Answer to Question #147620 in Microeconomics for Zainab Arif

Question

There are two goods, X and Y, and their marginal utiliy is as follow:
Units of X. MU of X. Units of Y. MU of Y
1. 10. 1. 8
2 8. 2. 7
3. 6. 3. 6
4 4. 4. 5
5. 3. 5. 4
6. 2. 6. 3
If the income is $9 and the prices of X and Y are $2 and $1, respectively, what quantities of each will you purchase in order to maximize utility? What total utility will be realized? Assume that, other things remaining unchamged, the price of X falls to $1. What quantities of X and Y will now be purchased? Using the two prices and quantites for X, derive a demand schedule for X.

Answer 1

If the income is $9 and the prices of X and Y are $2 and $1, respectively, then you will purchase 2 units of X and 5 units of Y in order to maximize utility and satisfy the equation MUx/Px = MUy/Py.

The total utility of 45 units will be realized.

If the price of X falls to $1, then 4 units of X and 5 units of Y will now be purchased.

The demand schedule for X is:

p1 = 2, q1 = 2,

p2 = 1, q2 = 4.