Question

exercise-Assume Mr mulugeta had budget of 150$ for the
Consumption of tomato (X)and Potatol(y) Per month.
assume Currently Price of tomato is 50 $Per kg
& Price of Potato is 10 $ per kg. It Wility function
Of Mr mulugeta is given by Tu=5yx^{2} find the
quantities of tomato and Potato that maximizes
his utility ?

Answer 1

$Tu=5yx^2$

Budget line $M = P(x) x +P(y)y$

$150 = 50x + 10y$

At optimum :

$\frac{MU(x)}{P(x)}= \frac{MU(y)}{P(y)} \\ MU(x) = \frac{ΔU}{Δx} = 10xy \\ MU(y) = \frac{ΔU}{Δy} = 5x^2 \\ \frac{10xy}{50} = \frac{5x^2}{10} \\ \frac{y}{5} = \frac{x}{2} \\ y=2.5x$

Putting y=2.5x in budget line

$150 = 50 x + 10 \times 2.5x \\ 150 = 75x \\ x = \frac{150}{75}=2 \\ y= 5$