Question #111426

You are choosing between two goods, X and Y, and your total utility from each is shown below:

Units TUX TUY

1 10 8

2 18 15

3 24 21

4 28 26

5 31 30

6 33 33

a. If your income is $9 and the prices of X and Y are $2 and $1, respectively, what quantities of each will you purchase in maximizing utility?

b. Specify the amount of total utility you will realize?

c. Assume that, other things remaining unchanged, the price of X falls to $1. What quantities of X and Y will you now purchase?

d. Using the two prices and quantities for X, graphically derive a demand curve for X.

Units TUX TUY

1 10 8

2 18 15

3 24 21

4 28 26

5 31 30

6 33 33

a. If your income is $9 and the prices of X and Y are $2 and $1, respectively, what quantities of each will you purchase in maximizing utility?

b. Specify the amount of total utility you will realize?

c. Assume that, other things remaining unchanged, the price of X falls to $1. What quantities of X and Y will you now purchase?

d. Using the two prices and quantities for X, graphically derive a demand curve for X.

Expert's answer

Solution:

a) To maximize utility, the following conditions must be met simultaneously:

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

I=9 ; "p_x=2" ; "p_y=1"

Only one option satisfies these conditions: x=2, y=5.

b)

"TU=TU_x+TU_y=18+30=48"c) If "p_x=1" then x=4, y=5,

d)

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