Prior to entry, firms face a sunk entry cost of hE t effective labor units, equal to hE t — units of the

At

consumption basket. hE is exogenous variable of the model. Given model assumption that each firm can be seen as a production line for a good, the entry cost can, in turn, be seen as the development and setup cost associated with a good (potentially influenced by market regulation). Producer does not face any fixed costs.

All firms that enter the economy produce in every period, until they are hit with a “death” shock, which occurs with probability d e(0,1) in every period. The exogenous “death” shock also takes place at the individual variety level.

Firms set prices in a flexible fashion as markups over marginal costs. In units of consumption, firm w’s price is

i \ w Pt H = ,

where m stands for the markup. The firm’s profit in units of consumption is

dt (M) =

7 7

KNt )

Yt

— , (1.4)

N

where YtC is total output of the consumption basket and will in equilibrium be equal to total consumption demand Ct.

We denote firm’s profits with dt having in mind that all firm’s profits are paid out as dividends.

1.3 SYMMETRIC FIRM EQUILIBRIUM

All firms face the same marginal cost. Hence, equilibrium prices, quantities, and firm profits and values are identical across firms: pt (w) = pt, pt (w) = pt, lt (w) = lt, yt (w) = yt, dt (w) = dt, ut H = ut.

In turn, equality of prices across firms implies that the consumption-based price index Pt and the firm-level

price pt are such that the following is fulfilled — = pt = p (Nt).

Pt

Therefore benefit of additional product variety is described by:

p (N ) = p =--------------------------r --------------------r = N ^

J pt (u)1 - du

&Ç.Qt

1-e N 1- (ptl-e )1-

An increase in the number of firms necessarily implies that the relative price of each individual good increases because p' (Nt) > 0. When there are more firms, households derive more welfare from spending a given nominal amount, i. e., ceteris paribus, the price index decreases. It follows that the relative price of each individual good must rise.

The aggregate consumption output of the economy is

Ytc = N ptyt = Ct

Importantly, in the symmetric firm equilibrium, the value of waiting to enter is zero, despite the entry decision being subject to sunk costs and exit risk; i. e., there are no option-value considerations pertaining to the entry decision. This happens because all uncertainty in the model (including the “death” shock) is aggregate.

1.3.1 EQUILIBRIUM UNDER MONOPOLISTIC COMPETITION

Given household’s demand for each individual good ct H t

P (-r

dt M = ( Pt M- costt ) c M = ( Pt H- costt ) Ct

P

(1.5)

where COStt is the (nominal) marginal cost of production.

Let us now assume that there is infinity of monopolistic firms, each one acts independently in the choice of its price in every period, and has no impact on the price index or the consumption index. Accordingly, from the first order conditions the profit-maximizing price is

q

pt =--------costt

1 q-1 t

for each firm, which corresponds to a common and constant markup for all goods:

9

9-1

1.3.2 EQUILIBRIUM UNDER BERTRAND COMPETITION

Let us denote expenditure in each sector of economy as EXPt = CtPt, then household’s demand for each indi-

/ \ i \ Pt iu) -

vidual good (1.3) can be re-written as ct M = EXPt------j——. Using expression for price index Pt (1.2)

Pt

we get that profit of a firm (1.5) is:

-e 1—e

Pt M

( ^\—1

dt (H) = (Pt (H) - cost, )c M = (Pt M - cost, )EXpt p t Hv,

I pt (h) dh

Under competition in prices we derive Bertrand equilibrium price as price that maximizes firms’ profit taking as given the prices of the other firms and expenditure in each sector. First order conditions of the profit maximization problem are:

f , Ye a( i \ , W (1 - 0) P‘ ^ (P‘ (m)- C°St<)P‘ ^

{ pt (m) - 0 (pt (m)- c°stt) pt (m) }--r-, ,1----------------

1 J J Pt M

Using the fact that equilibrium is symmetric we can replace I pt (w) = Ntpt pt

we get:

q (n-1) +1

(N,-1)(e-1)

COStt for each firm,

which corresponds to markup of:

i(n, ) =

S(N, -1) +1 (N, -1)(S -1)

