Question

In: Economics

Harry derives utility from two goods: X and Y . He has an income of 100...

Harry derives utility from two goods: X and Y . He has an income of 100 dollars. Both X and Y cost 2 dollars per unit Given the utility function U = XY (MUx = Y and MUY = X), how many units of X and Y should Harry consume in order to maximize his utility?

(a) X = 100, Y = 0

(b) X = 0, Y = 100

(c) X = 50, Y = 50

(d) X = 25, Y = 50

(e) X = 25, Y = 25

Solutions

Expert Solution

The utility function is given as:

U = XY

The consumer maximizes the utility at the point where the marginal rate of substitution equals the price ratio.

The marginal rate of substitution (MRS) is:

Price of good X equals the price of good Y which equals $2. So, the price ratio (Px/Py) = 1

Equating MRS and price ratio:

The money income is equal to $100.

The equation of budget line can be written as:

PxX + PyY = M

Where, Px is the price of good X, Py is the price of good Y, X is the quantity demanded of good X and Y represents the quantity demanded of good Y.

Putting the values:

Putting X = Y:

Since, X = Y,

Y is also equal to 25.

So,

So, the consumer should consume 25 units of good X and 25 units of good Y in order to maximize the utility.

Rahul Sunny answered 1 year ago
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