# Question: as a manufacturer produces more units of some product the...

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As a manufacturer produces more units of some product, the cost to produce each unit should decrease as the worker skills and workflow improve. This decline in cost-per-unit is called an experience curve or learning curve. One model of a learning curve is the “unit learning curve model”, which we will explore here. The unit learning curve model assumes that each time the number of units to be produced doubles, say from n to 2n, the cost to produce the 2nth unit is some fraction of the cost to produce the nth unit. This fraction, r, is usually expressed as a percent. For example, suppose there is a 90% learning curve and let C(x) be the cost to produce the xth unit. Then: C(2n) = 0.90C(n). It turns out that with a learning curve of r the cost to produce the xth unit is C(x) = C(1)x ln(r) ln(2) . 1. Use algebra to verify that C(2n) = rC(n) no matter what n is.a 2. Suppose the cost to produce 1 telephone switchboard is $271,000 and there is a learning curve of 90%. Calculate limx→∞ C(x); what does your answer mean in terms of the model? Does that seem reasonable? Why or why not? 3. Suppose the learning curve for some product is greater than 100%. Calculate limx→∞ C(x) in that case; what does your answer mean in terms of the model? Does that seem reasonable? Why or why not?