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Summative Assessment: The Microeconomics of Resource Markets

Stephanie produces earrings. She sells each pair of earrings for [tex]\[tex]$4[/tex]. The table below shows how many pairs of earrings can be produced, depending on the number of workers Stephanie hires. Fill in the "Total Revenue" and "Marginal Revenue Product" using the information given. Assume this is a perfectly competitive market.

Instructions: Enter your answers as whole numbers.

Stephanie's Earring Shop and Revenues

\begin{tabular}{|c|c|c|c|c|c|c|}
\hline
\begin{tabular}{l}
Labor \\
(workers)
\end{tabular} & \begin{tabular}{l}
Total Product \\
(pairs of earrings)
\end{tabular} & \begin{tabular}{l}
Marginal Product \\
(pairs of earrings)
\end{tabular} & \begin{tabular}{l}
Price \\
(dollars)
\end{tabular} & \begin{tabular}{l}
Total Revenue \\
(dollars)
\end{tabular} & \begin{tabular}{l}
Marginal Revenue \\
Product (dollars)
\end{tabular} \\
\hline
0 & 0 & - & [tex]\$[/tex]4[/tex] & [tex]\[tex]$0[/tex] & - \\
\hline
1 & 24 & 24 & [tex]\$[/tex]4[/tex] & [tex]\[tex]$96[/tex] & \\
\hline
2 & 42 & 18 & [tex]\$[/tex]4[/tex] & [tex]\[tex]$168[/tex] & \\
\hline
3 & 58 & 16 & [tex]\$[/tex]4[/tex] & [tex]\[tex]$232[/tex] & \\
\hline
4 & 73 & 15 & [tex]\$[/tex]4[/tex] & [tex]\[tex]$292[/tex] & \\
\hline
5 & 86 & 13 & [tex]\$[/tex]4[/tex] & [tex]\[tex]$344[/tex] & \\
\hline
6 & 96 & 10 & [tex]\$[/tex]4[/tex] & [tex]\[tex]$384[/tex] & \\
\hline
7 & 103 & 7 & [tex]\$[/tex]4[/tex] & [tex]\$412[/tex] & \\
\hline
\end{tabular}

Sagot :

GinnyAnsweridn
Let's break down the solution step-by-step.

1. Total Revenue (TR): Total Revenue is calculated by multiplying the Total Product (pairs of earrings) with the Price (dollars per pair).

2. Marginal Revenue Product (MRP): Marginal Revenue Product is calculated by multiplying the Marginal Product (additional pairs of earrings produced by hiring one more worker) with the Price (dollars per pair).

Let's populate the table using the given data.

### Calculations:

1. Total Revenue (TR)

For each row:
- [tex]\( \text{TR} = \text{Total Product} \times \text{Price} \)[/tex]

- For 0 workers: [tex]\( \text{TR} = 0 \times 4 = 0 \)[/tex]
- For 1 worker: [tex]\( \text{TR} = 24 \times 4 = 96 \)[/tex]
- For 2 workers: [tex]\( \text{TR} = 42 \times 4 = 168 \)[/tex]
- For 3 workers: [tex]\( \text{TR} = 58 \times 4 = 232 \)[/tex]
- For 4 workers: [tex]\( \text{TR} = 73 \times 4 = 292 \)[/tex]
- For 5 workers: [tex]\( \text{TR} = 86 \times 4 = 344 \)[/tex]
- For 6 workers: [tex]\( \text{TR} = 96 \times 4 = 384 \)[/tex]
- For 7 workers: [tex]\( \text{TR} = 103 \times 4 = 412 \)[/tex]

2. Marginal Revenue Product (MRP)

For each row (starting with 1 worker, as MRP for 0 workers is undefined):
- [tex]\( \text{MRP} = \text{Marginal Product} \times \text{Price} \)[/tex]

- For 1 worker: [tex]\( \text{MRP} = 24 \times 4 = 96 \)[/tex]
- For 2 workers: [tex]\( \text{MRP} = 18 \times 4 = 72 \)[/tex]
- For 3 workers: [tex]\( \text{MRP} = 16 \times 4 = 64 \)[/tex]
- For 4 workers: [tex]\( \text{MRP} = 15 \times 4 = 60 \)[/tex]
- For 5 workers: [tex]\( \text{MRP} = 13 \times 4 = 52 \)[/tex]
- For 6 workers: [tex]\( \text{MRP} = 10 \times 4 = 40 \)[/tex]
- For 7 workers: [tex]\( \text{MRP} = 7 \times 4 = 28 \)[/tex]

Now, let's fill in the table:

[tex]\[ \begin{array}{|c|c|c|c|c|c|c|c|} \hline \text{Labor (workers)} & \text{Total Product (pairs of earrings)} & \text{Marginal Product (pairs of earrings)} & \text{Price (dollars)} & \text{Total Revenue (dollars)} & \text{Marginal Revenue Product (dollars)} \\ \hline 0 & 0 & - & 4 & 0 & - \\ \hline 1 & 24 & 24 & 4 & 96 & 96 \\ \hline 2 & 42 & 18 & 4 & 168 & 72 \\ \hline 3 & 58 & 16 & 4 & 232 & 64 \\ \hline 4 & 73 & 15 & 4 & 292 & 60 \\ \hline 5 & 86 & 13 & 4 & 344 & 52 \\ \hline 6 & 96 & 10 & 4 & 384 & 40 \\ \hline 7 & 103 & 7 & 4 & 412 & 28 \\ \hline \end{array} \][/tex]

This completes the table with Total Revenue and Marginal Revenue Product for each number of workers hired by Stephanie.
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