F determined endogenously, and the separation of Yp into its Yp and

In document Linkages from the farm sector to the Australian macroeconomy : towards a theoretical and empirical analysis (Page 86-129)

Y real private investment expenditure

F determined endogenously, and the separation of Yp into its Yp and

NF

Yp components is endogenised more rigorously. An attempt is also

made to provide a structural basis for the specification of farm investment, I

The eight variables which are treated as endogenous to the farm sector in the present specification are:

(1) 0F (2) Lf (3) Yf (4) Yf F (5) Y fNF (6) CpF (7) R

(8) Ip F

The variables impinging upon the farm sector of the model

which are exogenous to the model as a whole are:

(1) Kp (2) J (3) a F (4) pp (5) pNFT (6) pNT (7) v

In addition, the interest rate, r, is exogenous to the farm sector of the model but endogenous to the non-farm sector.

Non-Farm Sector and Macroeconomic Aggregates

Aggregate production in the economy is obtained by summing the outputs of the three sectors identified in the model:

(9)

'NT + Y.'NFT + Y,

Yp has been determined endogenously within the farm sector of the model. The task, then, is to determine Y>7T7m and Y„m . We can

NFT NT

specify a production function for the non-farm traded goods sector:

+ + +

NFT = YN F T (KN F T ’ L N F T ’ a NFT •*

It is assumed, for simplicity, that the non-farm traded goods sector does not draw any non-primary inputs from either of the other sectors of the model, so that the gross output of non-farm traded goods is equal to value added in that sector. The demand for labour (or, equivalently, employment) in the non-farm traded goods sector is assumed to be a function of the marginal physical product of labour in that sector, and the real wage as a cost to employers.

+ 6Y.

(

11

)

NFT + NFT PNFT NFT NFT ÖL _ ? n, v) NFT NT

Equations (10) and (11) are consistent with the assumed

’classical' operation of the non-farm traded goods sector. Producers in that sector continually operate at their classical, profit m a x i ­ mising level of output and employment. With other factors unchanged, output and employment is largely independent of the level of demand for non-farm traded goods in the domestic economy. Any divergence between Y and local demand for non-farm traded commodities, Z ,

Nr 1 Nr 1

is implicitly assumed to be absorbed in an (unspecified) non-zero trade balance.

Similarly, we can specify a production function for the non- traded goods sector:

+ + +

(!2) Ynt = Yn t(Knt, Lnt, aNT)

We again assume, for simplicity, that no non-primary inputs are used in the non-traded goods sector, so that there is no requirement to distinguish between gross output and value added in that sector.

Our popular Keynesian view of the non-traded goods sector requires the specification of a rather complex demand for labour function in that sector. In particular, we need to specify a classical demand for labour function which would be relevant in the long run, or where there was no effective constraint on the demand

for non-traded goods, and a 'Popular Keynesian' demand for labour function which is relevant in the short run in the presence of an effective demand constraint.

+ + + _ ? (13) * 01NT PNT PNT * LN T (6L ’ p ’‘7 7 ’n *V) f°r ZNT = YNT ^KNT ’ LNT * aNT^ NT rNFT ^F 'NT NT + . LNT ^ T ^ N T ^ N T ^ for ZNT ^ YN T ^ ^ T ,LN T ,aNT^

The first part of (13) i.e. = L , is identical in structure

to the demand for labour functions assumed in the farm and non-farm traded goods sectors. In other words, it is a classical, profit maximising demand for labour function. However, it is constrained to apply only to circumstances in which the total demand for non-

traded goods, Z , is equal to the classical, profit maximising

level of Ynt, Yn t . If Z^T £ Y^ / then takes on the ’Popular

Keynesian' structure i.e. L = L D .

