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Bamey is eumently maximalaing his utility and has spent all available monthly income on popoom and movie tickets. The price of a hag of popcorn is \( \$ 6 \) and movie tickets are \( \$ 13 \). Bamey's monginal utility from the last bag of popcom is 60 Using the nule of ecual marginal utility per dollar spent, we know that his marginal utlity from the last movie must be .

Ask by Floyd Willis. in the United States
Mar 09,2025

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Bamey's marginal utility from the last movie ticket is 130.

Solución

To find Bamey's marginal utility from the last movie ticket, we can use the principle of equal marginal utility per dollar spent. This principle states that the consumer maximizes utility when the ratio of marginal utility to price is equal for all goods. Let's denote: - \( MU_p \) = Marginal utility from popcorn - \( MU_m \) = Marginal utility from movie tickets - \( P_p \) = Price of popcorn = 6 - \( P_m \) = Price of movie tickets = 13 According to the rule of equal marginal utility per dollar spent, we have: \[ \frac{MU_p}{P_p} = \frac{MU_m}{P_m} \] We know: - \( MU_p = 60 \) - \( P_p = 6 \) - \( P_m = 13 \) Now, we can substitute the known values into the equation: \[ \frac{60}{6} = \frac{MU_m}{13} \] Calculating the left side: \[ \frac{60}{6} = 10 \] Now we have: \[ 10 = \frac{MU_m}{13} \] To find \( MU_m \), we can multiply both sides by 13: \[ MU_m = 10 \times 13 \] Calculating this gives: \[ MU_m = 130 \] Thus, Bamey's marginal utility from the last movie ticket must be \( 130 \).

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Bonus Knowledge

To maximize utility, Bamey should allocate his income such that the marginal utility per dollar spent is equal for both goods. For popcorn, the marginal utility per dollar spent is given by dividing its marginal utility by its price: \( \frac{60}{6} = 10 \). Therefore, for the last movie ticket, the marginal utility per dollar should also be 10. Since movie tickets cost $13, we can calculate the required marginal utility from the last movie ticket to be \( 10 \times 13 = 130 \). So, Bamey’s marginal utility from the last movie must be 130 to achieve utility maximization. Remember, the idea is to balance your spending so that every dollar you spend brings you the same level of happiness from each choice!

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