optimum resource allocation in u.s. agriculture: comment

Agricultural & Applied Economics Association

Optimum Resource Allocation in U.S. Agriculture: CommentAuthor(s): C. Richard Shumway, Bruce R. Beattie and Hovav TalpazSource: American Journal of Agricultural Economics, Vol. 59, No. 4 (Nov., 1977), pp. 778-783Published by: Oxford University Press on behalf of the Agricultural & Applied EconomicsAssociationStable URL: http://www.jstor.org/stable/1239415 .

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Optimum Resource Allocation in

U.S. Agriculture: Comment

C. Richard Shumway, Bruce R. Beattie, and Hovav Talpaz

Over ten years ago, Tyner and Tweeten presented two imaginative and pervasive articles in this Jour- nal. The first notes past statistical difficulties in obtaining reliable parameter estimates for aggregate U.S. farm production functions with several input variables (Tyner and Tweeten 1965). In proposing an alternative approach, Tyner and Tweeten note that factor elasticities must equal their respective factor shares, given the assumptions of perfectly competitive product and factor markets and market equilibrium.' They also assume that entrepreneurs attempt to organize production such that actual factor shares adjust toward an equilibrium in a geomet- ric distributed lag fashion. Since the parameters of a Cobb- Douglas production function are factor elasticities, they propose computing elasticities from historical data on factor shares, avoiding the prob- lem of multicollinearity. Estimates of factor elasticities for nine input categories were developed by decade for 1912-61 using data from published and unpublished ERS sources.

The second article (1966) built upon the first by incorporating these elasticity estimates into a Cobb-Douglas production function for each decade. This was accomplished by regressing farm output (in constant dollars) on a composite input variable (in constant dollars) defined as the product of each factor raised to its exogenously estimated factor elasticity. A linear model with a zero inter- cept was used to estimate the constant term for each decade. Having in this manner synthesized a production function, minimum-cost input levels, equilibrium output and input levels, factor- substitution relationships, and factor-demand and product-supply elasticities were derived, and comparisons were made with the actual situation in each decade. Based on these comparisons, Tyner

and Tweeten conclude (a) adjustment to a least- cost input combination to produce the actual average 1952-61 output would have reduced the input dollar volume by $1.9 billion, or 5.6%; (b) adjustment of farm resources to an equilibrium level with all variable resources earning an opportunity-cost return would have entailed a reduction of $4.2 billion ($1947-49), or 12.5% of the actual input volume in the 1952-61 period; (c) labor was in excess supply by two-fifths in the 1952-61 period;2 and (d) capital inputs supplied by the nonfarm sector were not generally used in excess by farmers (1966, pp. 629-30). In summary, their results "serve as a guideline for public policy by indicating the magnitude of resource adjustment needed to achieve economic equilibrium, and the economic cost of maintaining nonoptimal resource levels and combinations in agriculture" (1966, p. 630).

These were, and remain, important conclusions resulting from an ambitious and innovative study-conclusions that added empirical credence to the popular notion of substantially excess labor resources in agriculture. The conceptual, meth- odological, and policy significance of this work was emphasized by the inclusion of the second article in the A.E.A. Readings in Agricultural Economics. Impressed with the ingenuity of the Tyner and Tweeten approach and its implications for agricultural policy analysis, we, like others, have used their articles in graduate teaching. In so doing, we have discovered an error in the Tyner and Tweeten analysis that substantially affects the policy conclusions presented in the second article. It is the pur- pose of this comment to present revised results for an article that remains an important source of economic hypotheses and policy prescriptions even a decade later.

Alternate Model Specifications

The error in Tyner and Tweeten's analysis-an error the consequence of which led to a substantial overstatement of resource misallocation in U.S. agriculture-is addressed by considering the first- order conditions for profit maximization under two alternative specifications of the production function

C. Richard Shumway, Bruce R. Beattie, and Hovav Talpaz are associate professors of agricultural economics, Texas A&M Uni- versity.

Texas Agricultural Experiment Station Technical Article No. 12896. The authors are appreciative of the many helpful comments and criticisms of colleagues John Penson and Bob Taylor. They are indebted to Fred Tyner for his assistance in providing and interpreting the data upon which this paper and his earlier work are based.

i Each factor elasticity, E, = MPP,/APP,, equals its share of total value product expressed as the ratio of expenditure on the input (rjx,) to total value product (py). Given perfect competition and equilibrium, MPP1 = r1/p, implying that MPPxady = rjxj/py or Ef = rjx/py, where MPPs, APP,, and rj are the marginal productivity, average productivity, and price of the ith factor, respectively; y denotes product and p the product price.

