Heijdra Foundations of Modern Macroeconomics (Oxford, 2002)

firms, an increase in govern-

. fE-locus. Note furthermore and side of (13.31). There number of firms affects the ")ct. The first term on the on aggregate demand of an increase in the number of

. This is the diversity effect. the negative effect on aggre- - 'ases, total overhead costs

tus theoretically ambiguous >osite directions. Our usual n correspondence principle se the model is stable for ility condition (al T aN < 0)

e GME line. IT\ (an

v zp

(13.32)

left-hand side are strictly

le ambiguity regarding the ity is resolved by ignor- :Ay of demand (9) and the parameter to regulate these - 7, p. 298) formulation is —1) in (13.2). Since 0 > 1 is petitive equilibrium (i.e. > 1) and strong enough

(13.33)

nment consumption shifts of firms is predetermined

!ition does furnish additional van der Ploeg (1996, p. 1291),

r different examples.

Chapter 13: New Keynesian Economics

(at N = No) and output rises as the economy jumps from E0 to E 1 . This is the shortrun multiplier given in (13.20). At point E1 there are super-normal profits to be had and entry of new firms occurs. Gradually, the economy moves along GME 1 from E1 to E2 and both output and the number of firms increase towards their new equilibrium values. Furthermore, as the lower panel of Figure 13.2 shows, the real wage rate also increases during transition. So, even though the model may not be vintage Keynesian in its basic mechanism, it does have some Keynesian features since the real wage and aggregate output move pro-cyclically.

Whereas in the first approach the long-run output multiplier exceeds the shortrun multiplier, this conclusion is reversed in the second approach. Startz (1989, p. 741) implicitly resolves the ambiguity concerning the slope of the GME locus by eliminating preference for diversity altogether, i.e. by setting ri = 1 in (13.2). The GME locus is downward sloping in that case as entry of firms only does bad things to the economy (such as using up additional resources in the form of overhead labour):

Furthermore, the pricing rule (13.28) implies a constant real wage in that case. In a diagram like Figure 13.2, the GME curve is downward sloping in the top panel and the wage curve is horizontal in the bottom panel. At impact the multiplier is as in (13.20) but during transition the increase in the number of firms leads to a reduction in aggregate output. The long-run effect on output is equal merely to the first round of the multiplier process in (13.20) (i.e. the impact effect of the shock):

This prompts Startz (1989, p. 747) to conclude that ". . in the long run the short-run multiplier is eliminated by free entry".

In the most general version of the model, with 77 unrestricted, the long-run multiplier can be solved by combining (13.29) and (13.31):

where the inequality follows from the fact that the denominator is strictly between zero and unity if p > 1 (see (13.32)). Hence, whereas fluctuations in profit income explain the multiplication of the impact effect in the short run, it is the preference for diversity effect which plays this role in the long run.

Although Startz (1989, p. 751 n. 13) justifies the elimination of diversity preference by appealing to computational advantages, it is not an innocuous assumption at all as the discussion above reveals. In essence, if the diversity parameter (p) is greater than unity there are economy-wide increasing returns to scale that help

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The Foundation of Modern Macroeconomics

explain the "long-run" multiplier under free exit/entry of firms. Indeed, in the long run profits are zero and Y = OWNF = WL which implies (by (13.29)) that the macroeconomic "production function" can be written as:

Pv

,uk

Changes in the aggregate supply of the production factor(s) (labour in this case) are magnified more than proportionally. The importance of increasing returns to scale for Keynesian economics has been stressed time and again by seasoned warriors like Weitzman (1982, 1984, 1994) and Solow (1986, 1998) and allowing for preference for diversity is one particularly simple way to introduce scale economies. ?

13.1.5[1We effects

In a famous passage in the General Theory, Keynes argued that seemingly useless government consumption could actually improve welfare for the agents in the economy:

If the TreasurydV\were to fill old bottles with bank-notes, bury them at suitable depths in disusedkdGcoal-mines which are then filled up to the surface with town rubbish, and leave it to private enterprise on well-tried principles of laissez- faire to dig the notes up again (... ), there need be no more unemployment and, with the help of the repercussions, the real income of the community, and its capital wealth also, would probably become a good deal greater than it actually is. (1936, p. 129)

In the jargon of modern economics, Keynes suggests in this quotation that the marginal cost of public funds (MCPF, see Chapter 10) is zero or even negative: useless spending turns out to be useful after all! To conclude this section we now investigate the link between fiscal policy multipliers and the welfare of the representative agent. It turns out that the monopolistic competition model has some Keynesian aspects in this regard although they are not quite as extreme as the quotation suggests.

