DSE 2011 44

[MR]

Consider a firm using two inputs to produce its output. It is known that greater use of both inputs increase output. Moreover, for any combination of positive input prices, the firm employs an input combination of the form (x,ax) where a>0 is a constant. Which of the following functions represents this firm's technology?
a. f(x,y)= min{x^a,y}
b. f(x,y)= min {ax,y}
c. f(x,y)= min{x,ay}
d. f(x,y)= min{x,y^a}

Answer is b. But how do we conclude that?

[duck]

Hi MR.. :)

Its given in the question that the firm always employs inputs in some fixed proportion.
If it employs "1" unit of "x" then, "a" units of "y" [As y=ax ]
Therefore, f(x,y) = min{ax,y}