Applications in Production Economics

1. Applications in Production Economics Lecture XXVII

2. Akridge, Jay T. “Measuring Productive Efficiency in Multiple Product Agribusiness Firms: A Dual Approach.” American Journal of Agricultural Economics 71(1)(Feb. 1989): 116–25.

3. The purpose of this article is to determine how effectively a sample of retail multiproduct agribusinesses achieve an objective cost minimization.” • “In particular, the frontier multiproduct cost function, which reflects the minimum cost of producing any given output vector as defined by the sample’s least-cost firms, provides the benchmark to make valid cost comparisons in multiple product firms.”

4. “The frontier cost function can be used to compare the observed cost of any sample firm against the cost which the sample’s least-cost producers would incur if producing an identical output vector and provides the basis for computing Farrell-type indexes of productive, technical, and allocative efficiency.

5. Measuring Productive Efficiency • Let CR(Y,W,K) be the total variable costs of producing output vector Y using input vector XR, where W is a vector of variable input prices and K is a vector of quasi-fixed factors of production • XR is the vector of inputs actually used.

6. CT(Y,W,K) is the cost of producing the output vector Y using the input vector XR • XR is the efficient input vector. • CP(Y,W,K) is the cost associated with input vector XP to produce output vector • XP is allocatively and technically efficient.

8. Farrell measures of efficiency

9. Single-factor technical efficiency (STEi) relates the technically efficient use of xi holding all other inputs constant to the actual application of xi.

12. Estimation • Akridge estimates the frontier assuming a non-stochastic Translog cost function with associated share equations:

13. The residual from the cost function is assumed to be distributed Gamma • The residual vector in the share equations are assumed to be normal

14. The likelihood function is then

16. Featherstone, Allen M. and Charles B. Moss “Measuring Economies of Scale and Scope in Agricultural Banking.” American Journal of Agricultural Economics 76(3)(Aug. 1994): 655–61.

17. “Study of the production technology of financial institutions can determine whether and to what degree economies of size exist and how agricultural lending will fit into the overall business plans of consolidated banks.”

18. Multiproduct Cost Concepts • Product-specific economies are measured by incremental cost. • The incremental cost of the ith output (ICi) is defined as the cost of producing the entire multiproduct output bundle [C(Y) ] minus the cost of producing all the output except the ith output

19. Product-specific economies of scale (Si ) are the average incremental cost of producing the ith output ICi/Yi divided by the marginal incremental cost of producing the ithoutput

20. If Siis greater than 1, then product-specific economies of scale exist. • Product-specific economies of scale are analogous to the single-output case of scale economies.

21. Economies of scope (diversification) arise from savings obtained from the simultaneous production of several outputs. • Economies of scope [SCi(Y)] exist if the cost of producing the optimal level of outputs in “individual firms” is greater than the cost of producing the same optimal output levels in a multiproduct firm.

23. Both the economies of scope [SCi(Y)] and product-specific economies (Si) can be combined to give an overall measure of the returns to scale for an individual firm: