LOGARITHMIC UTILITY

[Tanu_Jaiswal]

Please help me with the following questions :

1)Does the utility function U=Log X show diminishing Marginal utility ??
2)A consumer spend 1/4th of his income on food. Price of food rises by 10% while his income rises by 3%. The consumer's utility rises/ falls/ remains same/ cannot say ?
3) If Q= aP^ alpha. Y^ gamma , where Q is quantity demanded,
then Price elasticity of demand is equal to Alpha or what ?

[sonal dhawan]

Q1:yes MU is dimnshing...bcoz the second differential of log x wrt x is negative

[The Villain]

@ tanu..
yes diminishing
it think it falls

[Homer Simpson]

1) MU = (1/x)
    MU' = -(1/x^2)

now for any x>0, MU' < 0

Thus it shows diminishing marginal utility

3) Yeah its alpha

[Homer Simpson]

2) Yeah utility will decrease - made a careless mistake will calculating F' !

[Aranya]

I m not sure but i think according to the qsn prportion of income spent on food is still 1/4 th( i mean after the changes), in that case (may be) utility decreases.

[Tanu_Jaiswal]

I think his utility worsens after the price rise because the income rise is much smaller

[Aranya]

Ans for 2 is utility decreases. You can check that by comparing initial (food,other goods) consumed with new consumption bundle ( i.e. after the change). Find optimal F and other good in each case from the given info.

[The Villain]

i'm also getting utility worsens..

[Tanu_Jaiswal]

how did u get F'  = 0.28325Y and C'  = 0.7725Y ???

[Aranya]

just set the new price of food as 110p/100 and income as 103M/100

[Homer Simpson]

Sorry calculation mistake ho gaya!

F = 0.25Y
1.10F' = 0.25Y' (Exp of F with new prices and income)

and Y' = 1.03Y

=> 1.10F' = (1.03x0.25)Y

Thats how i got F'

[Tanu_Jaiswal]

Yeah gotcha! thank u buddies

[Tanu_Jaiswal]

Hey an increase in foreign capital inflows would mean increase in domestic money demand or in dom. money supply and why ???