Average and marginal cost Consider the following cost functions. a. Find the average cost and marginal cost functions. b. Determine the average cost and the marginal cost when x=a. c. Interpret the values obtained in part (b). C(x)=500+0.02x,0≤x≤2000,a=1000

Question

Average and marginal cost Consider the following cost functions.  a. Find the average cost and marginal cost functions.  b. Determine the average cost and the marginal cost when x=a.  c. Interpret the values obtained in part (b). C(x)=500+0.02x,0≤x≤2000,a=1000

George Burge · Accepted Answer

Step1Given:Cost function C(x)=500+0.02x,0≤x≤2000a.The average cost =Cav(x)=C(x)x=500+0.02xxaverage cos⁡tCav(x)=500x+0.02The marginal cos⁡t=M(x)=ddxC(x)=C′(x)=0.02Step 2b.The average cos⁡t=Cav(x)=500+0.02xxaverage cos⁡tforx=1000=Cav(1000)=500+0.02(1000)1000=0.52The marginal cos⁡t=M(x)=0.02The marginal cos⁡tforx=1000 is M(1000)=0.02c. The marginal cost for x = 1000 is 0.02, whereas the average cost is 0.52. The average cost is higher because of the fixed cost of 500 in the cost function. The marginal cost does not take into account these fixed cost. It is only a measure of the incremental cost.

Average and marginal cost Consider the following cost functions. a. Find

Answered question

Answer & Explanation

New Questions in Differential Calculus