Question

You are choosing between two goods, X and Y, and your marginal utility from each is shown in the following table.

Units of X	MUx	Units of Y	MUy
1	20	1	16
2	16	2	14
3	12	3	12
4	8	4	10
5	6	5	8
6	4	6	6

Instructions: Enter your answers as a whole number.

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?

      units of X and  units of Y

b. What total utility will you realize?

      utils

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?

      units of X and  units of Y

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

Instructions: Start with the highest price first

Price of X	Quantity Demanded of X
$
$

Answer 1

a. Budget constraint:

9=2x+y

Consumer will purchase those Quantities of good X and good Y where MUx/Px= MUy/Py.

When X=3, MUx/Px= 12/2=6.

When Y=6, MUy/Py= 6/1=6.

Also 3*2+6*1=$9

b. Total utility = (TU from good x + TU from good y)= (20+16+12)+(16+14+12+10+8+6)= 48+66= 114.

c. Px=1

Budget constraint:

9=x+y

Consumer will purchase those Quantities of good X and good Y where MUx/Px= MUy/Py.

When X=4, MUx/Px= 8/1=8.

When Y=5, MUy/Py= 8/1=8.

Also 4*1+5*1=$9

d. When price of good x= $2, Quantity demanded for x= 3

When price of good x= $1, Quantity demanded for x= 4.

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