1. 9/3/2015 Estimation of Catfish Production Function Using Cross-Sectional Survey Data Aloyce R. Kaliba Southern University and A&M College, Baton Rouge, LA 70809 David Bouras Lincoln University, Jefferson City, MI 65102

2. 9/3/2015 Presentation Format Introduction Rationale & Significance Literature Review Source of Data Data Analyses Results and Discussion Summary

3. 9/3/2015 Introduction: Production Function A production function describes a mapping from quantities of inputs to quantities of outputs as generated by a production process. The production function presupposes technical efficiency and states the maximum output obtainable from every input combination.

4. 9/3/2015 Introduction: Production Function Y it = f(X n,it : B)+u it Y =output i = farm t = time X = input n = number of inputs B = parameter U =random noise Therefore f(.) is average output of the farm given the technology.

5. 9/3/2015 Introduction: Production Function Commonly used production Function Cobb-Douglas production function Polynomial production function Constant elasticity of substitution (CES) production function Translog production function.

6. 9/3/2015 Introduction: Translog Production Function Where, y is the gross output, x is real input, α is the intercept or the constant term, β j are first derivatives, θ j are own second derivatives, and γ j are cross second derivatives. The translog functional form imposes no a priori restrictions on the substitution possibilities between the factor inputs by relaxing the assumption of strong separability of input.

7. 9/3/2015 Rationale and Significance Catfish production is an important segment of the Aquaculture Industry Competitiveness of the industry depends on productive efficiency. Marginal productivity analyses identify the most efficient and inefficient input; therefore area of improvement. Discuss any other means of evaluation. Input Elasticity shows the most limiting input; therefore focus for research and extension efforts.

8. 9/3/2015 Literature Review Generic translog Production function Under perfect competition assumption, output elasticity with respect to input equals to cost share of that input. We can get a system of cost share equations by differentiating the translog production function with respect to each factor input. Where β j represents the average cost share of inputs j, θ j represent input j own constant share elasticity, and γ j represent input j constant share elasticity with respect to other input k.

9. 9/3/2015 Literature Review: Multilevel Generic translog Production function The parameters β j (average cost share of inputs j), θ j (own constant share elasticity), and γ j and cross-constant-share elasticity) depend on farm size and extension contacts. We can add the system:

10. Estimation of Marginal Product of Inputs The marginal product of a factor can be computed as the product of the factor’s elasticity times its average product. Therefore marginal productivities can be computed at any point of the production function. It is convenient, however, to present the discussion in terms of the “average farm”, i.e., at the geometric means of output and inputs. 9/3/2015

11. SOURCE OF DATA Farm Survey of 41 catfish producer (input and outputs) Complete data for 34 farms. Outputs: Live catfish Inputs: feed, lab, fuel and gas, electricity, other expenditures Created Pseudo Sample of 1000 farms using Cholesky Decomposition Method 9/3/2015

15. Summary and Conclusion Farm size and Extension Contact Matters Small Farms needs more research and extension efforts to optimize all input use. Apart from large farm, feeding is a limiting factor for all other farm sizes. 9/3/2015

16. THANK YOU FOR YOUR ATTENTION ----------------------------------------------------------- 9/3/2015