cost doubt

[The Villain]

the prices of inpits (x,.y,z,p) are (4,1,3,2).


a) if prodn fn is given as f(x,y,z,p)=min(x+y,z+p) then what is the min cot of producing 1unit of output??
b) if prodn fn is f(x,y)=min(x,y)+min(z,p) wht is min cost of producing 1 unit of output?



please help

[Prerna Rakheja]

Hi,

a) cost = 3 units
b) cost = 5 units

[XIPP]

Prerna, I am getting:

(a) cost=5,
(b) cost=3

instead of
(a) cost=3,
(b) cost=5
 
Where am I (or you?) are wrong?

[The Villain]

hii prerna ..thanxx..
i got the first part...wt abt thr second??
could you show the soultion part....

[Prerna Rakheja]

Hi Ron,

Lets assume you produce 'a' amount of the good using x and y and '1-a' amount of the good using z and p.

Note you will have to use 'a' amount of both x and y, cost = 4a + 1a = 5a
'1-a' amount of z and p, cost = 3(1-a) +2(1-a) = 5 - 5a

Total cost = 5

@ XIPP
For part (a) consider the allocation x=0, y=1, z=0, p=1. Therefore, output = min{1,1} = 1
cost = 1(1) + 2(1) = 3. Hence your allocation is not cost minimising.

I would request you to kindly provide the allocation for part (b) that leads you to an output of 1 unit while it costs 3 units.