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.)

(a) 3; 6

(b) 12; 6

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,

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,

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

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