1.3.3 EQUILIBRIUM UNDER COURNOT COMPETITION

Given household’s demand for each individual good C (w) (1.3) and using that in equilibrium demand equals supply — y (w) inverse demand function will be:

/ \ yt (w) 0

pt (w) =--------------------EXP

e-i

J yt (u) e du

where expenditure in each sector of economy are EXPt = CtPt. We get that profit of a firm (1.5):

dt (w)=( Pt (w)- cost, ) yt (w)

-i

y, (w) 0

t{ Vi EXP, - cost,

J yt (w) 0 dw

y (w)

Under competition in quantities each firm chooses yt (w) that maximizes profits taking as given supply of other firms. First order conditions of the profit maximization problem are:

_i

ß _1 ) y (J) ß

—1 { Vi EXP _

9

f yt(u)

u) ß du

ß_l) yt (u)

ß_2 u) ß

ç ß_1

f yt (u) ß d u

2 EXPt = costt

0-1 0-1

Using the fact that equilibrium is symmetric we can replace J yt (u) 0 du = Ntyt 0 . And solving for yt

(q -i)(N -i)

we

obtain: yt = ---------^—- EXp . Substituting back into inverse demand function, we get the equilibrium price:

0Nt costt

9

p —_________qNt_______rnst for each firm,

p'—(e -m -i)cos,t

which corresponds to markup for all goods:

( AT \ 0Nt

P(Nt )= '

(N-i)(e-1)

1.4 FIRM ENTRY AND EXIT

In each period there are Nt firms in economy and unlimited number of potential new entrants. Potential new entrants are forward-looking, and foresee their excepted profits ds in every future period s > t +1 as well

as the probability d (in every period) of incurring the exogenous “ death” shock. Entrants at time t only start producing at time t +1, which introduces one-period time-to-build lag in the model. The exogenous exit shock occurs at the very end of the time period (after production and entry). A proportion d of new entrants will therefore never produce. Prospective entrants in period t compute their expected post-entry value (vt ) given by the present discounted value of their expected stream of profits {ds (w)ir

J S=t +1

¿La (i - «)] i H

11 n u\c, ) A 1

(1.6)

This also represents the value of incumbent firms after production has occurred (since both new entrants and incumbents then face the same probability 1 — d of survival and production in the subsequent period). Entry occurs until firm value is equalized with the entry cost, leading to the free entry condition

ut M = wt A. (1.7)

At

The condition holds as long as the number NE t of new entrants is positive. It is assumed that macroeconomic shocks are small enough for this condition to hold in every period.

Finally, the timing of entry and production assumptions imply that the number of producing firms in period t is given by

N, =(1-d)(N+Nt,-). (1.8)

The number of producing firms represents the capital stock of the economy. It is an endogenous state variable that behaves much like physical capital in the benchmark RBC model.

1.5 HOUSEHOLD BUDGET CONSTRAINT AND INTERTEMPORAL DECISIONS

Without loss of generality let us assume that households hold only shares in a mutual fund of firms.

Let xt be the share in the mutual fund of firms held by the representative household entering period t. The mutual fund pays a total profit in each period (in units of currency) equal to the total profit of all firms that produce in that period, PtNtd . During period t, the representative household buys xt+1 shares in a mutual fund of NH t = Nt + Ne t firms (those already operating at time t and the new entrants). Only Nt+1 = (1 — d) NH t firms will produce and pay dividends at time t +1. Since the household does not know which firms will be hit by the exogenous exit shock d at the very end of period t, it finances the continuing operation of all pre-existing firms and all new entrants during period t. The date t price (in units of currency) of a claim to the future profit stream of the mutual fund of NH t firms is equal to the nominal price of claims to future firm profits, Ptut.

The household enters period t holding xt of mutual fund shares, it receives dividend income, the value of selling its initial share position, and income from supplying labor. The household allocates these resources between purchases of xt+1 shares to be carried into next period, consumption Ct. So in each period household budget constraint (in units of consumption) is of the form:

vtNH ,txt+i + Ct = (dt + vt) Ntxt + wtL (1.9)

The household maximizes its expected intertemporal utility subject to (1.9). The Euler equation for share holdings is:

( C+1 \dt+1 + Vt+1)

u, = ß (1 - ë) E,

u '(c, )

(1.10)

As expected, forward iteration of this equation and absence of speculative bubbles yield the asset price solution in equation (1.6).

