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The table below shows the number of harpsichords produced by Bach Instruments using different amount of capital (machinery) and labor (workers). In this analysis, capital is a fixed cost while labor is a variable cost. For each machine, the firm must pay \( \$ 150 \) regardless of how many harpsichords they produce, while the wage rate for workers is \( \$ 200 \) per worker employed. A machine cannot assemble a complete harpsichord. Number of Workers Output of Harpsichords with One Machine 20 1 2 25 50 3 38 76 4 45 90 For the following questions, assume Bach has one machine for producing harpsichords. 1. Calculate the marginal product of the second unit of labor. Show your work. 2. If Bach hires this second worker, will they be operating with constant, increasing, or diminishing marginal returns? Explain using numbers from the table. 3. When Bach has one machine, hiring which worker will show diminishing marginal returns? Explain using numbers from the table. 4. Calculate the average total cost of producing 45 harpsichords. Show your work. Suppose the firm decides to hire the two workers and employ the two machines. 1. Calculate the firm's average total cost for this level of production. Show your work. 2. Calculate the firm's average fixed cost for this level of production. Show your work. 3. Calculate the firm's average variable cost if they hire a third worker. Show your work.

Ask by Mcdonald Harmon. in the United States
Mar 15,2025

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1. The marginal product of the second worker is 1 harpsichord. 2. Bach is operating with constant marginal returns when hiring the second worker. 3. Hiring the third worker shows diminishing marginal returns. 4. The average total cost of producing 45 harpsichords is approximately \$21.11. 5. With two machines and four workers, the average total cost for 90 harpsichords is approximately \$12.22. 6. The average fixed cost for 90 harpsichords is approximately \$3.33. 7. Hiring a third worker increases the average variable cost to approximately \$11.11.

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Beyond the Answer

To dive into the world of harpsichord production with Bach Instruments, let’s explore some fun and educational nuggets! Think of Bach Instruments as a factory of music! Historically, the harpsichord is a fascinating instrument that predates the piano and was widely utilized during the Baroque period. It has a unique plucked string sound that shaped the musical landscape of the time. Imagine J.S. Bach himself composing magnificent pieces, where each note played on a harpsichord was a blend of craftsmanship and artistry, unfolding melody and harmony! Now, translating this into modern business practices, the production of harpsichords is all about balancing fixed and variable costs. In real-world applications, manufacturers often have to analyze their production function to optimize efficiency and costs. By understanding concepts like marginal returns and total costs, factories can avoid pitfalls such as over-hiring labor, leading to diminishing returns. In short, making sure those beautiful harpsichords don’t end up costing more to make than they can sell!

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