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Total cost (TC)
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Sum of fixed and variable costs
(The difference between Total Cost and Variable Cost is Fixed Cost)
(The difference between Total Cost and Variable Cost is Fixed Cost)
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Fixed costs (FC)
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Costs that do not change with changes in output; include the costs of fixed inputs used in production
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Variable costs (VC(Q))
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Costs that change with changes in output; include the costs of inputs that vary with output.
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Short run cost function
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A function that defines the minimum possible cost of producing each output level when variable factors are being used in the cost-minimizing way.
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Short run costs
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The short run is defines as the period over which the amounts of some inputs are fixed. The manager is free to alter the use of variable inputs but is "stuck" with existing levels of fixed inputs.
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Average fixed cost (AFC)
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Fixed costs divided by the number of units of output.
AFC=FC/Q
AFC=FC/Q
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Average variable cost (AVC)
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Variable costs divided by the number of units of output.
AVC=VC(Q)/Q
AVC=VC(Q)/Q
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Average total cost (ATC)
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Total cost divided by the number of units of output. ATC is analaogous to average variable cost, except that it provides a measure of total costs on a per-unit basis.
ATC=C(Q)/Q
ATC=C(Q)/Q
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Marginal (incremental) cost
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The most important cost concept: marginal cost is the cost of producing an additional unit of output, that is, the change in cost attributable to the last unit of output
MC=change in C/change in Q
(When only one input is variable, the marginal cost is the price of that input divided by its marginal product.)
MC=change in C/change in Q
(When only one input is variable, the marginal cost is the price of that input divided by its marginal product.)
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Relations among the cost curves
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The marginal cost curve intersects the ATC and AVC curves at their minimum points. This implies that when marginal cost is below and average cost curve, average cost is declining, and when marginal cost is above average cost, average cost is rising.(eg. Consider your grade in this course; if your grade on an exam is below your average grade, the new grade lowers your average grade. If the grade you score on an exam is above your average grade, the new grade increases your average. In essence the new grade is the marginal contribution to your total grade. When the marginal is above the average, the average increase; when the marginal is below the average, the average decreases.)
C(Q)=VC(Q)+FC(total cost=VC+FC)
C(Q)/Q=VC(Q)/Q+FC/Q(dividing both sides by output)
But C(Q)/Q=ATC, VC(Q)/Q=AVC, and FC/Q=AFC. Thus ATC=AVC+AFC
C(Q)=VC(Q)+FC(total cost=VC+FC)
C(Q)/Q=VC(Q)/Q+FC/Q(dividing both sides by output)
But C(Q)/Q=ATC, VC(Q)/Q=AVC, and FC/Q=AFC. Thus ATC=AVC+AFC
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Sunk cost
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A cost that is forever lost after it has been paid. Imagine you are a manager of a coal
Company and have just paid $10,000 to lease a rail car for one month. This expense reflects a fixed cost to your firm— the cost is $10,000 regardless of whether you use the rail car to transport 10 times or 10,000 tons of coal. How much of this $10,000 is a sunk cost depends on the terms of your lease. If the lease does not permit you to recoup any of the $10,000 once it has been paid, the entire $10,000 is a sunk cost— you have already incurred the cost, and there is nothing you can do to change it. If the lease states that you will be refunded $6,000 in the event you do not need the railcar, the only $4000 of the $10,000 in fixed costs are a sunk cost. Sunk costs are thus the amount of these fixed costs that cannot be recouped.
Company and have just paid $10,000 to lease a rail car for one month. This expense reflects a fixed cost to your firm— the cost is $10,000 regardless of whether you use the rail car to transport 10 times or 10,000 tons of coal. How much of this $10,000 is a sunk cost depends on the terms of your lease. If the lease does not permit you to recoup any of the $10,000 once it has been paid, the entire $10,000 is a sunk cost— you have already incurred the cost, and there is nothing you can do to change it. If the lease states that you will be refunded $6,000 in the event you do not need the railcar, the only $4000 of the $10,000 in fixed costs are a sunk cost. Sunk costs are thus the amount of these fixed costs that cannot be recouped.
