Suppose that a firm's technology is based on the following eight basic activities:
y1 = ( -3, -6,4,0)
y2 = ( -7, -9,3,2)
y3 = ( -1, -2,3,-1)
y4 = ( -8, -13,3,1)
y5 = ( -11, -19,12,0)
y6 = ( -4, -3,-2,5)
y7 = ( -8, -5,0,10)
y8 = ( -2, -4,5,-2)
which can be operated independently at any scal, The aggregate production possibility set is
Y = {y1; y2; y3; y4; y5; y6; y7; y8}
1. Show that it is impossible to produce output without using any inputs, that is,

This is called the no-free-lunch property.
2. Show that Y does not exhibit free disposal (exercise 1.12).
3. Show that activities y4, y5, y6, and y8 are ine½cient. (Compare with y2, y1, y7, and y3 respectively.)
4. Show that activities y1 and y2 are inefficient. (Compare with a combination of y3 and y7.)
5. Specify the set of efficient production plans.
The following results are analogous to those for convex hull.

Transcribed Image Text:

y e Y,y > 0 = y = 0