16Lecture

# 16Lecture - LECTURE 16 COST FUNCTIONS (CONTINUED) Let us...

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LECTURE 16 COST FUNCTIONS (CONTINUED) Let us review cost functions to this point. Columns (1), (2), and (3) from Table 15-1 are empirical relationships between key operating variables: Different levels of output of our firm (ounces of gold produced per week); total fixed cost per week for each level of output; and total variable cost per week for each level of output, respectively. Column (4), total cost per week for each level of output is merely the sum of Column (2) and Column (3) TC = TFC + TVC Equation 16-1 Where TC is total cost at each level of output; TFC is total fixed cost at each level of output; and TVC is total variable cost at each level of output. Column (5) is average fixed cost, discussed in Lecture 15, and defined as AFC = (TFC) / (Q) Equation 16-2 Where AFC is average fixed cost per ounce at each level of output; TFC is total fixed cost at each level of output; and Q is the level of output measured in ounces of gold (all variables per week ). Remember, a graph of Equation 16-1 for any firm is always a rectangular hyperbola , such as Figure 15-4. Column (6) is average variable cost, introduced in Lecture 15, and defined as AVC = (TVC) / (Q) Equation 16-3 Where AVC is average variable cost per ounce at each level of output; TVC is total variable cost at each level of output; and Q is the level of output measured in ounces of gold (all variables per week ). Column (7) is average total cost, introduced in Lecture 15, and defined as ATC = (TC) / (Q) Equation 16-4 Where ATC is average total cost per ounce at each level of output; TC is the total cost of each level of output; and Q is the level of output measured in ounces of gold (all variables per week ). Note, again, that ATC can be calculated two different ways. The first is Equation 16-4. The second is

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ATC = AFC + AVC Equation 16-5 Where ATC, AFC, and AVC are all defined above. The proof of this follows from the creation of Column (4), where TC = TFC + TVC (Equation 16-1 above). Since TC = TFC + TVC; it follows that (TC) / (Q) = (TFC) / (Q) + (TVC) / (Q) which is Equation 16-5. (We simply divided Equation 16-1 through by Q.) Column (8) is the all-important variable, marginal cost. 1 Marginal cost is the change in column (5) divided by the change in column (1). Marginal cost answers the question, "How much does total cost increase each time we increase output by one ounce of gold per week?" MC = ( TC) / ( Q) Equation 16- 6 Where MC is the marginal cost of each unit of output produced; defined as TC, the change in total cost, given a one-unit change in the level of output, Q. Since fixed costs never change in the short run, all increases in total cost that arise from producing ever more and more units of output per week must result from the increase in total variable costs incurred when we increase the level of output. Hence, marginal cost can also be defined as the change in total variable cost given a one-unit increase in output, or, the change in column (3) divided by the change in column (1). 2
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## This note was uploaded on 03/23/2011 for the course ECN 212 taught by Professor Nancy during the Spring '07 term at ASU.

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16Lecture - LECTURE 16 COST FUNCTIONS (CONTINUED) Let us...

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