One of the major advantages of macroeconomic models based on explicit microeconomic foundations is that they provide an explicit link between macroeconomic concepts (such as aggregate output, employment, etc.) and the level of welfare experienced by the representative household. To conduct the welfare analysis for the monopolistic competition model it is convenient to use the so-called indirect utility function, rather than the direct utility function given in (13.1). The indirect utility function is obtained by substituting the optimal plans of the representative

7 In the model developed here (and in most models in the literature) all scale economies are external to the firm in the long run. With a constant markup the zero profit condition in combination with markup pricing implies a unique (constant) optimal long-run firm size: Y F/[(p, — 1)k]. Hence, aggregate output expansion is solely due to increases in the number of firms in the long run.

household (namely (13.1 :mezzo above for

= IV +11,1

.1);

I

:;zed with this exprk.)

.1 policy. In the inte scussed above in suL iirst consider the cal

-:iced by means of a

11 aggregate profit ina

3.38) we obtain the to

I e N and thus also IA

a tax-financed fiscal exp

sR P)r-

T 31-

where we have substit,4

- ession. Under mono and the wc...

competition. The intuit ,on in the goods r

ut view. By raising go% Li

..e in the right, Wc ▪ must also be finai.‘ ipansion is not costles1 - ,.nced fiscal expans.

So unless there are o it spending discu ,

• not increase IN does not hold. This un-1

eN z lained by two sae labour market, and

studying the case (disc

• ck is financed by red is-dLG). In that case th

► of firms. Indeed, in the long rriplies (by (13.29)) that the I as:

(13.37)

:or(s) (labour in this case) are increasing returns to scale ain by seasoned warriors like and allowing for preference

r scale economies!

gued that seemingly useless fare for the agents in the

them at suitable depths in rith town rubbish, and leave it :o dig the notes up again (... ), of the repercussions, the real I probably become a good deal

s in this quotation that the -o or even negative: useless s section we now investigate -)f the representative agent. s some Keynesian aspects the quotation suggests.

's based on explicit microik between macroeconomic

.) and the level of welfare uct the welfare analysis for to use the so-called indirect cn in (13.1). The indirect plans of the representative

all scale economies are external

t condition in combination with size: Fi[(p. — 1)k]. Hence,

of firms in the long run.

Chapter 13: New Keynesian Economics

household (namely (13.6) and (13.8)) into the direct utility function (13.1) (see the Intermezzo above for details):

Armed with this expression we can evaluate the welfare effects of expansionary fiscal policy. In the interests of brevity, we only analyse the short-run multipliers discussed above in subsections 1.2. and 1.3.

First consider the case in which the increase in government consumption is financed by means of a lump-sum tax increase. By substituting the expression for real aggregate profit income (T1.3) and the government budget constraint (T1.4) in (13.38) we obtain the following expression:

Since N and thus also W, P, Pv are constant in the short run, the welfare effect of a tax-financed fiscal expansion is simply the derivative of V with respect to G:

where we have substituted the output multiplier (given in (13.20)) to simplify the expression. Under monopolistic competition, there is an intimate link between the multiplier and the welfare effect of public spending which is absent under perfect competition. The intuition is that under monopolistic competition there is a distortion in the goods market and the economy is "too small" from a societal point of view. By raising government spending output rises and that in itself constitutes a move in the right, welfare-enhancing, direction. Of course government consumption must also be financed somehow (here by means of lump-sum taxes) so that the expansion is not costless. Indeed, (13.40) shows that the overall effect of a lump-sum financed fiscal expansion is negative.

So unless there are other reasons (such as public goods aspects due to government spending discussed by Heijdra and van der Ploeg, 1996) the government does not increase welfare as a result of its increased spending and Keynes' insight does not hold. This un-Keynesian element of the monopolistic competition model is explained by two of its key properties: (1) the real wage is flexible and clears the labour market, and (2) every unit of labour contributes to production in the

economy.