2 There is a discrepancy in Tyner and Tweeten (1966) as to the extent of excess labor supply in the 1952-61 decade. In the text a two-fifths excess supply is mentioned, but in table 5 a 68% excess is implied.



Shumway, Beattie, and Talpaz Comment 779

(i.e., in physical versus constant dollar units) and two objective functions (i.e., in nominal versus constant dollar prices). (We are indebted to the Journal editors for suggesting this expositional approach.)

Starting with the conventional case in which output (yt) and inputs (xi,) in time period t are measured in physical units, the production function is given by

(1) yt = ft(Xlt .. . Xnt)" With p, and rit being product and factor i price,

respectively, and assuming zero price flexibilities, profit

irt in any time period t is expressed in actual

prices prevailing in that period:

(2) "rt

= Pt(Xlt, ... , xnt) - Aritxit,

and first-order conditions for maximizing nominal profits are

(3) airt/axit = 0 4 'yt/8xit = rit/Pt.

An equivalent approach is needed when output and inputs are measured as revenue and expenditures in base period (t = b) prices as was Tyner and Tweeten's case for all inputs except labor (which was measured in man-hours). This production function is given by (4) PbYt = ft(rlbXlt ...

.. rnbxnt).

Profit in any year t is

(5) 7t = (Pt/Pb)ft(rlbxlt, ... , rnbxnt)

- W(rit/reb)ritxit

,

where the appropriate product and factor prices are actual prices deflated by base period prices, i.e., Pt/Pb and rit/rib, respectively. These are the nominal price equivalents of a product or factor measured in constant dollars. First-order conditions for maximizing profits are

(6) a1rt/aribxit = 0 4 aPbyt/aribxit = ritPb/ribPt.

With the base year prices (Pb and rib) specified as unity, equation (6) is equivalent to equation (3). The only difference between equations (3) and (6) is that the former is measured in physical output and input units and nominal prices per physical unit and the latter is in constant dollar output and input units and nominal prices per constant dollar unit. For any time period t, producers, if rational and all the usual assumptions of static analysis are satisfied, allocate resources according to the conditions specified in equation (3) or (6). Either of these approaches is appropriate and yields equivalent results as resource allocation decisions are (and should be) based on existing (or anticipated) prices in that period.

Rather than following the approach in equations (5) and (6), Tyner and Tweeten implicitly assume a different specification of the objective function. They express product and input prices as well as

input and output levels in constant (base period) prices; that is, given the production function expressed in constant dollars (equation (4)), the following is maximized:

(7) rt

= (Pb/Pb)ft(rlxlt, ...

. rnlbXnt)

- Y(rzb/rzb)r~ix,.

First-order conditions would then be

(8) a7rt/aribxit = 0 4' aPbyt/ar2bxit

= ribPb/ribPb = 1.

Maximizing profit so expressed results in the same first-order conditions for every period and fails to take account of the prices actually faced by producers in any time period except the base period. Yet it is this function that Tyner and Tweeten apparently sought to maximize.

Except for labor, their input and output data series are measured in 1947-49 constant dollars. Consequently, the appropriate first-order conditions are those of equation (6). Yet, it appears that they use base period prices to derive least-cost input combinations, etc., in every decade despite the fact that those prices are relevant only in the 1947-49 base period. Tyner and Tweeten acknowl- edge assuming prices of $1 for output and all inputs except labor (1966, p. 617). Further, their results can be duplicated when prices of $1 are used in all decades but not when nominal prices are used.

The use of constant prices rather than nominal prices has a major empirical consequence as is demonstrated in this note by comparing results using prices actually prevailing in each decade with the results of the $1 prices used by Tyner and Tweeten. Nominal price equivalents (hereafter re- ferred to simply as "nominal prices") (i.e., Pt/Pb and

rtl/rib) can be computed directly from their two

data series-a USDA nine-input data series of PbYt and rixit, measured in 1947-49 constant dollars, and a comparable series developed by Tyner and Tweeten in current dollars, i.e., PtYt and ritxit. Prices (Pt/Pb and rit/rib) are given by dividing the respective current dollar series by the constant dollar series. These prices are reported in table 1 as decade averages and are substantially different from the 1:1 ratios assumed by Tyner and Tweeten.

