Question

Anatoly's marginal utility for DVDs (D) is MU_D = X ad his marginal utility for Xbox games (X) is MU_x = D. Anatoly's income is $120, the price of a DVD is $20.00, and the price of an Xbox game is $10.00. How many DVDs and Xbox games does Anatoly consume to maximize his satisfaction? Anatoly consumes DVDs and Xbox games.(Enter your responses using integers.) Suppose the price of DVDs decreases to $5.00. What is Anatoly's new satisfaction-maximizing bundle? Anatoly now consumes DVDs and Xbox games. Enter your responses using integers.)

Answer 1

(a) 3; 6

(b) 12; 6

Step-by-step explanation:

(a) Marginal utility for DVDs (D), MU_D = X

Marginal utility for Xbox games (X), MU_X = D

Income, m = $120

Price of DVD, P_D = $20

Price of Xbox game, P_X = $10

For maximizing utility,

`(MU_D)/(MU_X) =(P_D)/(P_X)`

`(X)/(D) =(20)/(10)`

X = 2D............(1)

Budget constraint:

(P_D × D) + (P_X × X) = m

(20 × D) + (10 × X) = 120

(20 × D) + (10 × 2D) = 120 [from (1)]

40D = 120

D* = 3

Therefore, X* = 2D

X* = 2 × 3

X* = 6

(b) Suppose the price of DVDs decreases to $5.00,

For maximizing utility,

`(MU_D)/(MU_X) =(P_D)/(P_X)`

`(X)/(D) =(5)/(10)`

X = 0.5D............(2)

Budget constraint:

(P_D × D) + (P_X × X) = m

(5 × D) + (10 × X) = 120

(5 × D) + (10 × 0.5D) = 120 [from (2)]

10D = 120

D* = 12

Therefore, X* = 0.5D

X* = 0.5 × 12

X* = 6