The importance of the second property of the model can be demonstrated by studying the case (discussed in detail in subsection 1.3) in which the spending shock is financed by reducing the number of (unproductive) civil servants (i.e. dG = —WdLG). In that case the lump-sum tax is constant and the relevant expression for

375

The Foundation of Modern Macroeconomics

indirect utility is:

Pv/P

from which we obtain the welfare effect:

In this case only the beneficial effect of government-induced output expansion is operative and welfare rises. The intuition is the same as in Keynes' story: units of labour are shifted from socially unproductive to productive activities. The monopolistically competitive sector absorbs the former civil servants without prompting a change in the real wage.

Intermezzo

Multipliers and the marginal cost of public funds. There exists a simple relationship between the macroeconomic concept of the output multiplier and the public finance concept of marginal cost of public funds (MCPF). This link is particularly useful to study issues of optimal public spending and taxation. As was pointed out in Chapter 10, MCPF measures how much it costs to raise a guilder of public revenue. In the context of the monopolistic competition model MCPF is defined as follows:

MCPF r 1 dV (a) Uc dG'

where Uc is the marginal utility of composite consumption. Intuitively, the minus sign appears on the right-hand side to convert benefits into costs (a negative benefit is equivalent to a positive cost!) and the division by Uc occurs in order to compare "likes with likes" and to render MCPF dimensionless.

It is not difficult to show that Uc equals P/Pv. Recall that the representative household maximizes utility, U(C, 1 — L), subject to the budget constraint, IF = PC + WN(1 — L). The first-order conditions for this problem are Uc = AP and U1_,/, = AWN, where X is the Lagrange multiplier of the budget constraint representing the marginal utility of (full) income, i.e. X = dU/dIF (see Intriligator, 1971, ch. 3). The indirect utility function (13.38) shows that dV/d/F 1/Pv dU/dIF. By combining these results we derive that Uc = P/Pv so that (13.40) and (13.42) can be re-expressed in terms of MCPF:

U dGLG=

Hence, it costs (more t of revenue if lump-su,.. .. negative if useless civil 9 M. Heijdra and van c competition model and u which optimal public spe

[

13.2 Monopolistic

`n the monopolistic compel iv marized in Table 13.1) 1 d the nominal wage are letermined within the MO(

.0 the model and study

- gat money plays a role it simplest of these and 1 t.presentative household. 1

U [ca(1 -L) 1 -1° c.

i►aere M is nominal mont: , ney, Mo, and the

PC + WN (1 — L) + M

10.ich says that the sum ( • left-hand side) must eci

The household chooses

Jney balances (M) in of ire:8

PC = aPIF, IF Mu —

WN(1 - = p(1 - «}.,

M = (1 — i3)/F .

ne first two expressions an -lough IF now includes i

Shows that money demand

The demand for variety j of d

(13.411'

n . (13.4_

induced output expansion e as in Keynes' story: units eductive activities. The mono- 1 servants without promptir

tnds. There exists a simple the output multiplier and )lic funds (MCPF). This link hlic spending and taxation. - low much it costs to raise monopolistic competition

(a)

Isumption. Intuitively, the ert benefits into costs (a id the division by Uc occurs

MCPF dimensionless. Recall that the representact to the budget constraint,

-"- is problem are Uc = plier of the budget con-

income, i.e. A = dU/dIF iction (13.38) shows that

is we derive that Uc P/Pv - rns of MCPF:

Chapter 13: New Keynesian Economics

Hence, it costs (more than zero but) less than one guilder to raise a guilder of revenue if lump-sum taxes are used (expression (b)) and the MCPF is even negative if useless civil servants can be made socially productive (expression (c)). Heijdra and van der Ploeg (1996) develop a more general monopolistic competition model and use the concept of MCPF to derive the conditions under which optimal public spending is countercyclical.

13.2 Monopolistic Competition and Money

In the monopolistic competition model used throughout the previous section (and t•immarized in Table 13.1) money is abstracted from and as a result nominal prices ld the nominal wage are indeterminate although, of course, relative prices are determined within the model. The objective of this section is to introduce money to the model and study its properties. Although there are several ways to ensure that money plays a role in the model (see Chapter 12), we focus attention on "le simplest of these and postulate that real money balances yield utility to the

representative household. The utility function (13.1) is changed to:

where M is nominal money balances. The household has an initial endowment of money, Mo, and the budget constraint (13.5) is changed to:

which says that the sum of spending on consumption, leisure, and money balances (the left-hand side) must equal total wealth (the right-hand side of (13.44)).

