# ECON5005 Production Economics and Efficiency Analysis

INSTRUCTIONS: Do the following exercises and submit your results as a single PDF le using the link provided in the LMS. Provide complete and clear answers. Hand written answers are acceptable but need to be neat and well formatted. The weight marks for exercises 1, 2 and 3 below are 30, 50 and 20, respectively. If you have questions about this assignment, post them on the discussion board or ask during the last session so that any clari caitons can be provided in class. 1) Given the single-input production function y = 3x 1 2 , answer the following questions. a) Show that the input distance function is ID(x; y) = 9x y2 . b) Derive the output distance function OD(x; y). c) Derive the directional distance function DD(x; y). For this exercise assume that the direction vector used for the translation of the input- output vector (x; y) is g = (0; gy), i.e. this is an output directional distance function. d) Complete the following table by inserting for each observed input out- put combination the input-oriented technical eciency (TEx), output- oriented technical eciency (TEy) and the input/output/directional distance function values. Assume gy = 1 in the calculation of the di- rectional distance function values