1.6 AGGREGATE ACCOUNTING AND EQUILIBRIUM

Summing up individual budget constraints of households (1.9) across all the economy and imposing the equilibrium condition Xt+1 = xt = 1 "t we obtain the aggregate accounting identity that should be fulfilled in each period:

Ct + NE,tVt = WtL + Ntdt : (1.11)

Total consumption plus investment (in new entrants) must be equal to total income (part of which is coming from supplying labor and the other — from return on investments in the form of dividends).

As opposed to RBC model, in the current model we need to distinguish between labor that is used in production of consumption goods and labor employed in setting-up new firms (increasing capital stock of the economy). So current model can be viewed as a two-sector economy. While in the benchmark RBC model, capital stock is accumulated by using as investment part of the output of the same good used for consumption and all labor is allocated only to the productive sector of the economy.

The total output of the economy, Yt, is equal to total income, w L + N d . On the other side, Y is also given

n/\ t t t *

by consumption output, YC (= Ct), plus investment output, ft v . We also note that, firm value vt can be viewed as the relative price of the investment “good” in terms of consumption.

Equilibrium on the labor market requires that the sum of amount of labor used in production of consumption goods Lt and amount of labor employed in setting-up the new entrants’ plants Lf must equal aggregate labor supply:

L+L = l ,

where the amount of labor used in production of consumption can be expressed as Lt = Ntlt, and the

E _ Ar hE,t

amount of labor used to build new firms can be expressed as Lt = NE , t .

A

When labor supply is fixed, there are no labor market dynamics in the model, other than the determination of the equilibrium wage along a vertical supply curve. In the model, even when labor supply is fixed, labor market dynamics arise in the allocation of labor between production of consumption and creation of new firms. The allocation is determined jointly by the entry decision of prospective entrants and the portfolio decision of households who finance that entry. The value of firms, or as we also call it the relative price of investment in terms of consumption vt, plays a crucial role in determining this allocation. (When labor supply is elastic, labor market dynamics operate along two margins as the interaction of household and firm decisions determine jointly the total amount of labor and its allocation to the two sectors of the economy.)

Uniqueness and stability of the model equilibrium is guided by the choice of the utility function. Here following BGM (2007) we assume that utility function is of the form:

j.

u(C,l) = lnc - XLl) / 1, (i.2i)

where X > 0 and f > 0 is Frish elasticity of labor supply to wages, and intertemporal elasticity or substitution in labor supply. The choice of utility function of this particular form was guided by results in King, Plosser, and Rebelo (1988): Given separable preferences, log utility from consumption ensures that income and substitution effects of real wage variation on effort cancel out in steady state; this is necessary to have constant steady-state effort and balanced growth if there is productivity growth. BGM (2007) provides also the proof that the steady state will be non-explosive. E. Stepanova (2011) analyses differences in steady states under different forms of market competition.

2 MODEL DYNAMICS - PROPAGATION OF SHOCKS

In this section we study transmission of economic fluctuations due to shock to the entry cost by means of computing impulse response functions. We perform comparison between classical supply shock (productivity shock) and entry cost shock. We are interested in economic implications of government policy aimed to support and protect green technology companies.

The model allows for a large variety of combinations of substitutability between goods (6 ) and markup (m), which in turn depends on the form of competition. We consider cases of Cournot, Bertrand and monopolistic competition discussed in section 1.3.

Calibration of structural parameters is standard and follows King and Rebelo (1999). The time unit is a quarter. The discount factor, /3, is 0.99, while the rate of business destruction, d, equals 0.025 implying an annual rate of 10%. The Frish elasticity of labor supply is f, and we fix it at 4 as in King and Rebelo (1999).

Government spending is financed by lump sum tax and is 20% of total output of the economy, replicating the real world economy.