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Cubic cost function
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Costs are a cubic function of output; provides a reasonable approximation to virtually any cost function.
C(Q)= f+aQ+bQ^2+cQ^3
(Where a,b,c, and f are constants. Note that f represents fixed costs.
C(Q)= f+aQ+bQ^2+cQ^3
(Where a,b,c, and f are constants. Note that f represents fixed costs.
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Marginal cost function
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MC(Q)=a+2bQ+3cQ^2
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Long run costs
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In the long run all costs are variable, because the manager is free to adjust the levels of all inputs.
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Long-run average cost curve
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A curve that defines the minimum average cost of producing alternative levels of output, allowing for optimal selection of both fixed and variable factors of production. The LRAC is the lower envelope of all the short-run average cost curves. This means that the long-run average cost curve lies below every point on the short-run average cost curves, except that it equals each short run average cost curve at the points where the short run curve uses fixed factors optimally. Different short run average cost curves are associated sigh different plant/factory sizes. In the long run the firms manager is free to choose the optimal plant size for producing the desired level of output, and thus determines the long run average cost of producing that output level.
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Economies of scale
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Exist when long-run average costs decline as output is increased. (Graphically the cost curve is depicted as a U, the first half of the U signifies and increase in plant size that it turn lowers costs. Increasing the size of the operation decreases the minimum
Average cost.)
Average cost.)
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Diseconomies of scale
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Exist when long-run average costs rise as output is increased.
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Constant returns to scale
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Exist when long-run average costs remain constant as output is increased. (Sometimes the technology in an industry allows a firm to produce different levels of output at the same minimum average cost. Which is known as constant returns to scale)
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Multi-product cost function
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A function that defines the cost of producing given levels of two or more types of outputs assuming all inputs are used efficiently. The cost function for a multiproduct firm is given by C(Q1,Q2), where Q1 is the number of units produced of product 1 and Q2 is the number of units produced of product 2. Unlike with a single product cost function, however, the costs of production depend on how much of each type of output is produced. This gives rise to what economists call economies of scope and cost complementaries.
C(Q1,Q2)= f+aQ1Q2+(Q1)^2+(Q2)^2
1. Exhibits cost complementarity whenever a<0
2. Exhibits economies of scope whenever
f-aQ1Q2>0
C(Q1,Q2)= f+aQ1Q2+(Q1)^2+(Q2)^2
1. Exhibits cost complementarity whenever a<0
2. Exhibits economies of scope whenever
f-aQ1Q2>0
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Economies of scope
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When the total cost of producing two types of outputs together is less than the total cost of producing each type of output separately. (Eg. Producing steak and chicken dinners in the same restaurant to avoid having to operate two separate restaurants with one serving only chicken and the other serving only steak, there would be a lot of wasted costs on duplicate equipment). There are economies of scope when:
C(Q1,0)+C(0,Q)>C(Q1,Q2) or rearranging
C(Q1,0)+C(0,Q2)-C(Q1,Q2)>0
f-aQ1Q2>0( thus economies of scope are realized in producing output levels Q1 and Q2 if f>aQ1Q2
C(Q1,0)+C(0,Q)>C(Q1,Q2) or rearranging
C(Q1,0)+C(0,Q2)-C(Q1,Q2)>0
f-aQ1Q2>0( thus economies of scope are realized in producing output levels Q1 and Q2 if f>aQ1Q2
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Cost complementarity
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When the marginal cost of producing one type of output decreases when the output of another good is increased. (Eg. Donuts and donut holes) The cost function exhibits cost complementarity if
Change in MC1(Q1,Q2)/change in Q2 <0
Change in MC1(Q1,Q2)/change in Q2 <0
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Quadratic multiproduct cost function
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C(Q1,Q2)= f+aQ1Q2+(Q1)^2+(Q2)^2
Corresponding MC functions
MC1(Q1,Q2)=aQ2+2Q1
MC2(Q1,Q2)=aQ1+2Q2
Corresponding MC functions
MC1(Q1,Q2)=aQ2+2Q1
MC2(Q1,Q2)=aQ1+2Q2
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