You are choosing between two goods, X and Y, and your marginal utility from each is as shown below.

Units of x             MUx      Units of Y             MUy

1              23           1              18

2              16           2              16

3              12           3              14

4              8              4              10

5              4              5              8

6              2              6              4

a. If your income is $9.00 and the prices of X and Y are $2.00 and $1.00, respectively, what quantities of each will you purchase to maximize utility?

b. What total utility will you realize?

c. Assume that, other things remaining unchanged, the price of X falls to $1.00. What quantities of X and Y will you now purchase? 

d. Using the two prices and quantities for X, derive a demand schedule (a table showing prices and quantities demanded) for X.