2.1 DIFFERENCES IN RESPONSE TO A PRODUCTIVITY SHOCK AND A SUNK ENTRY COST SHOCK

A shock of 1% increase in productivity decreases marginal cost of production and respectively causes markups decrease. A shock of 1% increase in sunk entry costs augments up-front investments and respectively causes markups increase. Keep in mind that we assume, for example, government policy of obligatory use of green technologies if a company wants to enter the market. Of course, this creates additional preproduction investments into green technologies and increases sunk costs of firm entry to the market. High entry cost compared to the size of the market leads to a smaller number of competitors and thus to higher markups. As consequence of markups moving in contrary directions for these two types of shocks, all other variables also respond contrarily. We may say that productivity shock is a positive one, while sunk entry cost shock is a negative one. To correct this and keep the same direction of variable responses for both shocks we will consider a shock of 1% decrease in sunk entry costs, and will compare it to a shock of 1% increase in productivity. Keep in mind that decrease in sunk entry costs corresponds to government subsidizing use of green technology.

In case of the productivity shock we set the steady state productivity value to A = 1 and the baseline value for the entty cost is set to h = 1. Shock to the model technology parameter follows the first order autoregressive process: At = 9AAt-l + £A,t where hat above the variable means percent deviation from steady state level for this variable, jA £ (0,1) is the autocorrelation coefficient, and eA t is a white noise disturbance, with zero expected value and standard deviation a2 .

£ a

In case of the sunk entry cost shock we set the steady state entry cost value to V = 1 and the baseline value for productivity to A = 1. Shock to the sunk entry cost parameter follows the first order autoregressive process:

+ £v t where hat above the variable means percent deviation from steady state level for this

variable, e(0,1) is the autocorrelation coefficient, and £v t is a white noise disturbance, with zero expected value and standard deviation c .

Figure 1 depicts percentage deviations from the steady state of key variables in response to a 1% productivity shock and sunk entry cost shock with persistency 9A = = 0,9. We simulate for the case

of Cournot competition and the degree of substitutability is 6 (6 = 6 ). Time on the horizontal axis is in quarters.

f1 f11

— = —

1 n t 1 n J

- sunk entry cost shock -sunk entry cost

technology shock 0 -

number of firms

consumption

markup

10 20 30 40 50

total profit s

10 20 30 40 50

profit_ind

10 20 30 40

firm value

5 10 15 20 25 30 35

Figure 1. Decrease in sunk cost of entry shock vs production shock ( 0 — 6 ) - impulse response functions (IRF).

-0.1

We see that the productivity shock has a stronger effect in terms of deviation from the steady state. Response of the markup and the number of firms to the productivity shock is more than double in comparison with the sunk entry cost shock. Explanation of this is the fact that the productivity shock initially impacts a bigger number of firms (i. e., all firms that are on the market at the moment of the shock), while decrease in the entry cost initially impacts a smaller number of firms — only “new entrant firms”. So the propagation of a productivity shock happens with a higher strength.

We further proceed with the comparison of variables response to both shocks. In advance we need to say that even if directions of convergence back to the steady state are the same, the incentives to this behavior are different.

First, we explain our intuition for the variables response to the sunk entry cost shock. The number of entrants increases, it strengthens market competition and reduces the markups. A reduction in the markup means a reduction in profits and, consequently, in the firms’ value, as it is discounted sum of future profits. The consumption initially decreases as households decide to postpone it in favor of investments and the entrance to the market by investing into creation of new firms. The firms’ value is very cheap. At the same time households feel poorer due to reduction in profits as it is a source of their income, and no changes in their wages as another source of their income, so they increase labor supply.

An increase in the total number of firms leads to increase in labor demand from the firms’ side and this pushes up wages. Thus households reduce labor supply. At the same time as the total profits and the firms’ value grow households feel richer and increase their consumption. They start decreasing investments as creation of new firms becomes more expensive due to the wages increase.

Table 1. Differences in response to a productivity shock and a sunk entry cost shock.

Variable Initial response Behavior along the transition path

A shock h shock A shock h shock

consumption + -

individual profit + - Decreases Increases

wage + No reaction Decreases Hump shaped that starts from increase

output + -

firm value No reaction - Hump shaped that starts from increase Increases

Figure 2. Increase in sunk cost of entry shock - comparison of different forms of competition (6 — 6,6 — 3) - IRF.

