JNU -1999

[Anjali]

In a closed economy output is given by Y= min(4K , 6L ). In period 1 , out of total labour force of 10000 , 1000 are unemployed. If the economy , habitually saves and invests 15% of output , and if rate of growth of its labour force is 10% per period , what would be the percentage of unemployment in period 2 ?

[Arushi :))]

hey ! i gave it a try. But pata nahin where i ended up.
U give me any suggestion after reading it :P
Y= min{ 4K, 6L}
Y= 4K
K/Y = 1/4 ( capital-output ratio)
now, using harrod domar equation,
s/theta= n+g
15%*4= 10%+g
g= 50%
 i.e output grows by 50%.
In period 1,
L= 9000 , Y = 6L = 54,000
then, in period 2, output grows by 50%
and new output will be , 81,000
now ,
to find L in period 2
6L= 81,000
this gives L = 13,500
But  the total labour force is 10,000!!
So............

[kangkan]

Hi.....we dont need to use harrod domar equation here..too many assumptions in that theoy...

Since people are unemployed, it means the economy faced a capital constraint

Y= min[0.4k,6l]... draw the isoquants..we will see that for 1 unit of capital, we can use 2/3 units of labbor...

Hence, 1 unit of labot will use 3/2 units of capital..now 9000 labor is employed,they must have used 1.5*9000=13500 units of capital..therfore capital stock is 13500...now Y=[0.4 k,0.6l]=min[5400,6000]=5400..

Now savings is 0.15..in closed economy savings=investment=0.15*5400=810..therefore new capital stock =13500+810=14310..now labou used will be=14310*(2/3)= 9540..new labor force is 11000..unemployment will be 11000-9540/11000=13.2%.

[Ashima]

Hey, I have understood the concept.

I am just not able to understand one thing.

     4 units of capital = 6 units of labor
=> 1 unit of capital = 3/2 units of labor

and you have taken exactly the opposite...
Is it by mistake or i am missing something? Please someone explain..

[kangkan]

Hi ashmia..

i made the mistake to first.. lets assume i have 1 unit of capital... anything above 2/3 units of capital will be useless to me.. because if l>2/3 than 6l will be greter than 4...but y=min[4k,6l] ..for k=1 and l=2/3 we have y=min[4,4]=4..lets assume l=0.75(>2/3)..than y=min[4,4.5]=4..hence any extra labor will be useless..

hence for 1 unit of capital,i can use only2/3 units of labour

[Anjali]

@ kangkan why have you taken .4 and .6 instead of 4 and 6 ? And how did you arrive at this new labour force ?

[Granpa Simpson]

Even I am getting 13500 as the labour force in the second period...!!!!

[Akshay Jain]

Total output in 1st period vl b min(4*k,6*9000), it is given that out of total 10000 labor 1000 is unemloyed so 9000 is emplyed
4*k=54000, k=13500 in the 1st period
now output is 54000 of which 15% dat is 8100 is investd in nxt period as additional investment
labor force in period 2 vl be 11000
so output in period 2 vl b min(4*21600,6*11000)=66000
hence no unemplyment nd capital vl be extra....

[kangkan]

Hi..akshay..but the prod function is given as=min[0.4k,0.6l)..hence if k=13500 wont the output be 0.4*13500=5400 in the 1st period?

Regards

[Homer Simpson]

The production function is Min(4K, 6L) - why have you taken min(0.4K, 0.6L)?

Y produced is based on the minimum i get of 4K and 6L. So if the economy is employing 9000 people in period 1, clearly output produced should be 54000. K has to be 13500 for this level of output.

Anything higher is contradictory if we are starting out with the idea that there just isnt enough capital available for the entire labor force to use. Anything below 13500 also doesnt make sense as lesser Y would be produced.

[kangkan]

@tsuki..my printout of the jnu paper says 0.4 and 0.6  :(

On Wed, May 7, 2014 at 2:07 PM, tsuki [via Discussion forum]
<[hidden email]> wrote:

> The production function is Min(4K, 6L) - why have you taken min(0.4K, 0.6L)?
>
> Y produced is based on the minimum i get of 4K and 6L. So if the economy is
> employing 9000 people in period 1, clearly output produced should be 54000.
> K has to be 13500 for this level of output.
>
> Anything higher is contradictory if we are starting out with the idea that
> there just isnt enough capital available for the entire labor force to use.
> Anything below 13500 also doesnt make sense as lesser Y would be produced.
>
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[Anjali]

Akshay in second period why have you taken L= 11000 ? That is total labour force and not the no of employed ?

[Homer Simpson]

Ooh acha! I dont have the 1999 paper actually :) i guess the answer would wary accordingly.

[Akshay Jain]

the ques is:
In a closed economy output is given by Y= min(4K , 6L ). In period 1 , out of total labour force of 10000 , 1000 are unemployed. If the economy , habitually saves and invests 15% of output , and if rate of growth of its labour force is 10% per period , what would be the percentage of unemployment in period 2
so total labor force in nxt period is 10000*(1.1)=11000

[Anjali]

But in period 1 , we took L= 9000 ( employed and not the labour force )
But in period 2 , where unemployment is unknown , we are taking L = 11000 ( which is the total labour force ) . Iam not clear with this part.
Btw Akshay , what are capital exports ?

[Dreyfus]

@anjali, because production function is of fixed proportion nature ......that's y Akshay took L=11000 as at optimum 4k=6L
As K grewed to 21600 so Labour employed in next period has to be equal to 11000 as it satisfies 4k=6L

[Anjali]

@vaibhav , Iam not convinced . Because
When K= 21600
4K is not equal to 6L
4*21600/6 = 14400

[Dreyfus]

Yes anjali there will be shortage of labour when capital stock of 21600 is used...so full labour ie 11000 will get employed in period 2 along with the capital stock,K=16500 ...therefore there will be no unemployment in period 2 but there will unutillise stock of capital=5100!

[Anjali]

My point is that how do we decide that L = total labour force ? In period 1 no of employed were given so we took L = no of employed , but why in second period we directly took L=entire labour force ? It means that we knew that there will be no unemployment

[Dreyfus]

@anjali ...hope this will clear ur confusion!