Costs of Production: Fixed, variable and total costs
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Cost functions, a part of the definition of profit, are useful to gauge the performance of the business. Suppose an economist estimated that the cost function of a single-product firm as:
C(Q) = 10 + 10Q + 10Q2 + 10Q3
Based on this information, determine the followings and show all steps (first, you must define each of the terms in the cost function, and then plug in the numbers to have your answers; not just the answers):
a. Define fixed cost and offer an example. Next, compute the fixed cost of producing 20 units of output using the cost function above.
b. Define variable cost and offer an example. Next compute the variable cost of producing 5 units of output using the cost function above.
c. Define total cost and then compute the total cost of producing 5 units of output using the cost function above
d. Define and compute the average fixed cost of producing 5 units of output
e. Define and compute the average variable cost of producing 5 units of output
f. Define and compute the average total cost of producing 5 units of output
g. Define marginal cost an offer an example. Next, compute the marginal cost when Q = 5, using the cost function above
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Solution Summary
Computation of various types of costs given a total cost function.
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a) Fixed cost is the portion of total cost that does not depend on output, it's not 0 when the firm produces nothing and it doesn't change with changes in Q. Example: rent.
In the function, the part that doesn't depend on Q is 10 (or you can solve it by saying: when Q=0, TC = FC, plug in 0 for Q ==> TC = FC = 10). It's regardless if Q is 20 or any other number.
b) Variable cost is the portion of total cost that depends on ...
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