Answer to Question #111426 in Microeconomics for tran thi chinh

Question

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.

Answer 1

Solution:

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

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

$$q_xp_x+q_yp_y=I$$

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)

$$Q_d=6-2p$$