The household chooses composite consumption (C), labour supply (L), and money balances (M) in order to maximize (13.43) subject to (13.44). The solutions are:8

The first two expressions are qualitatively the same as before (see (13.6) and (13.8)), although IF now includes initial money balances. Furthermore, equation (13.47) shows that money demand is proportional to full income. For future reference we

8 The demand for variety j of the composite consumption good is still given by (13.7).

377

The Foundation of Modern Macroeconomics

Table 13.2. A simple monetary monopolistic competition model

substitute the solutions (13.45)-(13.47) back into the direct utility function (13.43) to obtain the indirect utility function-see equation (T2.8) in Table 13.2 above.

Assuming a constant money supply (M0), the money market equilibrium condition is:

The rest of the model is unchanged and we summarize the main equations of the monetary monopolistic competition model in Table 13.2.

It is tempting (though wrong) to conclude from the form of the indirect utility function (T2.8) that the government could increase the welfare of the representative household by simply bringing more money into circulation (and boosting full income, IF, in the process), for example by engineering a helicopter drop of money (dMo > 0). The reason why such a ploy would not work is that money is neutral in this model and the classical dichotomy holds (see Chapter 1). This can be demonstrated formally by noting that the equilibrium conditions (in Table 13.2) are homogeneous of degree zero in WN , P, T, 11 , IF, and Mo (see Dixon, 1987, p. 141). By substituting WN , 4"P, 4- T 4-11 , 41F, and "-Alo > 0) into Table 13.2 the real equilibrium is unaffected. All that happens if the money supply is multiplied by is that all nominal variables are increased equiproportionally and all real variables are unchanged. Hence, a helicopter drop of money does not succeed in raising household welfare because both IF and Pv go up by the same proportional amount thus keeping V in (T2.8) unchanged. The upshot of this discussion is that monopolistic competition does not introduce monetary non-neutrality. Put differently, if money is neutral in a model-economy without monopolistic competition

then it is also neutral if (Silvestre, 1993, p. 122).

The model can be sump (GME) locus is obtained 1,1 market equilibrium (MME) (T2.2) as well as (T2.3)-(T2.

= a [1 - NF - 4,1

Y

1 - _

Mo1= - 13) R1- 2,

P

The two loci provide a cle,;. run, N and thus W are fix( money supply does not a, , rium output. According to equiproportional increase it

The GME and MME loci a financed increase in public c ) but a reduction in the d, Since nominal money balar and supply of real money b

prices of different varieties a

From the monetary side of

:ices and wages are fle x . ,

I

13.3 Sticky Prices are

In the previous section it :11y competitive agents in non-neutral. This is not to

macroeconomic model is predictions. In,‘

how the monopolistic comp _ cults that are quite dit:

un model

(T2.1)

(T2.2)

(T2.3)

(T2.4)

(12.5)

(T2.6)

(12.7)

(T2.8)

direct utility function (13.43) 12.8) in Table 13.2 above. money market equilibrium

. L! the main equations of the 13.2.

form of the indirect utility the welfare of the represen- o circulation (and boosting ineering a helicopter drop of 1 not work is that money is ( see Chapter 1). This can be !conditions (in Table 13.2) are ' ' , (see Dixon, 1987, p. 141). > 0) into Table 13.2 the real PV supply is multiplied by is Ally and all real variables are not succeed in raising house- ne proportional amount thus ,scussion is that monopolistic Tv non-neutrality. Put differ- t monopolistic competition

Chapter 13: New Keynesian Economics

then it is also neutral if monopolistic competition is introduced into the 'model (Silvestre, 1993, p. 122).

The model can be summarized with two equations. The goods market equilibrium (GME) locus is obtained by using (T2.2)-(T2.4) and (T2.6) in (T2.1). The money market equilibrium (MME) locus is obtained by using the second expression of (T2.2) as well as (T2.3)-(T2.4) in (T2.7):

The two loci provide a clear demonstration of the classical dichotomy. In the short run, N and thus W are fixed and GME determines equilibrium output. Since the money supply does not appear in (13.49), monetary policy cannot affect equilibrium output. According to (13.50), an increase in the money supply leads to an equiproportional increase in the price level.