NT NT

Note that, in the 'Popular Keynesian' component of L ,

appears as an argument. In other words, given K^ and oi , the

effective constraint on output and employment in the non-traded goods sector is the demand for non-traded goods, and not the real wage as a

*

cost to employers, as is the case in L . This is reflected in the

assumed signs of the ordinary partial derivatives of L ^ with

respect to K ^ and a^,. An increase in either K ^ or ot^ would be

expected, in general, to raise the marginal physical product of

*

labour in the non-traded goods sector, and hence to raise L , other

factors unchanged. However, the increase in the marginal physical

product of labour is not relevant for L Here, the important

consequence of the increase in K ^ or a ^ is the rise in the average

product of labour thus brought about, so that fewer workers would be required in order to produce the given, demand constrained, level of output in that sector.

In the present variant of the model, non-traded goods prices are assumed to be fixed. It is interesting to note, however, that equation (13) provides an important point of reference when some gradual adjustment of non-traded goods prices is allowed, in some later analyses. In particular, it would seem sensible and consistent to assume that movements in non-traded goods prices would be influenced by the gap between the classical optimum level of non-traded goods production (ie. the level associated with L ) and

the actual level of non-traded goods production (the level associated

The next step is to determine Z - which, of course, will then allow L and to be determined, assuming that the non-traded goods sector continually faces an effective demand constraint in the short run. Z.Trn can be determined from the demand side of the

NT

model, as follows. First, we need to consider consumption expenditure by non-farm households.

+ + +

NF NF NF

('14') c = c (Y Y Y r) U4J P ^ N T ’ F ’ NFT’ ;

It is assumed that consumption expenditure by non-farm households is a function of production in the non-traded and non-farm traded goods sectors, that part of value added in the farm sector which accrues to non-farm households, and the interest rate.

Aggregate private consumption expenditure is then defined to be the sum of the consumption expenditures by farm and non-farm house­ holds :

F NF

(15) Cp = Cp + Cp

It is assumed that investment expenditure in the non-farm sector is a function of the change in non-traded goods production, and the interest rate:

(16)

+

(AY

N T ’ r)

This could be interpreted as a very simple reduced form of a

structural investment model which features 2 separate modules: (1) an accelerator model of investment in the non-traded goods sector

(which would seem to be a plausible complement to the 'Popular Keynesian' specification of the non-traded goods sector); and (2)

a more classical investment model in the non-farm traded goods sector, which emphasises changes in r.

Aggregate private investment expenditure is then defined as the sum of farm and non-farm investment expenditures:

Aggregate final expenditure in the economy is defined as the sum of these private consumption and investment expenditures, and

their counterparts in the public sector:

(18) Z - Cp + CG + Ip + IG

Given Z, we can readily ascertain the level of domestic demand for non-farm traded goods and non-traded goods:

+ Pm1?-p ? (19) Z.T__ = j (20) Z NT NT-J

T(Z

k n f t fNFT

e)

1

PNT PF ’ + _ - ? (Z, PNT PNT ---,

e)

. + PNFT PF

The R.H.S. of (20) is made up of two parts. The first part specifies the component of aggregate final expenditure which is directed onto

non-traded goods. The second part is J - the volume of non-traded goods used as intermediate inputs in the farm sector. It is clear that both represent components of the total demand for non-traded

Given ZlTT_m and Z.T_, then Z^ can be obtained from the identity:

NFT NT F

(21) ZF = a ZNFT - (ZNT-J)

In order to determine the actual level of the demand for labour in the farm sector, the non-farm traded goods sector, and the

classical optimum level of the demand for labour in the non-traded

JL

goods sector, L , we need a measure of the real wage, n. Given the composition of a real wage unit, v, namely 'a' units of non- traded goods, ’b units of non-farm traded goods and fc ’ units of farm goods, the real wage can be defined a s :

(22) n = --- —^ --- apNT + bpNFT + cpF

where w is the nominal wage and is common to all sectors of the economy.

Aggregate demand for labour is then defined as the sum of the demands for labour in the three sectors of the economy:

(23) L = Ln f t + Ln t + Lf where, under most circumstances in the short run, the relevant measure of LNT would be L ^ 0 .

