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Cost Function: Fixed, Variable, and Total Costs

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38. An economist estimated that the cost function of a single-product firm is:

C(Q) = 60 + 30Q + 25Q2 + 5Q3.

Based on this information, determine the following:

a. The fixed cost of producing 10 units of output.


b. The variable cost of producing 10 units of output.


c. The total cost of producing 10 units of output.


d. The average fixed cost of producing 10 units of output.


e. The average variable cost of producing 10 units of output.


f. The average total cost of producing 10 units of output.


g. The marginal cost when Q = 10.

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Solution Preview

a) The fixed cost (FC) of producing 10 units of output is $60 since the the amount Q produced has no effect on cost. It is the constant term (the first term on the right hand side of the equation).

b) The variable cost of ...

Solution Summary

This solution gives calculations for fixed cost, variable cost, and total cost.

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Costing/Cost Function

Jersey Subs, Inc. wants to find an equation to estimate monthly utility costs. Jersey Subs has been in business for one year and has collected the following cost data for utilities:

(see attached table)

a. Which of the preceding costs is variable? Fixed? Mixed? Explain.

b. Using the high-low method, determine the cost function for each cost.

c. Combine the preceding information to get a monthly utility cost function for Jersey.(What is meant here is to get a total fixed cost for the three utilities and then add the formula for the variable amounts for each utility to get a formula that includes them all. The "function" is just having them all together in one complete formula.)

d. Next month, Jersey Subs expects to use 2,200 kilowatt hours of electricity, make 1,500 minutes of telephone calls, and use 32,000 gallons of water. Estimate total cost of utilities for the month.

2. Bolder Bikes, Inc. manufactures mountain bike frames in Boulder Colorado. In 2012, they produced 24,000 frames at a total cost of $1,296,000. Frames Unlimited, Inc. has offered to supply as many frames as Boulder Bikes wants at a cost of $49.50. Boulder Bikes anticipates needing 26,000 frames each year over the next few years. Boulder Bikes uses historical cost data to come up with the following regression equation with total manufacturing costs of the frame as the dependent variable and frames produced as the independent variable:
y=$545,000 + 21X

During the years used to estimate the regression equation, the production of frames varied from 22,000 to 26,000.

a. Using this equation, estimate how much it would cost Boulder Bikes to manufacture the 26,000 frames.
b. How much more or less costly is it to manufacture the frames rather than to acquire them from Frames Unlimited?

Please see attachment.

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