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# Microeconomics problem

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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?

https://brainmass.com/economics/utility/solve-microeconomics-problem-30064

#### 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.

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