At some point the variable “the number of new entrants” crosses its steady state level. It happens at the same time for the both shocks. At this point the total number of firms reaches their maximum and the markup — their minimum level. From this moment net exit from the market starts. This makes the markup start increasing towards the steady state level. Individual profits as well as individual output start increasing. Wages start decreasing with decreasing labor demand from the firms’ side. Labor supply increases in response.

As shocks vanish variables converge to initial steady state levels.

The Table 1 summarizes main differences in the variables behavior for both shocks.

The explanation for these differences is the dissimilar incentives driving the variables reaction. Contrary to a sunk entry cost shock productivity shock increases individual output and profits on impact. There is a big

homogeneous good

number of firms

consumption

total profits

profit_ind

total output

output

Figure 3. Increase in sunk cost of entry shock - Cournot competition (6 — 6 ,6 — 20 , 6 = TO) - IRF.

demand for labor as production is profitable, that is why wages are initially pushed up. As there are more profits in the economy and also wages are high households feel rich — so they have a higher consumption level than in

( ) — nE ,t

(u) — wt a doesn’t change as two

the steady state. The firms’ value being equal to the cost of entry effects — increase in labor productivity and increase in labor cost — cancel each other out.

2.2 RESPONSE TO A SHOCK UNDER DIFFERENT TYPES OF COMPETITION

It is important to outline the difference between variables responses in case of different markup types, i. e. different forms of competition. On Figure 2 we report impulse response functions for a temporary shock of 1% increase in sunk entry cost. We consider degree of substitutability 6 of 6 and 3 (6 — 6 , 6 — 3 ) and we consider three forms of competition (in quantities — in green, in prices — in blue and monopolistic — in red).

First we report difference in the variables steady state values. Under competition in prices and in quantities (for 6 — 6 ) the market structure is generated endogenously and the steady state markups are respectively 23,7% and 36,8%, both belonging to the empirically reasonable range, for the monopolistic competition markup is 20% and is constant. When firms compete in prices the equilibrium markups are lower, which in turn allows for a lower number of firms to be active in the market: this implies that the model is characterized by a lower number of goods compared to the model with competition in quantities. Since this requires a smaller number of new firms to be created in the steady state, lower markups are associated with a lower saving rate as well.

In spite of these substantial differences in the steady state of the economy, Figure 2 shows that the quantitative reaction of the main aggregate variables to the shock are similar under all forms of competition. The impact of the shock is strengthened by competition effect. Along the transition path we see how new firms’ entry starts reduction of markups by strengthening market competition. But we cannot unambiguously conclude which type of competition creates stronger response to the shock as it differs from variable to variable and also with degree of substitutability.

teta 6

2.3 RESPONSE TO A SHOCK UNDER DIFFERENT DEGREE OF SUBSTITUTABILITY

When we increase the degree of substitutability (for example as we pass from 6 — 6 to 6 — 20 and 6 = to — case of homogeneous good) the same qualitative results hold, but the impact of the shock on competition and mark ups becomes stronger.

We depict this situation on Figure 3 for the case of Cournot competition.

The noticeable difference is the total profits decrease along all transition path in case of low degree of substitutability, while total profits are hump-shaped in case of high degree of substitutability. This can be explained by significant decrease in the number of firms in case of low substitutability so that individual profits generated by firms are not enough to make total profits grow.

CONCLUSIONS

We see that government intervention aiming to promote use of green technologies by restricting market access to firms that are not having them reduces the number of firms on the market, increases their profits and motivation to produce more. Government subsidizing entry for firms using green technologies have the opposite influence on economy: we see strengthening of competition, decrease in markups and reduction of profits. We studied the effect of different forms of competition and different degrees of products substitutability. The model can be based on real country economy’s data, which will give the country’s government real figures to measure impact of its green technology policies.

Further research directions are the following: within current model framework it will be interesting to see the impact of different taxation schemes. In the model government spending is financed by the lump-sum tax, while it would be more realistic to consider different forms of financing of government spending. It will be also interesting to study the same problem in the framework of agent-based model, where one can allow for differences across firms in their productivity based on whether they are or are not using green technology.

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