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Calculating Various costs for given cost function.

3. Economists estimated the following cost function for X Corporation

C = 50 + 16 Q - 2 Q² + 0.2 Q³
C = Total Cost
Q = Quantity produced per period

a. Plot the TFC, TFC and TC for the values of Q = 0, 1, 2, 3,.......... 10
b. Calculate the ATC, AVC and MTC and plot on another graph.
c. Explain the relationships between ATC and MTC
d. Discuss the results in terms of the decreasing, constant and increasing marginal costs.
e. Mathematically calculate the level of output at which MC is at minimum.
f. Mathematically calculate the level of output at which ATC = MC and AVC = MC. Which intersect ion happens at a lower level of activity?

Solution Preview

Please refer attached document for complete solution. Work done with the help of equation and graphs may not print here.

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a. Plot the TFC, TVC and TC for the values of Q = 0,1,2,3,...10

From the cost function it is clear that constant part is 50. And remaining Part is variable cost.
Constant Part is Total Fixed Cost, and Variable Part is Total Variable Cost.
Total Cost C= 50 + 16 Q - 2 Q² + 0.2 Q³
Total Fixed Cost (TFC) =50
Total Variable Cost (TVC) = 16 Q - 2 Q² + 0.2 Q³ or we can say
TVC=Total Cost-Total Fixed Cost
From the above relations we can put value of Q (0,1,2...10) and get corresponding values of Various Costs.

Q Total Cost (TC) Total Fixed Cost (TFC) Total Variable Cost
(TC-TFC)
0 50.00 50.00 0.00
1 ...

Solution Summary

Solution describes the steps in finding MC, AVC, TC, TFC for given cost function. Various costs are compared with graphics.

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