Aggregate Supply Response

The Profit Function Approach to Supply and Factor Demand

3.7. Aggregate Supply Response

In studying the elasticity of supply response in agriculture, a critical distinction must be made between the response of an individual crop and that of broad agricultural aggregates.

While individual crops do respond strongly to price factors, even in the short run, the growth in any crop usually takes resources away from other crops. So the price elasticity of all

agriculture is very low in the short run. The problem is that the main factors of agricultural production—total land, labor, and capital—are fixed in the short run. Aggregate agricultural production can grow only if additional resources are devoted to agriculture or if technology changes. The long-run response to increased profitability thus occurs through slowing emigration from rural areas and increasing investment in agriculture and rural areas.

3.7.1. Linking the Aggregate Elasticity to the Factor Supply

There is an interesting quick calculation that can give an order of magnitude for the price elasticity of aggregate production Q. For simplicity, let the production function be approximated by a Cobb-Douglas in the variable factors x_i (at price w_i) and one fixed factor z:

Q x_i^i



i z^. T

he associated supply function derived from profit maximization is:

(14) Qp



1 (_i/wi

i )

i

1 z



1, where   _i

i .

This shows that the supply elasticity, /(1), is directly linked to the degree of homogeneity of production with respect to the variable inputs. The parameter _i can be approximated by the share of the input i in the value of production and by the share of all variable inputs. If, for example, the different factor shares are 0.14 for land, 0.16 for livestock, 0.09 for fertilizer, 0.06 for tractors, 0.01 for irrigation, 0.38 for labor, and 0.16 for the residual fixed factors, public and private capital, then assuming that only fertilizer, tractors, and irrigation can adjust in the short term gives a supply elasticity of 0.16/0.84 = 0.19.

All the theory discussed until now, including the last result on the aggregate supply elasticity, is based on the distinction between variable and fixed factors. Such a dichotomy suggests a zero supply elasticity for the fixed factors and an infinite supply elasticity for the variable inputs. While this may be true for an individual farmer, it cannot hold for the whole sector. For instance, a very large increase in fertilizer demand cannot be matched by unlimited supplies at the current price. In addition, supply of some “fixed” inputs can be changed somewhat if prices justify it and if time is allowed. Taking these considerations into account, the analysis can be generalized by introducing explicitly the factor supply functions.

In doing so, we extend the partial analysis of the supply model to integrate the factor markets, an approach that will be further developed in Chapter 11 with multimarket models. In this general case, the supply elasticity is written (Mundlak, 1985):

E(Q/p) 1 1

 ^{ EiQsi/}_i

i ^,

where E_iQ = ∂lnx_i / ∂lnQ is the elasticity of x_i along the expansion path (i.e., for the optimum factor combination) obtained under constant prices, s_i is the share of input i in the variable

cost (equal to _i / for the Cobb-Douglas case), and _i (_i ≠ 0) is the supply elasticity of the variable input x_i .

In order to obtain a quick order of magnitude, consider again the Cobb-Douglas with all the factors variable, which gives E_iQ = 1, and consider the unrealistic assumption where _i =

. In this case, the elasticity of supply is simply equal to  the elasticity of factor supply.

Alternatively, consider the case where some inputs are fixed. To simplify, group all inputs into two classes, a variable aggregate with elasticity of supply _x and a fixed aggregate with shares  and 1 – , respectively. In this case, E_iQ is 1/ for the variable factor and zero for the fixed factor, and the elasticity of aggregate output becomes:

E(Q/p)  11/_x^.

This expression clearly shows how the supply elasticity of the product is modified by the supply elasticity of the variable factor. Thus, for  = 0.16 and _x = 1, the product supply elasticity is 0.09 instead of 0.19 obtained above under the assumption of _x = ∞.

3.7.2. Econometric Estimates

An estimate of the aggregate supply response can be derived from estimation of a disaggregated system of individual crops of the type described above. Consider, for example, the estimated system in Table 3.1. The implied aggregate supply elasticity with respect to an overall price increase is a weighted average of the individual crop elasticities:

, E(Q/p) E(Q/p_i



i ^{) s}jE(q_j/p_i

i



,j ⁾

where s_j is the share of crop j in aggregate crop revenue. While the results of direct individual crop price elasticities range from 0.25 to 0.77, the aggregate elasticity is only 0.05.

