Question

An individual consumes products X and Y and spends $36 per time period. The prices of the two goods are $3 per unit for X and $2 per unit for Y. The consumer in this case has a utility function expressed as:
U(X,Y) = .5XY


a. Express the budget equation mathematically by plugging in the given information. Use capital letters and a single space between operators.


b. Determine the values of X and Y that will maximize utility.


c. Determine the total utility that will be generated per unit of time for this individual. (no decimals)

Answer 1

Answer:

a) 3X + 2Y = 36

b) X = 6 , Y = 9

c) 27

Explanation:

Individual consumes : X and Y

Spends : $36 per time period

unit cost : $3 per unit for X

                 $2 per unit for Y

utility function : U( X, Y ) = .5XY

A) Budget equation mathematically

X* Px + Y* Py = M

3X + 2Y = 36

Px and Py = unit cost for X and Y

M = Total spent ( revenue )

b) Values of X and Y that will maximize utility

Maximum utility ( MRS )  = Px / Py ,

MRS = MUx / MUy

 = Y/X  = 3/2

∴ 2Y = 3X

From BC : 6X = 36 ( X = 6 plug into mathematically equation above )

∴ X = 6 , hence Y = 9

c) Total utility generated per unit of time

U( X,Y ) = .5XY

            = 0.5 * 6 * 9 = 27