# Microeconomics problem

Subject: Microeconomics problem

Details: A consumer with the money-left-over utility function u(x) + m = 10 ln(x+1) +m is endowed with 100 units of x and $1000. This consumer can buy or sell the commodity in question, depending on its price. If, for instance, the price of x is $4 per unit and the consumer sells 25 units, she ends up with 75 units of the good and $1100 in money left over, for an ending utility level of 10 ln( 76) + 1100. If she buys 25 units, she ends with 125 units of the good and $900 in money left over, for an ending utility of 10 ln(126) +900. Given the price p of the good, the consumer buys or sells, doing whatever makes her ending utility as high as possible. As a function of the price p, what will this consumer do?

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#### Solution Preview

u(x) + m = 10 ln(x+1) +m

Xo = 100

Mo = 1000

Px = p

The consumer will maximize his utility u(x) + m = 10 ln(x+1) +m

Subject to:

p * x + m = p*Xo + Mo = 100p + 1000

Then we write ...

#### Solution Summary

Microeconomics problem is solved. The ending utility of ln functions are found.