Question

Martha s preference over two goods x and y is represented by the utility function U = 5xy. Her budget constraint is given by 5x +y =30. Plot budget constraint with y on the vertical - axis on the horizontal axis.. Find the marginal utility of x and y...Find the MRS.. Find the MRT...Given her budget how much of each good should she consume in order to maximize her utility show your work.

Answer 1

a)

b)i) $Mu_x= 5Y$

ii) $Mu_y= 5X$

c) Maximum combination for utility maximization

$\frac{Mu_x}{Mu_y}= \frac{P_x}{P_y}$

$\frac{5Y}{5X}= \frac{P_x}{P_y}$

$\frac{Y}{X}= \frac{P_x}{P_y}$

$X= \frac{P_yY}{P_x}$ .........(i)

$Y= \frac{P_xX}{P_y}$ -...........(ii)

Plug into the budget constraint

5X+Y=30

5($\frac{P_yY}{P_x})+Y=30$

$\frac{5P_yY}{P_x}+Y=30$

$5P_yY+P_xY=30P_x$

$Y(5P_y+P_x)=30P_x$

$Y^*= \frac{30P_x}{5P_y+P_x}$

$5X+ \frac{P_xX}{P_y}=30$

$5P_yX+P_xX=30P_y$

$X(5P_y+P_x)= 30P_y$

$X^*= \frac{30P_y}{5P_y+P_x}$