(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Given that the natural log of the growth consumption rate is conditionally normally distributed. I am trying to convert it to a lognormal distribution, but I keep getting a variance that is different from what is in the solution manual. The problem is #3 in the document below

http://www.wiwi.uni-frankfurt.de/profs/faia/welcome_files/ch2ans.pdf [Broken]

2. Relevant equations

Log Ct+1/Log Ct ~ N[Et(logCt+1/logCt), Var (logCt+1/logCt)]

3. The attempt at a solution

I re-wrote Log Ct+1/Log Ct as an exponential function since log and e cancel out, and the mean is simply the expected value of function, but the variance I got was -1/2σ(Var Ct+1/Ct) which is different from what the solution manual says.

My problem is I dont understand how they got 1/2σ^2(Var Ct+1/Ct).

If anyone can explain that to me, I would be highly grateful.

For a clearer understanding of the question, you can look at #3 from the Solution Manual I posted above. It is Chapter 2, # 3 from Obstfeld and Rogoff's Foundation of International Economics. Thanks

https://docs.google.com/viewer?a=v&...2MtYmIxZi00OGVmLTkyMWUtYmU1M2E4Y2U0NGE4&hl=en

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# Homework Help: Mean and Variance of Lognormal Distributions

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