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 .

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

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