Implications

We compare several results-minimum-cost input combinations, supply function, and equilibrium output and input levels-by using Tyner and Tweeten's aggregate U.S. production functions and correcting the output and input prices used.3 Our

3 The parameters of the aggregate U.S. agricultural production function estimated by Tyner and Tweeten for each decade, 1912- 61, are accepted for purposes of this exposition without challenge. Our efforts to reestimate those parameters using an alternative distributed lag hypothesis result in only minor differences (Shum- way, Talpaz, and Beattie).



780 November 1977 Amer. J. Agr. Econ.

Table 1. Nominal Output and Input Prices by Decade

Output or Input 1912-21 1922-31 1932-41 1942-51 1952-61

Output 0.602 0.572 0.422 0.945 0.967 Inputs

Fertilizer and lime 1.329 1.100 0.808 0.979 0.970 Feed, seed, and livestock 0.528 0.491 0.399 0.870 0.928 Labor _ a _ a 0.145 0.501 0.758 Machinery 0.577 0.641 0.627 0.962 1.422 Real estate 1.033 1.088 0.667 1.124 1.864 Machinery operating expenses 1.122 0.905 0.732 0.948 1.203 Misc. operating expenses 0.639 0.722 0.596 0.998 1.128 Crop and livestock inventory 0.540 0.500 0.359 0.867 0.906 Real estate taxes 0.571 0.626 0.491 0.884 1.155

a Labor data incomplete.

Table 2. Estimated Minimum-Cost Levels of Inputs Required for Average Actual Output by Decades, 1912-61

Input Item a 1912-21 1922-31 1932-41 1942-51 1952-61

---------------- Million 1947-49 Dollars b

Fertilizer and lime T-T 261.9 333.0 626.0 975.0 1,282.0 T-T* 161.4 261.1 289.2 719.9 1,364.2 A 182.7 249.2 286.4 753.4 1,364.7

Feed, seed, and livestock T-T 381.2 425.6 1,457.8 2,962.0 2,627.3 T-T* 591.5 747.5 1,363.5 2,460.7 2,922.4 A 528.7 761.1 896.7 1,978.4 2,698.0

Labor T-T _e _e 9,388.6 10,566.0 6,280.6 T- T* _ C 21,096.9 16,809.3 11,688.6 A 23,400.3 23,277.2 21,075.0 17,855.1 11,782.2

Machinery T-T 1,065.6 809.5 1,431.9 2,642.8 2,789.3 T-T* 1,513.0 1,088.6 851.4 1,972.7 2,023.6 A 1,000.1 1,187.8 1,066.2 1,606.8 2,642.4

Real estate T-T 4,033.6 4,191.8 5,584.7 5,014.2 7,060.0 T-T* 3,198.1 3,322.8 3,122.5 3,224.8 3,907.9 A 3,387.2 3,389.9 3,356.6 3,471.5 3,742.8

Machinery operating expenses T-T 315.9 655.2 1,539.9 2,331.8 3,059.9 T- T* 230.6 624.5 784.4 1,779.0 2,624.1 A 331.2 558.4 743.9 1,783.7 2,502.4

Misc. operating expenses T-T 971.4 1,122.1 1,785.2 1,734.6 2,310.5 T-T* 1,244.2 1,356.4 1,116.6 1,256.5 2,113.1 A 1,342.2 1,337.3 1,121.9 1,411.0d 2,100.7

Crop and livestock inventory T-T 656.3 632.8 1,084.7 1,500.7 1,219.0 T-T* 995.9 1,092.0 1,127.0 1,251.1 1,388.5 A 1,106.5 1,079.2 1,102.7 1,314.7 1,441.4

Real estate taxes T-T 374.7 649.7 912.8 697.4 1,050.0 T-T* 537.2 895.6 694.0 583.9 938.0 A 546.7 853.5 825.1 643.1 902.2

Average output 17,822.7 19,791.4 20,737.5 27,291.7 32,452.5 a T-T is the minimum-cost level reported by Tyner and Tweeten (1966, table 2) with labor priced at 85% of the nonfarm rate and all other inputs at $1; T-T* is the minimum-cost level using appropriate nominal input prices; A is the actual average for the period as reported by Tyner and Tweeten (1966, table 2). b Except for labor, which is in million man-hours.

