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The pork meat industry in Chile exhibits significant rates of production growth, with a decreasing trend in the wholesale market price and growing levels of concentration of the supply in a reduced number of companies. The structural element that johnsron concentration and expansion of the production is the presence of increasing returns to scale in the production process. This investigation had the objective to verify the presence of economies of scale in metdos industry.

Using a Cobb-Douglas cost function and the assumption of maximization of the benefits of the company in imperfect competition markets, an econometric model was estimated, that allowed considering indirectly the coefficients of the function of underlying production.

One was that for the periodthe industry presented increasing returns to scale, with an elasticity product-scale of 1. It was concluded that this industry economwtria conditions to increase its advantage in costs and of expanding its competitiveness in international markets. Se concluye que esta industria presenta condiciones para incrementar su ventaja en costos y expandir su competitividad en los mercados internacionales.

The pork meat industry has shown great dynamism in production growth rates as well as growing export volumes ODEPA, This dynamism has been accompanied by significant changes in the industrial organization of this sector. In effect, a fundamental element which allowed this growth in the vertical integration front and back, and the concentration of the demand in the corn market, which ecpnometria is open to foreign markets.

The pork meat offer has also been concentrated in a dominant company, revealing important cost advantages for it Dinzrdo and Foster, ; Vargas et al. These trends have caused a decrease in the wholesale market price levels; this trend was also documented wconometria the U.

### Estimación de Economías de Escala en la Industria de la Carne de Cerdo en Chile

Furthermore, agricultural policy elements function in this sector, linked jobnston the compliance to sanitary regulations for dlnardo slaughter as well as the domestic and exterior marketing dinaddo pork meat. There are also export quotas towards markets with which Chile has subscribed trade agreements, thus generating important business opportunities for this industry. One of the theoretical conditions for a market to respond to competition conditions is that the technology present in the industry should show yields at constant rates, both for the factors market as well as for the end product, since the companies will produce their optimum economic level in such quantities as will not have an influence in the balance Varian, If a company shows yields in a growing scale of its technology and the perfect information conditions are not present, this company can increase its participation in the market and in this way modify the structure of it, as is argued by Panzar and Amir Therefore, the presence of economies of scale in the technological process of a company of the industry generates the conditions for that company to have cost advantages as regards its competition, and eventually consolidate itself as a dominant or leader company in the market.

Carried to extremes, scale economy sustains the argument for the existence of a natural monopoly, since in that case the optimum production level coincides with the total demand of the market. This process can benefit the consumers, in the context of markets functioning with imperfect information, since the price paid is relatively lower, reflecting the greater efficiency of the company that shows economies of scale in its technological processes, as regards that which would prevail in a competitive market.

The identification and econometric estimation of economies of scale has been done using a trans-logarithmic costs function over panel data, linking size of the plant and variables related to technology, which emphasis on the cost elasticity at the level of primary production, such as happens econometriaa MacDonald and Ollinger and Ollinger et al. This functional form is flexible and, under determined restrictions on its coefficients, can represent several functional forms and can be applied to multi-product enterprises.

Ogunyinka and Featherstone arrive at this same conclusion after estimating a generalized Box-Cox production cost model, applied to agricultural products and raw materials in the United States. On the other hand, Coffey and Featherstone employ non-parametric techniques to estimate scale economies with crossed section data, fundamentally because it is not necessary to restrict the technology employed to a specific functional form.

The objectives of this research were: In this research the estimated model is based in a time series, is of aggregate character and takes into account the fact that the industry is highly concentrated. The model is of partial equilibrium and the main analytic assumptions are the following: The technology of the industrial sector of pork meat production, by hypothesis, can be structured according to the Cobb-Douglas technology Varian,that is: Starting from johmston expression and considering a long term situation, a technology shows yields in a growing scale when the sum of the exponents accompanying the variables labor and capital is greater than one, so that said technology shows economies of scale.

In johnstom context, the average dde cost decreases while the production level increases, up to a certain limit. An indirect way of estimating the coefficients of function 1 is by johnsron estimation of the costs function obtained from the Cobb-Douglas technology, more specifically, by means jojnston the marginal costs function, since this is expressed in terms of the price of the factors and the level of the production.

This is the fundament to set out the following assumptions. Maximization of benefits in imperfect competition. The maximization of the benefit is binding to obtain an observable relationship and fundament the jhonston model.

The optimum condition of an representative enterprise which determines its production level at the level at which the market price Py equals the marginal cost.

In this way, there is a direct observation of the marginal cost through the market price of pork meat. Thus, we see that the total cost function, issuing from a Cobb-Douglas technology, can be expressed as: Now, we can state that the market price of pork meat Py is equal to the marginal cost CMga condition of the first order for the maximization of the benefit. We consider the optimum condition for the case of a highly concentrated market in the market of the final product pork meat.

In this case, the price is weighted by a factor which measures the power of monopoly of dknardo representative enterprise, whose estimation is found in dknardo pioneer work of Bresnahan This factor alters the median price level to be observed in the industry, but not the estimation of the exponents of the function.

