DSE2008 (Ques 46, Option A)

[vikram]

This question is last one belonging to question set where we are given the production function as Y = A*L^a*K^(1-a) and then later on U = C^b + (L-Ls)^b. We get the labour supply and labour demand functions. In the question it is asked to find out the shape of aggregate supply curve.

Shouldn't it be upward sloping? In the answer key it is given 'vertical' and explanation is given as "perfect foresight hypothesis".

Please help!

[aditi5000]

Even i am stuck on this question.. What would vertical AS look like btw? (in the equation form)

[lovekesh]

Vertical AS curve will be any equation in Y that does not contain P.
AS curve should be upward sloping considering the optimal labor supply will change as P changes for the consumer. Even equations don't turn out independent of P.

[aditi5000]

So is the answer key wrong.. Even my equation is not turning out to be independent of P. What's the correct answer then.. Upward sloping naa?

[s]

hey vikram,
if there is perfect foresight/information then it means workers perfectly revise their price expectations ie they get to know when actual price level changes and accordingly revise their real wage..as in if P rises Lab dd schedule shifts up and at the same time labor ss schedule shifts up such that nominal wages rise by the exact amount of rise in P..in that case N unchanged Y unchanged with P rise and W rise..AS is vertical for perfect foresight
 @ aditi i got the same prob, the AS i got for this problem  Y = A(Ls)^a(Kbar)1-a where Ls =[Lbar(W/P)^b/1-b]/[1+(W/P)^b/1-b] is dependent on P ....
 
someone please help!

[Amit Goyal]

All of you are incorrectly interpreting Aggregate Supply. This is how you define Aggregate Supply:
AS = {(Y, p) | demand for labor(W, p) =  supply of labor(W, p) = equilibrium employment, Y = f(equilibrium employment)}
Now rethink about it.

[aditi5000]

Oh ok! Sir I reworked this and equated labour demand and labour supply functions to get the following equation...
L eqbm = L bar - K bar* (A. alpha)^1/(1-alpha) (w/p)^(1-beta.alpha)/(alpha-1)(1-beta)

(i am not sure about this)

Then i put the above into the production function and got

Y= A {L bar - K bar* (A. alpha)^1/(1-alpha) (w/p)^(1-beta.alpha)/(alpha-1)(1-beta)}^alpha (kbar)^(1-alpha)

So i have the following 2 doubts
1. - when we equate labour ss and dd, should we find eqbm w/p or eqbm L* ? is the thing i have done correct and,
2. how can we assert vertical nature of AS curve by looking at the AS curve equation where labour dd=labour ss and Y at eqbm output and eqbm employment?
Please help Sir!!

[Amit Goyal]

Ok. Let me ask you this question first. Do you agree that the labor market clear at a fixed real wage? If yes, then what is it?
Hint: See Problem 45

[aditi5000]

Thank you for your response Sir :)
Yes Sir, equating labour ss and dd should give us eqbm w/p and then we should get eqbm employment by plugging in eqbm wage rate into labour dd or ss.
I'm getting the following in parameters... (question 45 answer came out easily because of numbers!!)
for labour mkt to clear, I'm getting
(W/P) ^alpha.beta -1/(beta-1)(alpha-1) + (W/P)^1/(alpha-1) = Lbar/Kbar * (A.alpha)^1/(alpha-1)
=> W/P * [(W/P)^beta/(beta-1) + 1] ^ alpha - 1 = (L bar/K bar)^alpha -1 *A . alpha

Now how can I get W/P from here? I am not able to separate the variables... that is why I (wrongly) found out eqbm employment of labour from the above!

[Rain Man]

Hi Aditi
In this series of questions..how did you find the labor
Demand and labor supply curve in the first place..what was your approach..
Pls share

Thx

[aditi5000]

Hi rain man. I got labour demand by maximising profit of the firm and got labour supply by solving the utility max problem of the households.

[aditi5000]

Someone please help with this problem of vertical AS curve. Would really appreciate it. Thanks in advance. :)

[Amit Goyal]

Aditi, Can you first answer Q 45? And interpret what it means? And then I will tell you the answer to Q 46.

[aditi5000]

Sir in question 45, i put labour ss = labour dd .. and plugged in the values provided in the question.. From this, i found out an eqbm w/p that clears the labour market... and this eqbm real wage rate is unique and non-negative..

[Amit Goyal]

Well done. So, no matter what the price (p) is, the ratio of wage to the price (w/p) stays the same and since equilibrium employment is determined by wage price ratio in the model in question, so equilibrium employment also remains unaffected by change in price. This means that aggregate supply will remain unchanged if you change the price. And thus we have vertical aggregate supply curve.

[aditi5000]

Ohhhh!! So it's a concept... Lovely! Enlightening! Thank you Sir!!  I kept looking at (what I believed was) the AS curve was and differentiating wrt P to get god only knows what!! Thank you Sir!

[aditi5000]

Sir in the introduction to this question, it is provided that "general price level is exogeneously fixed at P bar".. So can we conclude vertical AS from this statement too.. ? my rationale is that if P is fixed and economy starts from an equilibrium position (also provided in the question) ... this could mean vertical AS. does this make sense Sir?

[Amit Goyal]

Aditi, the first thing to note is this: The convention is that we take Price on the vertical axis and Y on the horizontal axis. So vertical AS means that equilibrium Y remains unchanged even when the price changes. This is precisely what we got from the analysis. When they say price is exogenously given, they mean that for all the analysis you are going to do you will take them as given. And then the question that was asked in 46 is what happens to the output if we change this price level and thats what we answered.

[aditi5000]

Hmmm... yes... that makes sense... thank you again Sir :) And Sir what about the statement "producers and workers have perfect info about P and W"... what does this signify? i understand this means perfect foresight hypothesis in which p=pe but how can we use this in practical questions?