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The utility function and the prices are the following: U = 39 x1 + 6 x2...

The utility function and the prices are the following:

U = 39 x1 + 6 x2

P1=8,   P2=33 and I =6,657

What is the amount of maximized utility?

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Answer #1

The given utility function is

The decision to consume a good depends on the maximum or equal per dollar marginal utility, where the utility function is linear so the consumer will consume one good with more per dollar marginal utility as the utility function is for substitute goods.

MU per dollar =MU/price

MU per dollar of X1=39/8=4.875

MU per dollar of X2=6/33=0.181818182

MU per dollar is higher for X1 so the consumer will purchase only good 1.

The quantity of good 1 =income /price=6657/8

=832.125

the amount of utility is

U=39*832.125

=32452.875

The amount of maximum utility is 32452.875 utils

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