A Study of the Costs to Produce Airplanes in World $M C(x)=M M_{0} x^{\log _{2} 0.9}$

Short Answer

A study of the costs to produce airplanes in World War II led to the theory of "learning curves," the idea of which is that the marginal cost per plane decreases over the duration of a production run.In other words, with experience, staff on an assembly line can produce planes with greater efficiency.The 90% learning curve describes a typical situation where the marginal cost, MC, to produce the x^th plane is given by $M C(x)=M M_{0} x^{\log _{2} 0.9}$ , where $M_{0}$ = marginal cost to produce the first plane.[Note: You may use the fact that $\log _{2} x=\frac{\ln x}{\ln 2}$ .] If a plant produces planes with a 90% learning curve on production costs, and the marginal cost for the first plane is $700,000, then what is the marginal cost to produce the fourth plane? Round to the nearest thousand dollars.