Answer to Question #106659 in Microeconomics for Miriam Moubarak

Question

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



Instructions: Enter your answers as whole numbers.

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? X = units. Y = units.

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? X = units. Y = units.

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

Instructions: Start with the highest price first.

Price Quantity Demanded
$

Answer 1

Solution:

Marginal utility is not given, so for good x it will be MUx, for good y MUy.

$$\frac {MU_x}{p_x}=\frac {MU_y}{p_y}$$

If px=2, py=1

$$\frac {MU_x}{2}=\frac {MU_y}{1}$$

$$MU_x=2MU_y$$

$$I=p_xq_x+p_yq_y$$

I=9, Px=x. Py=y

$$2x+y=9$$

$x=1. y=7; x=2,y=5; x=3,y=3; x=4,y=1$

These are the possible options for acquiring x and y. Knowing the marginal utility, you can choose the most profitable option.

I=9; x=1; y=1

$$MUx=MU_y$$

$$x+y=9$$

$x=1,y=8; x=2,y=7; x=3,y=6; x=4,y=5; x=5,y=4; x=6,y=3; y=7.y=2; x=8.y=1$