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 $\log _{2} x=\frac{\ln x}{\ln 2}$ .] Recall that marginal cost is related to total cost as follows: $M C(x)=C^{\prime}(x)$ , where C(x)= total cost to produce x units. Given this, and the formula for MC(x)with $M_{0}$ = $500,000, find a formula for C(x).What, physically, is the meaning of the constant of integration in your formula? A)The cost of producing the first plane. B)The cost if no planes are produced (the cost of setting up the plant for production). C)The marginal cost of the x^th unit. D)The average cost of producing x units.

Question

Quizplus · Accepted Answer

The constant of integration in the context of integrating a marginal cost function to find the total cost function represents the initial fixed costs or setup costs before any units are produced. This is not the cost of producing the first unit, but rather the costs incurred to prepare for production, such as setting up the plant or assembly line.

A Study of the Costs to Produce Airplanes in World MC(x)=MM0xlog⁡20.9M C(x)=M M_{0} x^{\log _{2} 0.9}MC(x)=MM0​xlog2​0.9

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