Determine the supply curve and price elasticity of supply of Oyster mushroom (Pleurotus spp.) in the markets of Raipur, Durg and Dhamtari districts of Chhattisgarh

Introduction

Since its establishment, Chhattisgarh has been an agricultural state. The main crop in Chhattisgarh, whose central plains are referred to as the "Rice Bowl of central India," is paddy. Mushrooms, which are really fleshy, spore-bearing fungus creatures that typically arise above the ground surface or their source of food and belong to the botanical class Agaricomycetes and order Agaricales, are another interesting crop produced in Chhattisgarh. It is a waste-to-wealth crop with great therapeutic qualities that farmers can readily cultivate with little infrastructure. The term "mushroom" can mean different things to different individuals in different nations. They were considered "food of gods" by the Romans and a source of strength for warriors by the Greeks. Growing mushrooms requires less water and vertical space than other crops. It's a crop that turns trash into profit. Mushroom growing further supports farmers' livelihoods by offering steady farm income and employment opportunities. It is an indoor crop that doesn't require fertile land and may be grown without sunshine. Because it doesn't require a significant amount of cash, it may also be farmed on a small scale. This study focuses on the supply of the mushroom, for which primary data were collected from the mushroom growers and the markets of wholesalers belonging to the same districts. The primary data on supply was mostly collected from wholesalers except the disposable income, which was collected from some of the randomly selected consumers of oyster mushrooms (Pleurotus spp.) from the same markets.

Data & Methodology

There are around 2000 edible fungus species documented around the world, with 200 species available in India. Only six of these species are used in the growing process for commercial reasons in the Country, and they are: Pleurotus spp. (Oyster or Tropical mushroom), Out of all above types of mushrooms, this study focuses on the oyster mushroom (Pleurotus spp.) on the grounds of highest rank score achieved by it, based on seven parameters namely production process (PP), cost of cultivation (CC), popularity (P), affordability (A), nutritiousness (N), availability of substrate (AS) and environmental condition (EC) as shown in above Table.

Collection of Data

The producers were selected from the list of producers, who were associated and trained by the Mushroom Research Laboratory, Department of Plant Pathology, College of Agriculture and Research Station, Indira Gandhi Krishi Vishwavidyalaya (IGKV), Raipur, C.G., mostly belonging to Raipur, Durg and Dhamtari districts of Chhattisgarh. Along with the producers, data were also collected from some randomly selected consumers of some markets where the products of above-mentioned producers were being sold. The primary data were collected through interview method by personally visiting the mushroom growers and the markets of wholesalers belonging to the same districts or by telephonic interview method. Three questionnaires were prepared for the interviews from the respondents of Raipur, Durg and Dhamtari.

Method

A simple model of demand and supply

Demand

Supply

Where, P and Q are endogenous variables, and X is exogenous variables.

The Identification

In a system of M simultaneous equations, which jointly determine the values of M endogenous variables, at least M -1 variable must be absent from an equation for estimation of its parameters to be possible. In other words, we can say that the identification of the simultaneous equations is most important process for making their parameters estimable. When estimation of an equation's parameters is possible consistently, then the equation is said to be identified. If fewer than M-1 variable is omitted from an equation, then it is said to be unidentified, and its parameters cannot be consistently estimated.

In our supply and demand model, there are M=2 equations, so we require at least M-1=1 variable to be omitted from an equation to identify it. There is a total of three variables: P, Q, and X in simultaneous Equations (1-2).

In the demand Equation ( 1), none of the variables are omitted; thus, it is unidentified and its parameters cannot be estimated consistently. In the supply Equation (2), one variable, i.e., income (X), is omitted; thus, the supply curve is identified, and its parameter can be estimated.

The identification condition must be checked before trying to estimate an Equation. If an Equation is not identified, then changing the model must be considered before it is estimated. However, changing the model should not be done in a haphazard way; no important variable should be omitted from an Equation just to identify it.

The Reduced-Form Equations

The two structural simultaneous Equations ( 1) and ( 2) can be solved to express the endogenous variables P and Q as functions of the exogenous variable X and this reformulation of the model is called their reduced form given below as Equations ( 5) and ( 8). This reduced form is very important in its own right, which helps in understanding the structural Equation system. To find the reduced form, we solve (1) and ( 2) simultaneously for P and Q.