Bapna and his associates also directly estimated an aggregate supply elasticity for a larger region which includes the subregion for which the elasticity matrix is shown. They found an aggregate elasticity of only 0.09, which is consistent with the implied elasticity from crop responses.

Most aggregate supply models follow the Nerlovian approach (presented in the next chapter), where fixed factors are generally omitted. There are few direct estimations of the aggregate supply response which explicitly specify the contribution of nonprice factors as is done for individual crops in the system approach described in this chapter. The results of the few studies where this has been done are described in Binswanger (1989) and Binswanger, Yang, Bowers, and Mundlak (1987) and can be summarized as follows:

a. The short-run aggregate response of agriculture to price changes is low. Note, however, that this does not imply that price policy reforms are not important. Given the very high levels of direct and indirect taxation that have prevailed in agriculture (see Chapter 7), structural adjustment may bring price changes on the order of 100%. Assuming an overall elasticity of even 0.1 or 0.2, such price reforms will result in a significant aggregate response.

b. Public investments and services have a strong effect on agriculture. Table 3.4 shows that infrastructure, services, and human capital strongly affect aggregate output and the demand for fertilizers and tractors. Roads are a clear example of infrastructure with a strong

impact. From India’s study, regulated markets (featuring a formal auction mechanism to sell individual farmers’ output) can be seen as a low-cost government investment with a powerful output effect and, in the cross-country study, broader literacy is shown to boost output as well as the demand for fertilizer.

Table 3.4 approximately here

c. While research and extension have been shown in other studies to have a strong effect on the production of individual crops, their impact on aggregate supply is much lower, in much the same way that aggregate price elasticity is lower than individual elasticities.

d. Because output is so dependent on private investment, one would expect credit to be a critical factor in aggregate response. A study of the role of credit in India found that the main effect of institutional credit growth and higher lending volumes has not been a substantial increase in aggregate crop output but rather a substitution of capital for labor. Thus, the credit-supply approach to agricultural growth pursued over the last three decades in India has failed to generate employment or to reach its agricultural output objectives.

e. Because fixed factors have strong effects on output, an explanation of long-run supply requires an analysis of the determinants of change in these factors themselves. Result show that farmers, government, and providers of services all respond to agroclimatic potential. As public infrastructure and services are targeted to the better agroclimatic regions, more workers migrate to these regions. Private investment is then attracted by this abundance of natural resources, labor, and infrastructure. And private suppliers of services respond to the better opportunities associated with good agroclimate, improved infrastructure, and high private investment.

Exercise 3

Price Incentives and Public Goods for Indian Agriculture

This exercise consists of an analysis of output supply and factor demand with a system of equations derived from the profit function. The subjects addressed are: (1) the interdependencies between tradable and nontradable products and the consequences that price policies have on each; (2) the contrasts between the price elasticity of a single product and the elasticity of aggregate supply; (3) the respective roles of price and structural variables in the determination of output levels. On this last point, the exercise will analyze the importance of public goods in conditioning the response of producers to price incentives, and the contrast between short-run and long-run price elasticities calculated by taking into account the changes in the structural variables induced by price variations. Prepare a report in which the results to the following questions are discussed with reference to these subjects.

The problem presented here (file 3PROFIT) is largely inspired by Evenson’s 1983 study,

“Economics of Agricultural Growth: The Case of Northern India.” We consider a system of production with three crops (wheat, rice, and coarse cereals), produced with three variable factors (labor, bullock traction, and tractors), and two fixed factors (irrigation, and research and extension). The impact of other fixed factors we do not wish to investigate (such as land, rainfall, etc.) has been incorporated in the model’s constant term. The model is derived from

a normalized quadratic profit function. The system of product supply and factor demand is written as:

qi ao bij(pj/w)



j ^ bik zk



k , i1,, 6, j1,, 5, k1, 2,

where q_i represent the three products and three variable factors (positive values for the products and negative values for the factors), p_i / w their prices relative to wage (w), and z_k the structural variables.

The first part of Table 3E.1 gives the parameter estimates for the a’s and the b’s. The supplementary row, “Research own price,” will be used for the analysis of cross effects and is ignored for the moment. On the right, column J reports the average values of the exogenous variables in the sample. Irrigation is measured by the percentage of crop land irrigated, research and extension by cumulated expenditures in constant price over the past 5 years, and quantities of product and input in values in constant prices.

