ISI , ME II ,2011, Q. no. 7

[AJ]

7.  An economy produces two goods, food ( F ) and manufacturing (M ).
Food is produced by the production function F= Lf^1/2.T^1/2 , where Lf  is the labour employed, T  is the amount of land used and  F  
is the amount of food produced. Manufacturing is produced by the
production function M = Lm^1/2.K^1/2 , where  Lm is the labour
employed,  K  is the amount of capital used and  M  is the amount of
manufacturing production. Labour is perfectly mobile between the
sectors (i.e. food and manufacturing production) and the total amount
of labour in this economy is denoted by  L.   All the factors of
production are fully employed. Land is owned by the landlords and  
capital is owned by the capitalists. You are also provided with the
following data:  36 = K ,   49 = T , and  100 = L . Also assume that the
price of food and that of manufacturing are the same and is equal to
unity.
(a) Find out the equilibrium levels of labour employment in the food
sector and the manufacturing sector (i.e. Lf  and Lm  respectively)
(b) Next, we introduce a small change in the description of the
economy given above. Assume, everything remains the same except
for the fact that land is owned by none; land comes for free! How
much labour would now be employed in the food and the
manufacturing sectors?
(c) Suggest a measure of welfare for the economy as a whole.  
(d) Using the above given data and your measure of  welfare,
determine whether the scenario given in problem (b), where land is
owned by none, better or worse for the economy as a whole, compared
to the scenario given in problem (a), where land is owned by the
landlords?  
(e) What do you think is the source of the difference in welfare levels
(if any) under case (a) and case (b).


.....

for (a) part I got, .. Lf=57.64 ... and Lm=42.36

.... what to do for remaining parts... ????

[ritu]

hi aj :)
we had a long debate on this question....5-6 weeks back....but apart from a part we couldnt reach any conclusion for remaining parts...:(((

[anon_econ]

lol

[AJ]

Okay..

So, What do you think about this answer....



I personally wasn't able to convince myself with 'b' part's 'all labour will be spent on food' logic...

What I think is that
division of labour among two will be same.. cuz.. we were equating VMP of labor in both industries (cuz wage rate wud be same in both) .. which is now also same..
earlier also all the units of Land and capital were employed in respective industries...
with land as free good..it will still be fully employed...

so, there's no change in outputs....

So, what this free land assumptions changes?
it changes the cost of producing F...

earlier both prices were 1.. so MC in both industries were less than or equal to one..
And the output was divided in economy as.. rent(for land), interest(for capital), wage(for labour) and profits(if any, i.e. if MC<P)

and now... (since acc to me output is same) .. interest on capital will be same... wages will be same...
just the 'rent' part now forms the part of profit... (since cost has reduced and thus profit increases) ...

so.. for c part... measure of welfare... <smiley image="anim_confused.gif"/> .. may be we can have output or income as the measure....

and as a whole there's no change in welfare...


So, is any of this making any sense at all....among both answers above can anything apply here....

or I have lost it completely....

[AJ]

Ah, the size of pic is too big...
U will have to scroll right- left- right- left..
Sorry for inconvenience!