The learning curve depicted in Figure 4.2 can be represented algebraically by the following equation:

Average time to produce x units = ax-b 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 its first product 1a = 452 and 40.5 hours to assemble the second. 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, a 40.5/45, or 90 percent, learning curve). The

β for a 90 percent learning curve is 0.3219. Thus, this firm’s learning curve is:

Average time to produce x units = 45x-0.3219 What is the average amount of time it will take this firm to produce six products? (Hint:

Simply plug “6” in for x in the equation and solve.) What is the total time it took this firm to produce these six products? (Hint: Simply multiply the number of units produced, 6, by the average time it will take to produce these six 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? (Hint: Subtract the total time needed to produce five products from the total time needed to produce six products.)

Suppose a new firm is going to start producing these same products. Assuming this new firm does not learn anything from established firms, what will its cost disadvantage be when it assembles its first product? (Hint: Compare the costs of the experienced firm’s sixth product with the cost of the new firm’s first product.)