At his current level of consumption, Cameron get 3 times more marginal utility from an additional game of pinball than from an additional game of ping pong. If the price of a ping pong game is $0.50, then he is maximizing utility if the price of a pinball game is:
A)$1.00
B)$1.50
C)$2.00
D)$3.00

Question

Quizplus · Accepted Answer

Cameron is maximizing utility when the marginal utility per dollar spent on both goods is equal. Let's call the price of a pinball game "p". Since Cameron gets 3 times more marginal utility from an additional game of pinball than from an additional game of ping pong, we can express his marginal utilities as:

MU_pinball = 3 x MU_ping_pong

And we know that the marginal utility per dollar spent on ping pong is:

MU_ping_pong / $0.50 = MU_ping_pong / (1/2)

Simplifying this expression, we get:

MU_ping_pong / (1/2) = 2 x MU_ping_pong

Now we can set the marginal utility per dollar spent on pinball equal to the marginal utility per dollar spent on ping pong, and solve for "p":

(MU_pinball / p) = (MU_ping_pong / (1/2))

(3 x MU_ping_pong) / p = 2 x MU_ping_pong / (1/2)

Multiplying both sides by (1/2) and simplifying, we get:

3 x MU_ping_pong = 4 x MU_pinball

MU_pinball / p = MU_ping_pong / (1/2)

MU_pinball / p = 2 x MU_pinball / 3

Simplifying this expression, we get:

p = (3/2) x $1.00 = $1.50

Therefore, Cameron is maximizing utility if the price of a pinball game is $1.50.

At His Current Level of Consumption, Cameron Get 3 Times