Production

[Devika]

Consider the following production technology func-
tions. For each, identify whether the firm has
increasing returns to scale, decreasing returns to
scale, constant returns to scale, or if the returns to
scale varies with input levels.
(a) f(x1; x2) = min {ax1; bx2} where a; b > 0
(b) f(x1; x2) = min {ax1^2, bx2^0.5} where a; b > 0
(c) f(x1, x2) = 1/2 log(x1) + 1/2 log(x2)  for x1x2 >=1
                          0                            for x1x2 <1

[Sumit]

a)constant return to scale..
b) increasing return to scale..
c)constant return to scale

[vandita24x7]

A) IRS

B)DRS

C)VARIES WITH INPUT LEVEL COZ WE GET LOG(x1^1/2*x2^1/2), if x=1 then log 1 =0 but for x>1 CRS

 M NOT SURE... others confirm pls

On Fri, May 17, 2013 at 7:21 PM, Devika [via Discussion forum] <[hidden email]> wrote:

Consider the following production technology func-
tions. For each, identify whether the firm has
increasing returns to scale, decreasing returns to
scale, constant returns to scale, or if the returns to
scale varies with input levels.
(a) f(x1; x2) = min {ax1; bx2} where a; b > 0
(b) f(x1; x2) = min {ax1^2, bx2^0.5} where a; b > 0
(c) f(x1, x2) = 1/2 log(x1) + 1/2 log(x2)  for x1x2 >=1
                          0                            for x1x2 <1

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[vandita24x7]

sorry A is CRS

On Fri, May 17, 2013 at 7:30 PM, Sumit [via Discussion forum] <[hidden email]> wrote:

a)constant return to scale..
b) increasing return to scale..
c)constant return to scale

---

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[vandita24x7]

SUMIT CAN U PLS SOLVE THIS

 q1 in an economy whr capital and labour are only factors of production.  capital stock  : 1000, output capital ratio : 0.4 ,employment : 200,wage rate:1 ,rate of profit is: 
 a)5% 
b)10% 
c)20% 

On Fri, May 17, 2013 at 7:31 PM, vandita 24x7 <[hidden email]> wrote:

sorry A is CRS

On Fri, May 17, 2013 at 7:30 PM, Sumit [via Discussion forum] <[hidden email]> wrote:

a)constant return to scale..
b) increasing return to scale..
c)constant return to scale

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[Taanya]

CONTENTS DELETED

The author has deleted this message.

[vandita24x7]

I SUPPOSE IN 2 SINCE ITS A MIN FUNCTION HENCE WE GO WITH THE MIN FACTOR AVAILABLE WHICH IS X2^.5(acc to theory of minimum functions)

On Fri, May 17, 2013 at 7:34 PM, Taanya [via Discussion forum] <[hidden email]> wrote:

Shouldn't 2 be IRS?

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[Devika]

heyy..
could you explain your method for part b. I'm having a hard time solving it.

[vandita24x7]

arre minimum function jab hota hai say a company is producing 4monitors and 2 keyboards n function is min(4,2) so effectively it is producing only 2 pc's na.. dats d definition of min function

On Fri, May 17, 2013 at 7:40 PM, Devika [via Discussion forum] <[hidden email]> wrote:

heyy..
could you explain your method for part b. I'm having hard time solving it.

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[Devika]

Ok. So its DRS.

Thank you!

[vandita24x7]

1 in an economy whr capital and labour are only factors of production.  capital stock  : 1000, output capital ratio : 0.4 ,employment : 200,wage rate:1 ,rate of profit is: 
 a)5% 
b)10% 
c)20% 

pls try dis asap

On Fri, May 17, 2013 at 7:48 PM, Devika [via Discussion forum] <[hidden email]> wrote:

Ok. So its DRS.

Thank you!

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[Sumit]

@Vandita 24x7:
 part.b) certainly not IRS.. but I also doubt that it's certainly DRS....I think it can be vary acc..to level of input..bcoz If you take a,b both=1,,,n take initial input x1=1,x2=1....n then doubling both the inputs....then you will see that ouput remain same..

n for part c) its CRS bcoz if you see it closely its nothing but cobb-douglas prod. fn...which is always constant return to scale....


n the question you asked I think has incomplete information....

[vandita24x7]

yes c is a monotonic transformation i did not consider that :p. and B is  DRS for both x1, x2>1 right??

On Fri, May 17, 2013 at 8:04 PM, Sumit [via Discussion forum] <[hidden email]> wrote:

@Vandita 24x7:
 part.b) certainly not IRS.. but I also doubt that it's certainly DRS....I think it can be vary acc..to level of input..bcoz If you take a,b both=1,,,n take initial input x1=1,x2=1....n then doubling both the inputs....then you will see that ouput remain same..

n for part c) its CRS bcoz if you see it closely its nothing but cobb-douglas prod. fn...which is always constant return to scale....


n the question you asked I think has incomplete information....

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[MI]

HI Vandita,

Y/K= 0.4 ...given

=> Y= 0.4 x 1000 = 400

As K and L are only factors of production, whole output (read income) will be divided in these two factors.

Labor will get = Employment * wage rate = 200

Profit will be ( or total rent on capital) = Y- labor income = 400 -200 = 200

Profit rate ( rental rate of capital ) = Profit ( or capital income) / K = 200/1000 = 20%