Table 3E.1 approximately here

1. The price and fixed factor elasticities in this model are variable. Therefore, their values can be calculated only for a given value of the exogenous variables. Using the average value observed in the sample, the price elasticities of supply of wheat are calculated in column L:

E(q_i/p_j)(b_ij p_j/w)(1/q_i), E(q_i/w) – b_ij p_j/w

j



 

(1/qi) – E(q_i/p_j)

j ^{, and}

E(q_i/z_k)b_ikz_k/q_i.

Complete the table of price and fixed factor elasticities of supply for the other products and of demand for the factors. Note, in cell L23, that the formula used to calculate the elasticity with respect to wage is different from the others. Discuss the results in terms of complementarity/

substitutability between products and between factors. Verify the signs of the other price elasticities, that is to say, for the products in relation to the prices of factors and for the factors in relation to the prices of products. Analyze, in particular, why the signs for the elasticities of factor demand have been reversed. Contrast the values of the elasticities of supply and factor use with respect to the two structural variables.

2. Simulations of the impact of changes in the exogenous variables are given in the lower part of Table 3E.1. The first entries of that part of the table include the values of the exogenous variables; the second give the predicted levels of production and factor use; and last, beneath, the third block reports the percentage changes in the endogenous variables relative to their base values. The first column reproduces the base values. In the second column, the price of wheat is increased by 10%. The new values are 16,950 for wheat production, 11,355 for rice production, and so on. This corresponds to an increase of 3.6%

for wheat, a decrease of 2% for rice, and so on. (Dividing these results by 10 also gives you the different direct- and cross-price elasticities with respect to the wheat price.) Notice that even if an increase in the price of wheat can induce a slight increase in the production of that

product, this occurs at the cost of a decrease in the production of rice, and therefore the impact on aggregate agricultural output will be low. Repeat this exercise for an increase in the price of rice. Comment on your results.

3. Considering wheat and rice as tradable products, considering that the price of tractor services is linked to the international price of imported tractors, and considering that the services of draught animals and labor are not tradable, what will be the impact of an exchange rate devaluation of 15% on agricultural production? Simulate for that purpose the impact of a simultaneous increase of 15% in the prices of wheat, rice, and tractor services. You should observe a drop in the production of the nontradable product. It is precisely this reallocation effect which a policy of exchange rate devaluation attempts to achieve. Going beyond the framework of this production model, what can be expected for the evolution of the demand for nontradable products and, therefore, for their equilibrium prices? In our case, there is complementarity between nontradables and wheat, and substitutability with rice is not very strong. The fall in production of nontradables is consequently not large. Analyze the perverse effect of a devaluation on the utilization of tractors, even though these are imported.

4. We will consider that the structural variables represent respectively a private investment (tube well irrigation) and a public investment (research and extension). Simulate in columns G and H the effects of a 10% increase in each of these structural variables.

Analyze the impact on the production structure. Compare the total increase in outputs with the total increase in factors. What can be induced about the total factor productivity of the variable factors?

5. The structural variables, considered fixed in the short run, change in the long run.

Private investment is often considered to respond to global profitability and, therefore, to product and factor prices. Based on the study cited above, add in column I, under the heading

“irrigation,” the coefficients of an equation that determines the level of the private structural factor, here irrigation. This equation is written:

irrigation10.0920p_wheat/w0.015research.

You see, in this equation, the effects of price incentives and of complementarity between public goods (research) and private investment (irrigation). Introduce the parameters of this new equation in column I (that is, 10.09 in cell I10, and so on) and an additional row (row 70) in the block of endogenous variables in which you calculate the estimated value of the irrigation variable. The expression that you must enter is analogous to those used in the calculation of supply of different products or of factor demand. To calculate the long-run price elasticity which includes these investments, proceed in two stages:

a. Use your simulation of a 10% increase in the price of wheat in column D. Read the new values for irrigation in cell D70.

b. Report the value in cell I39 as the new irrigation level and combine it with the effect of a 10% increase in the price of wheat.

Compare this long-run price elasticity of wheat production with the short-run elasticity of question 2. Print and/or save your results, as the model will be changed in the following questions.