The GME and MME loci can also be used to compute the short-run effects of a taxfinanced increase in public consumption. An increase in G leads to a boost in output Y but a reduction in the demand for real money balances (as real full income falls). Since nominal money balances Mo are constant, the price P rises to bring demand and supply of real money balances back into equilibrium. The nominal wage and prices of different varieties also rise equi-proportionally. In summary:

From the monetary side of things the model is more classical than Keynesian if prices and wages are flexible.

13.3 Sticky Prices and the Non-neutrality of Money

In the previous section it was demonstrated that the presence of monopolistically competitive agents in the economy does not in and of itself render money non-neutral. This is not to say that the introduction of price-setting agents in a macroeconomic model is merely a theoretical nicety yielding no novel insights or additional predictions. Indeed, in the first section of this chapter it was shown how the monopolistic competition model with flexible prices and wages generates results that are quite different from the standard competitive model. An additional

379

The Foundation of Modern Macroeconomics

advantage of assuming monopolistic, rather than perfect, competition is that one can do away with the fictional notion of the Walrasian auctioneer.

By modelling price-setting agents explicitly, it is also possible to study quite precisely the conditions under which such an agent would change his price (or keep it unchanged) following a shock in some nominal variable such as the money supply or the money wage rate (Rotemberg, 1987, p. 71). The key ingredient of the New Keynesian approach is to postulate that it costs the firm real resources in order to change its price. As a result, prices may not be adjusted after some nominal shock and money may be non-neutral. In the remainder of this section a number of the main macroeconomic price-adjustment models will be discussed. The key feature distinguishing these models lies in the nature of the price adjustment cost that are postulated.

As is pointed out by Rotemberg (1982, p. 522) there are two main reasons why prices may be costly to change. First, there may be administrative costs having to do with informing dealers, reprinting price lists, etc. Such costs tend to have the nature of a fixed cost per price change, independent of the magnitude of the change: it costs the same to reprint your restaurant menu card when you double or triple your prices. Such price adjustment costs are often referred to as menu costs in the new Keynesian literature. The second reason why prices may be costly to change is that there may be an implicit cost due to an adverse reaction of customers to large price changes. According to this view customers may prefer frequent small price changes over infrequent but large price adjustments. It is conventional to assume that such costs are increasing and convex in the price change. 9

We now turn to a discussion of some of the most popular models of price setting. In the first model only menu costs play a role (subsection 3.1) whilst in the second we assume that price adjustment costs are quadratic (subsection 3.2). In subsection 3.3 we discuss an alternative setting in which price adjustment costs are random and are either infinite or zero in any particular period. The models in subsections 3.2-3.3 both give rise to a new Keynesian Phillips curve which is similar in form (though not in interpretation) to the expectations-augmented Phillips curve of Friedman and Phelps (see Roberts, 1995, pp. 979-980).

13.3.1 Menu costs, real rigidity, and monetary neutrality

In this subsection we develop a simple monetary monopolistic competition model in which price-setting firms face small menu costs if they wish to change their prices. The model is a simplified version of Blanchard and Kiyotaki (1987) in that the labour market is assumed to be competitive and populated by wage-taking agents (firms and the representative household). Hence, the nominal wage is flexible and

9 Such costs are reminiscent of the adjustment costs often postulated in the theory of firm investment. See the discussion of Tobin's q theory of investment in Chapters 2 and 4.

=hour demand and sur :dive labour market is t..

identifies in a straightforw,. -ment runs into.

As in Blanchard and Kiyo tv function which is ad

on the one hand al

U(C, M IP, L) U l (C,M

= (M,

I re A > 0 is a simple sc

,ow) and a regulates the b.. .4et restriction is given b,

PC + M = WN L + Mo - r.

....cre I represents total situ site consumption is clef

., sent (i.e. we set 77 =

IISSumed that the number a money balances, and I

.3.53). Again a simple two-5 - st stage the household ch( subject to the b

PC = aI,

M = (1 — a)1,

1 71 (1 IP) = a" (1 — a) 1

re I/ 1 (11P) is the incl... ; e second stage, the househi subject to the deti:

the expressions for lab income:

L = ice(1 - °I-a V

yi. -

/i a' (1 — a) l-a

It is obtained by substitut

'ect, competition is that one 1 auctioneer.

