Question

1)     Consider a consumer with a utility function U (x, y) =X² + Y², the consumer intends to spend birr 80 on the two goods and price of good X and price of good Y are birr 2 and birr 4, respectively

A.   Calculate the optimum consumers consumption amount of X and Y

B.    Find the maximum utility that consumer obtain from consuming the two goods?

C.     Calculate MRS_xy at equilibrium, and interpret your result

Answer 1

U(X,Y)= $X^2+Y^2$

m=80

$P_X=2$

$P_y=4$

$\frac{MU_X}{MU_Y}=\frac{P_x}{P_y}$

$MU_x= 2X$

$MU_Y= 2Y$

$\frac{2X}{2Y}= \frac{2}{4}\implies y=2x$

From the Budget constraint

$2X^2+4Y^2=80$

$2X^2+4(2X)^2=80$

$X^2=4.4\implies X=2.1$

$Y= (2.1)^2= 4.4$

Combined Utility Maximization

$U(X,Y)= X^2+Y^2$

$= (2.1)^2+ (4.4)^2= 23.76$

$MRS=\frac{\delta U}{(\delta_x\delta_y)}$

$MRS=\frac{4}{(x+y)^2}=\frac{4}{(2.1+4.4)^2}$

$= 0.0946$

There is a very low substitution effect