A firm will build 8 units of a product. All costs are subject to an 85% learning curve. The first unit cost $75,000 to build. If the firm values inventory and cost of goods sold at the average cost for all units in the production run, what will be the cost to produce the second unit? Use the following values as needed to respond:
Ln(95%)/ ln(2)= -0.074
Ln(90%)/ ln(2)= -0.152
Ln(85%)/ ln(2)= -0.234
Ln(80%)/ ln(2)= -0.322
Ln(75%)/ ln(2)= -0.415
Ln(70%)/ ln(2)= -0.515
A)$63,750
B)$69,375
C)$75,000
D)Some other amount

Question

Quizplus · Accepted Answer

Using the 85% learning curve, we can calculate the cost to produce the second unit as follows:

Second unit cost = First unit cost * (2^(Log(1/L)/Log(2)^x))
where L is the learning rate (0.85) and x is the number of units produced after the first one (1).

Second unit cost = $75,000 * (2^(Log(1/0.85)/Log(2)^1)) 
Second unit cost = $75,000 * (2^0.234) 
Second unit cost = $69,375

Therefore, the cost to produce the second unit is $69,375. Choice B is the correct answer.

A Firm Will Build 8 Units of a Product