In the present work, the interest is centered in the exponent accompanying the production level, as it reflects the type of yield to scale present in the pork meat production process.

In this sense, it is fundamental to know the sign of this exponent. Dinarrdo logarithm to joynstonwe obtain: Then, the model to be estimated can be specified as: If it is positive, the technology shows yields on a decreasing scale, and if it is statistically equal to zero, this suggests a constant scale of yield. Metods error is assumed as white noise.

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Before the estimation was done, the variables were characterized from the statistical point of view and the hypothesis of normality of the same was assessed by means of the Jarque-Bera statistics Pindyck and Rubinfeld, The definition of the mettodos observed for the period was: Py, wholesale price of pork meat expressed in Chilean pesos per kilogram; w, salary index of the Chilean economy for the industrial sector, analysis unit of this research; r, interest rate of the financial system for one-year placements ; Y, port meat production level, measured in tons.

The statistical description of the series employed is shown in Table 1. Statistical characteristics of the series employed. Industria de la carne de cerdo. Unit root test for the variables of the model Given the characteristics of the estimated model, the variables were incorporated in their logarithm transformation.

The unit root test was applied in this manner. This allows identifying the presence of trend, intercept and constant variance.

## Comunidad del Centro Economía Aplicada

In this last case, the series has constant variance when, in absolute terms, the statistic of Dickey-Fuller Augmented DFA Johnston and Dinardo, calculated is higher than that tabulated. The result is shown in Table 2. It can be pointed out that all variables were stationary in the first differentiation, except for production, which was so in the second. Unit root test results in the model variables.

Estimation of the econometric model The estimated model considered controlling the autocorrelation of the residues and the presence of unit root in the variables considered. In this sense it was justified to incorporate the variables in logarithms; the salaries variable in the first difference and the correction factor of the autocorrelation of the residues AR 1 appearing in model 8.

## Estadística y Machine Learning con R

To this end the model was estimated with the Cochrane-Orcut correction Johnston y Dinardo,to attenuate the effect of the autocorrelation in the residues of the model. The AR 1 factor allows the introduction into the model of the systematic part which links the residues in t and t-1, generating a new residual term which complies with the assumptions of the classic model.

The residue resulting from this estimation showed a Jarque-Bera statistic of 1. This result suggests that the variables of the model co-integrate, that is to say, there is a long term balance relationship among them. Estimating model result for period Individual coefficients differed from zero, according to statistic t, as well as the group of the same, as seen in statistic F. The coefficient accompanying production resulted different and below zero, this suggests that the pork meat production process shows yields on a decreasing scale.

This is important in terms of competitiveness of the sector, as the mean costs follow a decreasing trajectory in the measure that production level increases. According to the estimated model, the addition of the elasticity product-labor and product-capital reached 1. This shows that the industry shows yields on a growing scale. Analyzing algebraically according to expression 2 in individual terms, the product-labor elasticity resulted as 0. To fundament these results, a contrast was effected upon a linear combination of the estimated coefficients, to validate that the sum of the interest rate coefficient To this end, a t test is applied, allowing to prove H0: Therefore the estimated t corresponds towhich is contrasted with t of the table.

These results suggest that the utilization of the factors in the industry is found in the rational steps, according to the theory of production, that is, the concave zone of the production function, where the benefit of the enterprise is positive. The case presented is characterized because the elasticity of the product factor is less than 1 and above zero Varian, On the other hand, given the product-factor elasticity found, it can be stated that the process aggregate is more capital-intensive.

Given the above results, the industry presents economies of scale, since the variation of the costs as regards production is estimated as 0. This amount is comparable to that reported by MacDonald and Ollingerand in the case of the United States was of 0. The true process sustaining the behavior of the port meat industry is its deep technological transformation, supported by the behavior of decreasing corn prices, a most important supply for pig feeding; this has taken place mainly since In this sense, it can be affirmed that the cost reduction associated to the behavior of the corn prices, has been a circumstance contributing to the processing industry to present economies of scale.

This fact is also reported for the case of the pork meat market in the United States Morrison, An additional incentive for the expansion of production is constituted by the opening of foreign markets by mean of trade agreements, as well as the restrictions to the import of beef meat due to animal health problems in some supplier countries. This is how that, considering equation 2the estimation of the coefficients and a hypothesis about the value of the parameter M, the following equation for the added cost for the pork meat industry was obtained: The result is shown in Figure 1.

Simulated average cost and meat pork production of the industry. The product-scale elasticity was estimated as 1. Market structure, scale economies and industry performance. The oligopoly solution concept is identified. The effects of U.

Nonparametric estimation of multiproduct and product-specific economies of scale. Scale economies and consolidation in hog slaughter. Equilibrio de un oligopolio con empresa dominante: Modelo de duopolio de Cournot: Cost economies and market power: Mercado de la carne de cerdo.

On the choice of functional forms in the measurement of scale and scope economies: Technological change and economies of scale in U.