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Let us suppose that a person consumes only goods X and Y, and his utility is...

Let us suppose that a person consumes only goods X and Y, and his utility is given by the function:U (X, Y) = √(X.Y)a. Find the marginal rate of substitution of X for Y. (Note: MRS = MUx/ MUy and MUx = ∂U/∂X, MUy = ∂U/∂Y) (point 1)b. If the price of X is $1.50 and that of Y is $3.0, and the person has $30 to spend on these goods, find the value of X and Y that maximize his utility. (point 1)(Hint: you need to use budget line to solve it)

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Answer #1

Budget line: 30 = 1.5X + 3Y, or

20 = X + 2Y [Dividing by 1.5]

U = (XY)1/2

MUx = U / X = (Y / X)1/2

MUy = U / Y = (X / Y)1/2

Utility is maximized when MUx / MUy = Px / Py = 1.5 / 3 = 1/2

MUx / MUy = Y / X = 1/2

X = 2Y

Substituting in budget line,

20 = X + X = 2X

X = 10

Y = X/2 = 10/2 = 5

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