The supply of labour is assumed to be fixed in the short run: (24) LS = L

It is also assumed that aggregate employment is always equal to the aggregate demand for labour:

(25) E = L

This assumption could also be interpreted as an assumption that L is S

always less than L , so that the fixed supply of labour does not represent an effective constraint on the level of employment.

The final two equations in this variant of the model specify the demand for and supply of nominal money balances:

The scale argument in the demand for money function is specified to be either Y or Z (which, of course, will differ where an imbalance exists in the current account). There is a lack of consensus in the literature on this point. It is common for Y to be used, in both the theoretical and empirical literature. However, to the extent that money balances, particularly narrowly defined money such as Ml, derives much of its utility from its role as a medium of exchange, there would seem to be strong theoretical grounds for supposing that

aggregate expenditure, Z, may be a more appropriate scale argument. As we shall see, many of the shocks which affect the farm sector can have quite disparate effects on Y and Z at a macroeconomic level, so

this issue could be of some consequence.

Finally, it is assumed that the money market is in equilibrium

S

at all points in time, and that the stock of money, m , is fixed.

/ 97n D S

(27) m = m

The non-farm and macroeconomic aggregates sector of the model thus contains 19 equations and identitites. The 19 variables which are, in that sense , treated as endogenous to this sector of the model are: (1) Y (2) Y y } NFT O ) y n t ^ l n f t ^ l n t (6) L (7) E / " “ N 00 NF Cp (9) Cp (10) IpNF (11) Ip (12) Z z n f t (15) Zp (16) n (17) L S (18) mD (19) r (14) Z NT

The variables which are exogenous to the non-farm sector of the model but endogenous to the farm sector are:

(1) Yf (2) YfNF (3) c / (A) IPF (5) Lf

The variables which appear in the non-farm sector of the model and which are exogenous to the model as a whole are:

(1) bjFT (2) “ NFT (3) PNT (4) PNFT (5) PF (6) V (7) ” (8) Kn t (9) 0,

(15) m S

III (3) An Approximate Geometric Characterisation of the Model

The model can be characterised geometrically in four interrelated sectors - (i) Sector I, which is an income/expenditure sector;

(ii) Sector II, which represents a macroeconomic Engel Curve; (iii) Sector III, the production functions; and (iv) Sector IV, the labour market.

Figure III (1) Sector I

In Sector I, the IS curve indicates the volume of expenditure, Z, that is associated with each level of the interest rate, other factors unchanged. The IS curve summarises equations (6), (8), (14),

negative relationship between final demand (C^, Ip) and r. A rise in non­ farm production would move IS to the right because of the effect of a rise in non-farm income on non-farm consumption expenditure, and because of the accelerator effect on non-farm investment. Similarly, a rise in farm income would move IS^, to the right because of the con­ sumption response of farm households, and the investment response via a change in farm residual funds - see equations (6), (7) and (8).

The IS^ curve indicates the relationship between the aggregate volume of production, Y, and the

interest rate. The farm and non-farm traded components of Y are, of course, independent of the level of Z, and hence are independent of r in the short run. However, the non-traded component of Y is neg­ atively related to r because of the assumed negative relationship between Z and r and hence between Z “Y ^ a n d r . In general, there is no reason to suppose that the IS^ and IS^ curves would be parallel. It is more probable that IS^ would be steeper than IS because only part of a change in Z, induced by a change in r, would fall onto non-traded goods.

Slnce y n t = ZN T > it is clear that the horizontal dis­ tance between ISy and ISZ is a measure of the balance of trade. In particular, if Y < Z, the balance of trade is in deficit, and conversely.

Equations (26) and (27) are incorporated into the familiar LM curve. The potential significance of the ambiguity as to the appro- Pria te scale argument in the demand for money function is immediate in Figure III (1). If Y was the scale argument, then r , Y and Z would be consistent with equilibrium in the money market. However, if Z was the scale argument then, given the same money stock, r°, Y° and Z would be consistent with money market equilibrium.