Insufficient data to compute. d Tyner and Tweeten report this figure as 1,211.0. Other differences between their reported averages and the decade averages of the Tyner data (appendix A, tables 2 and 3) are minor.




results are contrasted with those of Tyner and Tweeten, where their derivations assumed labor priced at 85% of the nonfarm rate.

Minimum-Cost Input Combinations

Minimum-cost input levels and actual expenditure levels (A) in constant dollars are presented by decade in table 2. Results using nominal prices (T- T*), as compared with the original Tyner and Tweeten results (T-T), were closer to actual expenditures in thirty-six of the forty-three cases.

Minimum-cost labor and land inputs were much closer to actual than implied by Tyner and Tweeten. Labor was in equilibrium in the 1932-41 decade and was in excess supply by only 6.2% in 1942-51 and 0.8% in 1952-61. Actual real estate level was also closer to the minimum-cost level: 5.9% in 1912-21, 2.0% in 1922-31, 7.5% in 1932-41, 7.7% in 1942-51, and -4.2% in 1952-61. In no period was labor in substantially excess supply nor real estate greatly below the minimum-cost level. These findings are in direct contrast to Tyner and Tweeten's conclusion that labor was greatly in excess supply and real estate in short supply in all decades.

With all inputs priced at $1 per unit, except labor, which they priced at 85% of the nonfarm rate, Tyner and Tweeten's estimates imply that input costs could have been lowered by 18.7% in the 1932-41 decade, 9.1% in the 1942-51 decade, and 10.5% in the final decade. However, with inputs correctly priced, the opportunity for reducing production costs is substantially less. Input costs could have been lowered by only 1.5% in the 1932-41 and 1942-51 decades and 0.9% in the 1952-61 decade. The large misallocation of resources suggested appears to have been illusory.

Because real estate enters their original derivations at levels higher than they believed reasonable (1966, p. 618), Tyner and Tweeten recalculated the minimum-cost combination of other inputs holding real estate fixed at actual average decade levels. Holding real estate fixed changed the minimum- cost combination of other inputs in their original calculations substantially and increased total cost of inputs by 3.9% in the 1932-41 decade, 1.3% in the next, and 5.4% in the final decade. Using nominal prices, the relative impact on input combinations and total cost was considerably less. The differences between assuming all factors variable and real estate fixed are minor when the appropriate nominal prices are used.

Equilibrium Output and Input Combinations

The aggregate U.S. agricultural supply and demand situation for the 1952-61 decade is depicted in figure 1. Demand curve DT-T is that reported by Tyner and Tweeten (1966, p. 623). Demand curve

Dr-r is the T-T demand curve using the nominal

1952-61 product price-0.967 (i.e., P*). In deriving their demand curve (DrT-T), Tyner and Tweeten assume an elasticity of -0.25 and pass a straight line through the output point (Y) at the assumed output price (P, i.e., 0.904), in figure 1. This output, $30,933 million ($1947-49), represents their estimate of farm output in the absence of government programs (5% lower than actual farm output- Y). Our demand curve

(Dr-,) was developed similarly

using the nominal output price (P*). The product supply functions presented in figure

I assume perfectly elastic input supply functions except for real estate, which was presumed fixed. The supply function derived by Tyner and Tweeten assuming labor priced at 85% of the nonfarm wage rate is identified as SrT-Tr. With nominal output and input prices, the supply function is represented by ST-T*

.

Each of these supply functions is supposedly derived based on expansion path conditions. Yet the T-T supply function lies above their estimated point of actual decade production adjusted for the effect of government programs (YP). Thus, the implica- tion is that producers were actually more efficient than they would have been if they had combined inputs optimally. The real reason that SrT-Tr lies above the point of actual production is that incorrect prices were assumed. Among other differences, the labor price was too high and output and real estate prices were too low. The supply function based on nominal prices (Sr-,) lies below our estimated point of actual adjusted production (Y, IP*) as in- deed it must if any misallocation of resources is to be claimed.

As expected, equilibrium output level based on nominal prices (rYT-r) was greater than the adjusted actual output (Y), but only slightly. Output was 0.6% above adjusted actual as opposed to Tyner and Tweeten's estimate of 2.1% lower. Elasticity of product supply was unaffected by using nominal prices; with real estate fixed, it was 3.41 for both STTr and ST-Tr* .