To solve for P, we equate the equations corresponding to the equilibrium quantity, Q, of both the demand and supply, as in Equation (3):

To solve for Q, substituting the value of P from (4) into the supply Equation ( 2):

= π 2 X + v 2 (8) The parameters π 1 and π 2 in ( 5) and ( 8) are called reducedform parameters. The error terms v 1 and v 2 are called reduced-form errors.

Two-Stage Least Squares Estimation (2SLS):

i) Least squares estimation of the reduced-form Equation for P and the calculation of its predicted value P ̂.

ii) Least squares estimation of the structural Equation in which the right-hand-side endogenous variable P is replaced by its predicted valueP ̂.

Result and Discussion

Since supply and demand work together to establish the amount and price of items in the market and achieve some equilibrium, they do so at specific price and quantity coordinates for the target markets, such as Raipur, Durg, and Dhamtari in the current context. Equations ( 1) and ( 2) already provide the supply and demand forces as simultaneous econometric models. These models are modified to meet the needs of the current study and are produced below in Equations ( 9) and (10), which explain the quantity and price behaviors of oyster mushrooms in the Raipur, Durg, and Dhamtari markets according to the equilibrium reached in each market.

Demand: Q= Int. + P + PS + DI (

Supply: Q= Int. + P + PF (10) In order to solve the simultaneous equations model Equations ( 9) and ( 10), the market dictated two substitute commodities of oyster mushroom, namely, soybean and chicken. Therefore, three simultaneous equations have been solved, each-consisting of substitute's soybean, chicken and chicken + soybean combine together.

Identification

In M simultaneous equations, which jointly determine the values of M endogenous variables, at least M-1 variable must be absent from an equation for estimation of its parameters to be possible. Here in supply and demand model there are M = 2 equations, so require at least M-1=1 variable to be omitted from an equation to identify it. There is a total of three variables: P, Q, and DI. In the demand Equation none of the variables are omitted; thus, it is unidentified and its parameters cannot be estimated consistently. In the supply Equation, one variable, income (DI), is omitted; the supply curve is identified, and its parameter can be estimated.

Derived reduce form for the Equation ( 9) and ( 10 For the analyses of price elasticity of supply of oyster mushroom in the Raipur market, the statistical methods of linear mixed effect model, has been applied because the supply data were collected for a random number of 5 weeks, neither for the whole year nor for any given season, therefore week may affect the supply of oyster mushroom in a random way. Hence statistically speaking, for fitting the supply curves it is more befitting to consider week as a random effect instead of being a simple fixed effect. Thus, the results of fitting the linear mixed effect model are given in the Table-4.5.1 followed by subsequent discussion From Table-4.5.1 the linear mixed effect model for the supply curve has been estimated using R as in Equations 4.7-4.8, where both the constant coefficient and the price elasticity coefficient of supply were found to be highly significant: For the analyses of price elasticity of supply of oyster mushroom in the Durg market, the statistical methods of linear mixed effect model, has applied because the supply data were collected for a random number of 5 weeks, neither for the whole year nor for any given season, therefore week may affect the supply of oyster mushroom in a random way. Hence statistically speaking, for fitting the supply curves it is more befitting to consider week as a random effect instead of being a simple fixed effect. Thus, the results of fitting the linear mixed effect model are given in the Table-4.5.2 followed by subsequent discussion. ---Signi.codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

From Table-4.5.2 the linear mixed effect model for the supply curve has been estimated using R as in Equations 4.9-4.10, where both the constant coefficient and the price elasticity coefficient of supply were found to be significant: For the analyses of price elasticity of supply of oyster mushroom in the Dhamtari market, the statistical methods of linear mixed effect model, has been applied because the supply data were collected for a random number of 5 weeks, neither for the whole year nor for any given season, therefore week may affect the demand and supply of oyster mushroom in a random way. Hence statistically speaking, for fitting the supply curves it is more befitting to consider week as a random effect instead of being a simple fixed effect. Thus, the results of fitting the linear mixed effect model are given in the Table-4.5.3 followed by subsequent discussion. From Table-4.5.3 the linear mixed effect model for the supply curve has been estimated using R as in Equations 4.11-4.12, where both the constant coefficient and the price elasticity coefficient of supply were found to be significant:

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