Figure III (2) Sector II (1)

Equations (19), (20) and (21) are represented in Sector II. It is assumed that farm and non-farm traded commodities can be combined into a single traded good, given their relative price. Then aggre­ gate expenditure, Z, from Sector I, can be separated into its traded and non-traded components, given the relative price of traded and non-traded goods and the macroeconomic preference mapping, £. The traded component of Z, Z^, can then be separated into its farm and non-farm traded components, given the relative price of farm and non­

farm traded goods, and the preference mapping. As discussed

previously, in order to obtain the level of total demand for non- traded goods, Z , J must be added directly to the non-traded com­ ponent of Z, as is done in Figure III (2).

nr CO

Figure III (3) Sector III

na)

V

HLCs)

y

(

k

, u ^

A/7- b aJT ' A/T.

L

A/T

Equations (1), (3), (10) and (12) are captured in Sector III. Given K^, and J, the gross volume of farm production is a function of farm employment L^. Farm value added, is obtained by subtract­ ing non-primary inputs, J, from the gross volume of farm production. Similarly, given and a , ^ F T Can rePresente<^ as a function of while Y.irr, can be represented as a function of LX7rri.

The actual levels of and can be obtained directly from the labour market, in Sector IV. However, the specification of L ^ , in Sector III (3) is a little more complex. In particular, we need to specify an optimal1 level of LXTm,- L Tm - which can be obtained

NT NT

from Sector IV, and a demand constrained level of - L ^ D , - which can be obtained directly from Sector III (3) . Given Z from

Sector II, then can be obtained by finding that level of for which Y NT " N T * Figure III (4) Sector IV L +L +L ' f W F T ajT \

The real wage, measured as the number, n, of real wage units, v, is represented along the vertical axis of Sector IV. It is clear from equation (22) that, given the make-up of v, the prices of farm, non­ farm traded and non-traded commodities, and the nominal wage, n can be readily calculated. With each of these variables given in the present analysis, the real wage will be fixed at (say) n. Equation (2) is represented by schedule L^. In other words, given p^, and

p , the marginal physical product of labour in the farm sector can be converted to real wage units, allowing to be represented as a

function of n. Similarly, equation (11) is represented by the

schedule L.TriT,, and the L.T_ component of equation (13) is represented

Nr 1 N 1

j« X)

by the schedule L The LNT component of (13) is represented by the vertical line and is obtained by inverting the production

function in Sector III (3), given Z .

It should be noted that, as drawn, the L ^ schedule is

D *

continued above the point of intersection between L and .

D *

Following Barro and Grossman (1976), one might allow L and L to be coincident above their point of intersection. This is equiva­ lent to an assumption that some degree of price rigidity in the non-traded goods sector is relevant only in the downward direction

(i.e. in the face of deficient demand), but prices are perfectly flexible in the upward direction (i.e. in the face of excess demand). On the other hand, the continuation of above the point of

intersection implies that there is a degree of price rigidity in both directions. It is clear, however, that this potential ambiguity can be avoided by an assumption that the point of intersection

D *

between and L always occurs at a real wage level equal to

D *

or above the ruling real wage i.e. L < L^, or, equivalently,

JU

ZNT ^ YNT (KN T ’ LNT ’ aN T ^ ’ Such an assuraP tion is adopted throughout the analysis in the present chapter, and again in the analyses with Models II, III, IV and V in subsequent chapters. The assumption is relaxed, however, in the analysis with the

theoretical simulation variants of Models I and II in Chapter X and

O ’Mara et al(1985). There,the demand for non-traded commodities may exceed the classical optimum level of output, given the real wage, with a similar degree of rigidity of non-traded goods prices

issues also need to be borne closely in mind when the quantitative results, presented in Chapter IX, are being assessed and

interpreted.

The aggregate demand for labour schedule, L, is obtained by horizontally summing the three individual labour demand schedules - which, of course, captures equation (23). The supply of labour is

fixed at L (equation (24)). It is assumed, for convenience» that,

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