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 $125 each, then Sarah should produce ______ cakes 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 $125 each, then Sarah should produce ______ cakes per day.

Quizplus · Accepted Answer

In a perfectly competitive market, firms should produce where marginal cost equals price. We can calculate Sarah's marginal cost by finding the change in total cost for each additional cake produced. The marginal cost for each level of production is:

1 cake: $180 - $100 = $80
2 cakes: $220 - $180 = $40
3 cakes: $300 - $220 = $80
4 cakes: $400 - $300 = $100
5 cakes: $520 - $400 = $120
6 cakes: $660 - $520 = $140

From this we see that Sarah's marginal cost is lowest at 2 cakes per day. However, producing 2 cakes would mean incurring an opportunity cost of $5,000 [(5 cakes per day) x ($125 per cake) - $220] because Sarah would be passing up the opportunity to sell 5 cakes at the market price. Therefore, Sarah should produce 5 cakes per day, since her marginal cost of $120 is only slightly higher than the market price of $125 per cake, and this level of production generates the highest total profit of $130 per day [(5 cakes per day) x ($125 per cake) - $520 total cost].

Suppose Sarah Owns a Small Company That Makes Wedding Cakes