Taylor's marginal utility from watching movies and from eating out (in utils) is shown below. Taylor spends exactly $100 every month on these two forms of entertainment, and the price of each movie is $10 and the price of each dinner is $20. $$\begin{array} { | c | c | c | c | }
\hline \begin{array} { c }
\text { Movies } \
\text { Per Month }
\end{array} & \begin{array} { c }
\text { Marginal Utility } \
\text { Per Movie }
\end{array} & \begin{array} { c }
\text { Dinners Out } \
\text { Per Month }
\end{array} & \begin{array} { c }
\text { Marginal Utility } \
\text { Per Dinner }
\end{array} \
\hline 1 & 60 & 1 & 150 \
\hline 2 & 50 & 2 & 140 \
\hline 3 & 20 & 3 & 120 \
\hline 4 & 5 & 4 & 100 \
\hline
\end{array}$$ If Taylor watches 2 movies a month, Taylor will eat out ______ times per month, and have marginal utility per dollar of ______ from movies and a marginal utility per dollar of ______ from eating out.

Question

Taylor's marginal utility from watching movies and from eating out (in utils) is shown below. Taylor spends exactly $100 every month on these two forms of entertainment, and the price of each movie is $10 and the price of each dinner is $20. $$\begin{array} { | c | c | c | c | } 
\hline \begin{array} { c } 
\text { Movies } \
\text { Per Month }
\end{array} & \begin{array} { c } 
\text { Marginal Utility } \
\text { Per Movie }
\end{array} & \begin{array} { c } 
\text { Dinners Out } \
\text { Per Month }
\end{array} & \begin{array} { c } 
\text { Marginal Utility } \
\text { Per Dinner }
\end{array} \
\hline 1 & 60 & 1 & 150 \
\hline 2 & 50 & 2 & 140 \
\hline 3 & 20 & 3 & 120 \
\hline 4 & 5 & 4 & 100 \
\hline
\end{array}$$ If Taylor watches 2 movies a month, Taylor will eat out ______ times per month, and have marginal utility per dollar of ______ from movies and a marginal utility per dollar of ______ from eating out.

Quizplus · Accepted Answer

If Taylor watches 2 movies a month, she will have spent $20 on movies, leaving her with $80 to spend on dinners out. To find the optimal combination, start by calculating the marginal utility per dollar for each option:

- Watching the first movie gives Taylor 60 utils, which works out to 6 utils per dollar spent ($10).
- Watching the second movie gives Taylor an additional 50 utils, which works out to 5 utils per dollar spent ($10).
- Spending $20 on the first dinner out gives Taylor 150 utils, or 7.5 utils per dollar spent ($20).
- Spending $20 on the second dinner out gives Taylor an additional 140 utils, or 7 utils per dollar spent ($20).
- Spending $20 on the third dinner out gives Taylor an additional 120 utils, or 6 utils per dollar spent ($20).

At this point, it's clear that spending the remaining $80 on dinners out will give Taylor more total utility than spending it on movies (since the marginal utilities per dollar are both greater). To maximize utility, it makes sense to keep buying dinners out until the marginal utility per dollar from eating out falls to 5 (since this is the marginal utility per dollar from watching movies). This occurs when Taylor has bought 4 dinners out. Therefore, the optimal combination is 2 movies and 4 dinners out.

Taylor's Marginal Utility from Watching Movies and from Eating Out