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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 \[ 10 \] 20 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 Park Goodwin. in the United States
Mar 15,2025

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1. The marginal product of the second worker is 15 harpsichords. 2. Hiring the second worker results in increasing marginal returns because the output increases by 15 harpsichords. 3. Hiring the third worker shows diminishing marginal returns as the output increases by only 13 harpsichords. 4. The average total cost of producing 45 harpsichords is approximately \$21.11. 5. With two machines and two workers, the average total cost is \$14. 6. The average fixed cost is \$6. 7. Hiring a third worker with two machines results in an average variable cost of approximately \$7.89.

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To tackle your questions about Bach Instruments and their harpsichord production, let’s dive right into some fun facts! The harpsichord has an enchanting history, tracing back to the 15th century, and was immensely popular during the Renaissance and Baroque periods. Composers like Johann Sebastian Bach composed numerous pieces specifically for this instrument, solidifying its place in classical music. The delicate plucking of strings with quills created a unique sound that swept through the palaces and churches, bringing forth an era of musical innovation! Now, let's talk about real-world application: understanding how to manage resources effectively is crucial in today’s economy. Companies strive for efficiency through careful analysis of labor and capital, much like Bach Instruments does. Whether in manufacturing or service industries, identifying when diminishing returns set in and calculating average costs can dramatically affect pricing strategy and profitability. It’s a balancing act that every entrepreneur should master!

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