Question: The learning curve depicted in Figure can be represented algebraically
The learning curve depicted in Figure can be represented algebraically in the following equation: Average time to produce x units = ax-β, where x is the total number of units produced by a firm in its history, a is the amount of time it took a firm to produce its first unit, and β is a coefficient that describes the rate of learning in a firm. Suppose it takes a team of workers 45 hours to assemble their first product (a=45) and 40.5 hours to assemble their second product. When a firm doubles its production (in this case, from one to two units) and cuts its production time (in this case from 45 hours to 40.5 hours), learning is said to have occurred (in this case 40.5/45 or 90% learning curve). The β for a 90% learning curve is .3219. Thus, this firm’s learning curve is: Average time to produce x units = 45x – .3219. What is the average amount of time it will take this firm to produce 6 products? Simply plug “6” in for “X” in the equation and solve. What is the total time it took this firm to produce these 6 products? Simply multiply the number of units produced “6” by the average time it will take to produce these 6 products. What is the average time it will take this firm to produce five products? What is the total time it will take this firm to produce five products? So, what is the total time it will take this firm to produce its sixth product? Suppose a new firm is going to start producing these same products. Assuming this new firm doesn’t learn anything from established firms, what will the cost disadvantage for this new firm be when it assembles its first product?
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