Answer:
(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,
[tex]\frac{MU_D}{MU_X} =\frac{P_D}{P_X}[/tex]
[tex]\frac{X}{D} =\frac{20}{10}[/tex]
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,
[tex]\frac{MU_D}{MU_X} =\frac{P_D}{P_X}[/tex]
[tex]\frac{X}{D} =\frac{5}{10}[/tex]
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
