Answer to Question #268775 in Microeconomics for kalehiwot

Question

given the utility function U=150X+40X2-X3, derive average and marginal utility functions, Find the value of X at which total utility is maximum, and the value of X at which average utility is maximum?

Answer 1

Average utility

$\frac{dU}{dX} = 150 + 80x -3x^2$

$3X^2 -80X -150 = 0$

$x(3X- 4 0) = 0, ( 40X -150) = 0$

Value of X when average utility is maximum

$3x^2 - 40X =0$

$3X^2 = 40X$

$3X = 40$

$x =\frac {40}{3} = 13.33 maximum$

Also

$40X -150 = 0$

$40X = 150$

$x = 3.75 minimum$

Marginal utility

$\frac{dU}{dX} = 150 + 80x -3x^2$

$\frac {dU}{dX} = 80-6X = 0$

$X =\frac {80}{6} = 13.3$

Value of X when utility is maximum

$X = 13.3$