Question

Given MUx = X, MUY = 4Y, Price of X is 3 Birr per unit and price of Y is also 3 Birr per unit. If
the income of the consumer is 1200 Birr, find the amounts of X and Y that the consumer chooses
to consume so as to maximize his utility.

Answer 1

Solution

$\frac{MU_x}{p_x}=\frac{MU_y}{P_y}$

$\frac{x}{3}=\frac{4y}{3}$

Budget line = I= P_xX+P_yY

1200=3x+3y

$\frac{MU_x}{MU_y}=\frac{P_x}{P_y}=\frac{x}{4y}$

x=4y

1200=3(4y)+3y

1200=15y

y=80

1200=3x+240

960=3x

x=320

Utility is maximized when

y=80

x=320

MU_x= 320

MU_y= 320