Suppose Sarah owns a small company that makes wedding cakes. The table below shows how Sarah's total cost varies depending on the number of wedding cakes she makes each day. $$\begin{array} { | c | c | }
\hline \begin{array} { c }
\text { Number of } \
\text { Cakes Per Day }
\end{array} & \begin{array} { c }
\text { Total Cost } \
\text { Per Day }
\end{array} \
\hline 0 & \$ 100 \
\hline 1 & \$ 180 \
\hline 2 & \$ 220 \
\hline 3 & \$ 300 \
\hline 4 & \$ 400 \
\hline 5 & \$ 520 \
\hline 6 & \$ 660 \
\hline
\end{array}$$ If the market for wedding cakes is perfectly competitive, and wedding cakes sell for $95 each, then at her profit-maximizing level of output, Sarah will earn a ______ of ______ per day.

Question

Suppose Sarah owns a small company that makes wedding cakes. The table below shows how Sarah's total cost varies depending on the number of wedding cakes she makes each day. $$\begin{array} { | c | c | } 
\hline \begin{array} { c } 
\text { Number of } \
\text { Cakes Per Day }
\end{array} & \begin{array} { c } 
\text { Total Cost } \
\text { Per Day }
\end{array} \
\hline 0 & \$ 100 \
\hline 1 & \$ 180 \
\hline 2 & \$ 220 \
\hline 3 & \$ 300 \
\hline 4 & \$ 400 \
\hline 5 & \$ 520 \
\hline 6 & \$ 660 \
\hline
\end{array}$$ If the market for wedding cakes is perfectly competitive, and wedding cakes sell for $95 each, then at her profit-maximizing level of output, Sarah will earn a ______ of ______ per day.

Quizplus · Accepted Answer

Sarah's profit-maximizing output is where marginal cost equals marginal revenue. The marginal cost for each additional cake is calculated from the total cost differences. At 5 cakes, the total cost is $520, and revenue is $475 (5 cakes x $95), resulting in a loss of $45. At 4 cakes, the total cost is $400, and revenue is $380 (4 cakes x $95), resulting in a loss of $20. The smallest loss occurs at 2 cakes, where the total cost is $220, and revenue is $190 (2 cakes x $95), resulting in a loss of $30. However, the smallest loss is actually at 1 cake, where the total cost is $180, and revenue is $95, resulting in a loss of $85. Therefore, the correct answer is a loss of $15 at 3 cakes, as this is the closest to breaking even.

Suppose Sarah Owns a Small Company That Makes Wedding Cakes