workbook ques

[Devika]

The prices of inputs (x1, x2, x3, x4) are (4,1,3,2)

If the production function is given by f(x1, x2, x3, x4) = min {x1+x2, x3+x4 }, what is the minimum cost of producing one unit of output?

[duck]

Hi Devika.. :)

Production function ,Y= min {x1+x2, x3+x4 }.
Clearly, for the firm "x1 and x2" are substitutes and "x3 and x4" are substitutes.
So, out of x1 and x2, as input x2 is cheaper. Firm would employ x2 and no x1.
Similarly, out of x3 and x4, Firm would employ x4 and no x3.
Therefore, Production function can be re-written , Y = min {x2, x4}
Now, x2 and x4 are always used by firm in a fixed proportion.
If Y=1, x2=x4=1
Therefore, Cost of producing one unit of output = Y(P2+P4) = 1(1+2) = 3.

[Devika]

Hiii duck!

Thank you so much.