Question

1. Given the utility fucntion u =150x +40x²-x³derive 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 maximinum?

Answer 1

Average utility;

Lets assume number of units consumed is $x$

Average utility=total utility$\div$ no of units consumed

=$\frac{150x+40x^2-x^3}{x}$

Marginal utility;

Marginal utility, MU=$\frac{\Delta u}{\Delta x}=150+80x-3x^2$

Total utility;

Total utility is maximized when MU=0

$150+80x-3x^2=0$

D = 8,200

$x_{1} = \frac{-80 + 8,200^{0.5}} {2×3} = 1.76.$

$x_{2}$ < 0, so is not suitable for our case

Value of x at which average utility is maximum;

=$\frac{150x+40x^2-x^3}{x}$

$150+40x-x^2=0$

$x=\frac{−40±√2200}{−2}$

$x_{1}=20−5√22 =-3.45$

$x_{2}=20+5√22=43.45$

Our value will be 43.45