Nominal Exchange rate Formula!!!!(Urgent) Amit sir/duck Plz help!!!!

[Sumit]

Hey Guys,
Help me in this there are two formula of Nominal exchange rate that I encounter while reading Mankiw And Dornbusch Fisher...plz tell me which one is correct..

Mankiw: Nominal exchange rate=real exchange rate*P^/P.....where P^=price of foreign goods and P=price of domestic goods..

Dornbusch Fisher: Nominal exchange rate=real exchange rate*P/P^.....where P^=price of foreign goods and P=price of domestic goods..


My Argument as follow:
Suppose we take Nominal exchange rate btw Rupee n Dollar...Say Rs.50/$..
Consider mankiw Formula:
Rs.50/$=Real exchange rate*P^/P..Also we are assuming Real exchange rate to be fixed...

Now, consider there is a depreciation of rupee or Appreciation of Dollar....Say Rs.55/$.

In the formula this depreciation of rupee means that price ratio(i.e P^/P) has increased (Note: we have assumed real exchange rate is fixed) which in other words means foreign goods become relatively more expensive than domestic goods....So, boz of this reason there is increase in net export.

Now, My argument is that in generally we know that the result of currency depreciation usually improves balance of trade( excluding J-curve condition)...Which we can also see in above case that the result of currency depreciation is to increase in net export...Is this means that Mankiw formula is right and dornbusch formula is wrong bocz as we take Dornbusch formula the depreciation of rupee means foreign goods become relatively more cheaper than domestic goods...which is opposite what we get in mankiw formula...????

Plz explain which one is right???
 

[Devika]

I've the same doubt.
There are two ways in which Nominal Exchange rate and hence Real exchange rate can be expressed.

For e.g., if nominal exchange rate says 56Rs/$ then your real exchange rate will be:
RER = NER * (Pu/Pi), where NER is 56Rs/$, Pi is price level in India and Pu is price level in USA. In this case, NX will be an increasing function of RER.

On the other hand if NER is 0.018$/Re, then your real exchange rate will be:
RER = NER * (Pi/Pu), where NER is 0.018$/Re, Pi is price level in India and Pu is price level in USA. Here, NX will decrease if RER rises.

India- Domestic and US- foreign.

Now, the IS curve will be downward sloping in the (Y,RER) space in the second case. Thats what mankiw shows. So what will be the slope of the IS curve for the first case?
Because NER rising is depreciation according to DBF.

[Sumit]

Hey devika one think...I'm quite sure of that NX is a decreasing function of real exchange rate....the reason for that Real exchange rate is nothing more than a relative price....we take RER formula as (RER=Price of domestic good(in terms of foreign currency Say $) divided by price of foreign goods i.e price of US good in terms of dollar) whenever we take exchange rate Say $0.018/Rs. where india-domestic n US-foreign.....So, in this case As RER increases which means NX of india will fall....bcoz increase in RER means Price of domestic good(in terms of foreign currency Say $) increases which in turn means for foreigners our Indian good is more expensive relative to there own good in terms of $...So, they will import less which means India export less...


I think Your second case where you take RER = NER * (Pi/Pu), where NER is 0.018$/Re...is correct boz you take india domestic & us-foreign....

N The first case is wrong  boz the RER you mentioning here will be for US ..i.e As this exchange rate increase NX for india will Increase n NX for US will decrease.... so, the point that NX is a decreasing function of real exchange rate is also true in this case If we take US-domestic n india-foriegn.....

I think the th discrepancy in the formulas given by mankiw n Fishers is due to this reason only....
but still I'm not sure....must need some expert view on this...

[Devika]

Agreed. Hopefully, Amit sir, duck will soon step in :)

[MaX]

Dornbush formula is correct which is giving the sensible outcome as already explained by sumot above, Real exchange rate increase means that domestic ptice of foreign goods have increased relative to domestic price of domestic goods, hence  a improvement I'm current account is witnessed. and vice versa

[Xiang]

see if this helps:

http://econ.la.psu.edu/~bickes/realex.pdf

[duck]

Hey.. :)

Dont know much about it. But as far as i know, real exchange rate is independent of units. (We never say Real exchange rate is Rs1/$. We always say Real Exchange Rate is 1). It tells how much goods and services in the domestic country can be exchanged for the goods and services in a foreign country.
So, RER should be  NER(P'/P)
where P'=foreign price and P=domestic price.

Consider an example:
A book costs $4 in US and the nominal exchange rate is Rs50/$ ,then with a real exchange rate of 1,
the book should costs 200rs in India. (Using above formula)

Also note:
The first currency quoted in a currency pair on forex is the base currency(domestic currency).
Now, If Nominal exchange rate "n"= Rs50/$
then, we're looking in view of India.
So, real exchange rate "r" would be = n(P'/P)
where P' is US price and P is price in India.

[Sumit]

I think I got My answer all this discrepancy is only coz of Exchange rate which can be expressed in Two ways...

Consider NER=Nominal exchange rate, RER=real exchange rate, P=Domestic good price, P*=Foreign good price
 
Let Assume India=domestic country and US=foreign country.
Also Assume NER=Rs.50/$ which can be written as $0.02/Rs, P=Rs.200 & P*=$4

Now, First consider Mankiw formula Which Says RER=NER(P/P*).In this Formula Mankiw take NER=$0.02/Rs.So as we calculate RER{(0.02*200)/4} we will get RER=1...In other words, what mankiw is doing that he is calculating RER by following method RER=Domestic good price in terms of foreign currency/foreign good price in terms of foreign currency.

Now, Consider Dornbusch & Fishers Formula which says RER=NER(P*/P).In this formula Dornbusch & Fishers fisher take NER=Rs.50/$.So as we calculate RER{(50*4)/200} we will get RER=1 which is same as given by Mankiw formula....In other words, Dornbusch & Fishers try to calculate RER by following method RER=Foreign good price in terms of domestic currency/Domestic good price in terms of domestic currency.

Conclusion: Both the formula is correct n provide us a same RER but the difference in formula occurs due to method of calculating RER...Mankiw take the Domestic currency price in terms of foreign currency(i.e NER $0.02/Rs) whereas Dornbusch & Fishers take foreign currency price in terms of  Domestic currency(i.e NER=Rs.50/$)....

PS: Thank you so much Devika n Duck your inputs help me to solve this problem...also thanks duck for reminding me that RER is independent of units....

thanks Xiang for your link...appreciate it!!!...

[Amrith]

question is nt abt the correctness of formula ...both r rt..
but the entire analysis wld change depending upon which one we use

for eg ...if r is increasing means real depreciation ...if we use r=R* (pf\pd)
 
it is real app if we use r=R(pd\pf)


in the exam which one shall we use...anwer will change acc..
 
this is wat the confusion is all abt....

 am i rt?