6. The impact of a public good is often considered as a factor increasing the elasticity of supply response. In order to reflect this, we can add a cross term, product of the research variable by the price of the product, corresponding to the following model:

qwheat ao(544133research)pwheat/w

jwheat



bij pj/w



k bik zk.

This is done in row 22, in the column of the wheat equation, by addition of the variable . In this cell, C22, introduce the value 33 for the corresponding parameter. Reduce the value of the intercept sufficiently (by subtracting the product 33

232.19, which is the average value of the new variable) in order to reproduce the base values with this new equation. Check that this is indeed the case in the first column of simulations. With this new model, calculate the direct price elasticity for wheat by simulating the impact of an increase in the price of wheat. Compare this with the simple elasticity obtained earlier in question 2.

research p_wheat /w

7. The following equations represent the total impact of public investment (in research and extension) on wheat production:

q_wheat a_o(544133research)p_wheat/w b_ij

jwheat



^pj /w56research531irrigation, where irrigation10.0920p_wheat /w0.015research.

These equations show that the total impact of public investment on wheat production can be decomposed into three related effects.

First, in the short run, a change in research investment affects wheat production directly.

This was simulated in question 4 by increasing research and extension by 10%.

Second, a change in public investment will also indirectly affect wheat production by changing the way production responds to a change in price (i.e., a change in research investment changes the own price elasticity of wheat production). To simulate these two effects together, create a column labeled 7(a) in the spreadsheet that you have just modified for question 6. In this column increase the research and extension variable by 10% as was done in question 4. The variable research wheat price in row 42 correspondingly increases. Now simulate the impact of this new set of exogenous variables on the endogenous variables.

Third, in the long run, a change in public investment will also have an indirect effect through the impact of public investment on investment in irrigation. To simulate the three effects together, extend the row labeled “estimated irrigation” across the bottom of all simulations. This row now shows the long-run impact of each simulated change in exogenous variables on investment in irrigation. The “estimated irrigation” in column 7(a) shows the long-run impact of a 10% increase in public investment in research on private investment in irrigation. Report this “estimated irrigation” to row 39 of a new column labeled 7(b). In this same column increase the research and extension variable by 10% as was done in 7(a). All other exogenous variables remain at base levels. Simulate the impact of this new set of exogenous variables on the endogenous variables.

Analyze these results.

References

Ball, Eldon. 1988. “Modeling Supply Response in a Multiproduct Framework.” American Journal of Agricultural Economics 70:813–25.

Bapna, Shanti, Hans Binswanger, and Jaime Quizon. 1984. “Systems of Output Supply and Factor Demand Equations for Semiarid Tropical India.” Indian Journal of Agricultural Economics 39:179–202.

Binswanger, Hans. 1974. “A Cost Function Approach to the Measurement of Factor Demand and Elasticities of Substitution.” American Journal of Agricultural Economics 56:377–86.

Binswanger, Hans. 1989. “The Policy Response of Agriculture.” World Bank Economic Review, Proceedings of the Annual Conference of Development Economics, 231–58.

Binswanger, Hans, M. C. Yang, Alan Bowers, and Yair Mundlak. 1987. “On the Determinants of Cross Country Aggregate Agricultural Supply.” Journal of Econometrics 36:111–31.

Evenson, Robert. 1983. “Economics of Agricultural Growth: The Case of Northern India.”

Unpublished paper, Yale University, Economic Growth Center.

Fulginiti, Lilyan, and Richard Perrin. 1990. “Argentine Agricultural Policy in a Multiple-Input, Multiple-Output Framework.” American Journal of Agricultural Economics 72:279–88.

Lopez, Ramon. 1980. “The Structure of Production and the Derived Demand for Inputs in Canadian Agriculture.” American Journal of Agricultural Economics 62:38–45.

Mundlak, Yair. 1985. The Aggregate Agricultural Supply Response. Working Paper no. 8511.

Rehovot, Israel: Center for Agricultural Economics Research.

Sidhu, Surjit, and Carlos Baanante. 1981. “Estimating Farm-Level Input Demand and Wheat Supply in the Indian Punjab Using a Translog Profit Function.” American Journal of Agricultural Economics 63:237–46.

Yotopoulos, Pan, and Lawrence Lau. 1979. “Resource Use in Agriculture: Applications of the Profit Function to Selected Countries.” Food Research Institute Studies 17:11–22.