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Calculating Various costs for given cost function.

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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?

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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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Production Function

Use the following information on a hypothetical short-run production function to answer questions a-d.

Units of Labor/Day 5 6 7 8 9

Units of Output/Day 120 140 155 165 168

The price of labor is $20 per day. Ten units of capital are used each day, regardless of output level. The price of capital is $50 per unit.

a. Calculate the marginal and average variable product of each unit of labor input. Hint: plot your Units of labor and Units of Output vertically.

b. Calculate total, average total, average variable, and marginal costs.

c. Can you tell where diminishing marginal returns sets in?

d. Graph the resulting cost curves similar to the graph 5.2 on Page 141 of the textbook.

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