Answer to Question #289263 in Microeconomics for mame

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

A. The optimum consumers consumption amount of X and Y are:

MUx/MUy = Px/Py,

MUx = U'(x) = 2x,

MUy = U'(y) = 2y,

2x/2y = 2/4,

x/y = 1/2,

y = 2x,

2x + 4×2x = 80,

x = 8 units,

y = 16 units.

B. The maximum utility that consumer obtains from consuming the two goods is:

$Umax = 8^2 + 16^2 = 64 + 256 = 320$

units.

C. MRSxy at equilibrium is:

MRSxy = -MUx/MUy = -x/y = -8/16 = -0.5.