exercise 1

The following production plans are feasible: (10, -10, -70) ; (10, -20, -40); (10, -35, -35) ; (10, -40, -20) ; (10, -80, -10); (20, -40, -80) ; (20, -50, -60) ; (20, -80, -40). The negative numbers stand for inputs and the positive one for output. Also, technology is convex and scaling up is possible (for scaling parameter t > 1). a. In a graph with the two inputs in each axis, plot all 8 production plans. b. Create 4 new feasible production plans according to the following specifica- tions: i. A combination of (10, -20, -40) and (10, -40, -20), where the weight on the 1" and 2" plans is (A + 6)/20 and (14 - A)/20 respectively. ii. A combination of (20, -40, -80) and (20, -80, -40), where the weight on the 1" and 2"d plans is (B + 6)/20 and (14 - B)/20 respectively. iii. A scaling of (10, -10, -70), with scaling parameter t = (11 + B)/10. iv. A scaling of (10, -80, -10) , with scaling parameter t = 2, where you should replace A and B with the last and second-to-last digits of your ASU ID# respectively. c. Which production plans can you eliminate for being non-efficient? Graph the isoquants for output equal to 20 and 10'. d. New technology is discovered. Now the production plan (20, -80, -30) is feasible. Eliminate non-efficient production plans and graph the new isoquant for y = 20. e. Now assume that the technology exhibits constant returns to scale (for all scaling t > 0). Eliminate more inefficient plans and graph the new isoquants for output levels 10 and 20