) possible to study quite pre- I his price (or keep it ' such as the money supply e key ingredient of the New real resources in order to d after some nominal shock is section a number of the

e discussed. The key feature ice adjustment cost that are

are two main reasons why ministrative costs having to ch costs tend to have the he magnitude of the change: 1 when you double or triple erred to as menu costs in the s may be costly to change is action of customers to large prefer frequent small price ft is conventional to assume

:hange.9

• .lar models of price setting. Dn 3.1) whilst in the second ibsection 3.2). In subsection -.lent costs are random and odels in subsections 3.2-3.3 I is similar in form (though Phillips curve of Friedman

I neutrality

polistic competition model `hey wish to change their and Kiyotaki (1987) in that Ilted by wage-taking agents ominal wage is flexible and

:ulated in the theory of firm

.apters 2 and 4.

Chapter 13: New Keynesian Economics

labour demand and supply are equated. The main advantage of assuming a competitive labour market is that it facilitates the exposition of the main results and identifies in a straightforward fashion some of the empirical problems the menu-cost argument runs into.

As in Blanchard and Kiyotaki (1987, p. 649) the representative household has a utility function which is additively separable in composite consumption and real money on the one hand and labour hours on the other.

U(C,M/P,L)=- U 1 (C,M/P)-U2 (L)

= " - YL r Li±i/a 0 < a < 1, a > 0, (13.52)

1/111-a [ 1 + 1/a

where yL > 0 is a simple scaling factor (to be used in the computer simulations below) and a regulates the slope of the labour supply function (see below). The budget restriction is given by:

PC-1-M=WNL+Mo+n-T (- I), (13.53)

where I represents total wealth of the household (including labour income). Composite consumption is defined by (13.2) and it is assumed that the diversity effect is absent (i.e. we set ri = 1). This is a useful and innocuous simplification as it is assumed that the number of firms is constant. The household chooses consumption, money balances, and labour supply in order to maximize (13.52) subject to (13.53). Again a simple two-stage procedure can be used to find the solutions. In the first stage the household chooses C and M/P to maximize the sub-utility function Ul (C,M/P) subject to the budget restriction PC + M = I. This yields the following expressions:

where V1 (I /P) is the indirect sub-utility function associated with Ul (C, m the second stage, the household chooses L and thus I in order to maximize

U2 (L) subject to the definition of I (given on the right-hand side of (13.53)). This yields the expressions for labour supply and real household wealth including labour income:

10 It is obtained by substituting the optimal values for C and M/P into the direct sub-utility function

381

The Foundation of Modern Macroeconomics

By using the utility specification (13.52), there is no income effect in labour supply and only the substitution effect survives. The advantage of this specification is that it enables us to demonstrate the crucial role played by the elasticity of labour supply with respect to the real wage. If a is very high, labour supply is highly elastic and large labour supply changes result from only a small increase in the real wage. Conversely, if a is low labour supply is relatively inelastic and a large change in the real wage is needed to produce a given increase of labour supply.

Each firm in the monopolistically competitive sector faces a demand for its product from the private sector (see (13.7)) and from the government (see (13.16)). Since we abstract from diversity effects (rj = 1), total demand facing firm j can be written as:

and where we have used (13.54)—(13.55) to relate private consumption to real money balances.

For reasons that will become clear below, we use a slightly more general description of technology than before. Instead of (13.10) we use the following production function:

with 0 < y < 1. If y is strictly less than unity, the marginal physical product of labour declines with output and the average cost curve of the firm is U-shaped (see Dixon and Lawler, 1996, p. 223). Of course, if y = 1 (13.61) and (13.10) coincide.

Firm j chooses its price, Pi, in order to maximize its profit: 11

The optimal price of firm j must satisfy the following first-order condition:

where MCi is marginal c, ticity of demand (9) in

which produces a positive I

This pricing rule general i, I (13.13)) by allowing for ai from this generalization, al assumed that the firm sc other producers' output it this section the firm sets other producers' prices as g costs the two assumptions this equivalence does not We now have all the in

menu costs. The main (T3.2) expresses consume tion of factors influence - (13.58), imposing money ernment budget constraint LG = 0 in (T2.4)). Equate is obtained by substitutii . 0. income (13.62) and sim:

Table 13.3. A simplified El

Y = C G