At the estimated equilibrium output level, Tyner and Tweeten conclude that labor was greatly in excess supply in the 1952-61 decade. Our findings using nominal prices indicate that it was much closer to optimal--only 5.0% in excess. They de- termine that there was underinvestment in capital items purchased from the nonfarm sector (i.e., all inputs except labor and real estate); our findings indicate overinvestment of about 6%. Their results indicate that machinery was used at less than the optimal level, yet we observed usage more than one-third greater than optimal.

Tyner and Tweeten conclude that adjustment of farm resources to an equilibrium level would have reduced actual input volume by 12.5%. We estimate that adjustment to equilibrium would have reduced expenditures only 4.9%. They further estimate that slightly more than half of this reduced volume of inputs would occur through reducing output level



782 November 1977 Amer. J. Agr. Econ.

1.00

]

ST-T

T-T

PT

S .95 S

T-T*

T-T .

.90

.,- T-T*

30,000 32,000 SY Y T-T T-T*

Farm output in million 1947-1949 dollars

Figure 1. Aggregate farm demand and supply for the 1952-61 period

and the remaining half through using the least-cost input combination. We estimate that less than one- sixth of the reduction could occur through reor- ganizing the input mix, and the remainder would be due to lowering output from its actual unadjusted level (Yin figure 1).

Conclusions

The pioneering research by Tyner and Tweeten, reported in two articles in this Journal in the mid- 1960s, was and remains imaginative and com- prehensive. However, an important error exists in their analysis, viz., inappropriate product and factor prices were used in estimating the extent of nonoptimality in input usage in U.S. agriculture. Consequently, Tyner and Tweeten's conclusions (1966) regarding differences between optimal and actual input usage appear not to be reliable as policy prescriptions. Many of the implications for "de- sired" change in factor usage were reversed in this study. Of major importance is the apparent large overestimation of excess labor in agriculture.

The following conclusions based on nominal prices are presented in contrast to the four Tyner and Tweeten conclusions presented at the begin- ning of this paper: (a) adjustment to a least-cost input combination to produce the actual average 1952-61 output would have reduced the input dollar volume by $282 million or 0.9% (i.e., less than one-fifth as much reduction as the Tyner and Tweeten estimate); (b) adjustment of farm re-

sources to an equilibrium level in the 1952-61 decade, with all variable resources earning an opportunity-cost return, would have entailed a reduction of $1.5 billion or 4.9% of the input volume (i.e., less than two-fifths as much savings as the Tyner and Tweeten estimate); (c) labor was in excess supply by only 5% in the 1952-61 period (i.e., only about one-tenth the Tyner and Tweeten estimated oversupply); and (d) capital inputs supplied by the nonfarm sector were used in slight excess (6.3%) by farmers in this period, and machinery in particular was used in substantial excess (36%).

While both farm output and input combinations appear to be somewhat out of equilibrium, that disequilibrium in the 1952-61 decade was apparently no more than about two-fifths the magnitude estimated by Tyner and Tweeten (1966). Thus, farmers appear to be producing considerably more efficiently than previously intimated. Further, as an anonymous reviewer pointed out, if adjustment costs were fully endogenized into the adjustment model, it seems reasonable to hypothesize that differences between optimal and actual resource allocation would be negligible.

[Received September 1976; revision accepted June 1977.]

References

Shumway, C. R., H. Talpaz, and B. R. Beattie. Resource Allocation in U.S. Agriculture: Application of an Im-




proved Polynomial Lag Estimation Procedure. Texas Agr. Exp. Sta. Agr. Econ. Dep. Techn. Rep. 77-6, Apr. 1977.

Tyner, F. H. "A Simulation Analysis of the Economic Structure of U.S. Agriculture." Ph.D. thesis, Ok- lahoma State University, 1967.

Tyner, F. H., and L. G. Tweeten. "A Methodology for

Estimating Production Parameters." J. Farm Econ. 47 (1965): 1462-67.

. "Optimum Resource Allocation in U.S. Agricul- ture." J. Farm Econ. 48 (1966):613-31. (Also in A.E.A. Readings in the Economics of Agriculture, vol. XIII, eds. K. A. Fox and D. G. Johnson, pp. 286-308. Homewood, I11.: Richard D. Irwin, 1969.)



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