Since land input is fixed at T0, short-run total cost is given by
The first component of this definition is short-run fixed cost,
and the second component is short-run variable cost,
The TPL0 curve can be thought of as a function of output rather than labour employment. Since this amounts to "inverting" the function Q = F(T0, L), we call such a curve an inverse total product of labour ITPL curve. Given T0 hectares of land, the (technically efficient) amount of labour required to produce Q1 units of output is given by the ITPL0 curve. The short-run variable cost of producing Q1 is therefore given by ITPL0 scaled up by the wage rate:
The assumption implicitly being made in representing the TPL by a stylized "S"-shaped curve is that initially the MPL is rising as labour is added to the production process. Since there is a fixed input of land, it is initially "underutilized" and labour's MP rises as the number of person-hours employed increases. Thus, SVC rises less rapidly as output expands. Beyond the point of inflection, the MPL begins to decline so that SVC rises more rapidly as output expands. Respectively, the shape and position of the STC0 curve are determined solely by the shape of SVC0 and the position of SFC0. It is important to understand that the costs given by STC0 are not necessarily the minimal required outlays for producing the various feasible output levels. Since land input is fixed in the short run, the firm does not have the flexibility in input choice that was assumed in the discussion of profit maximization above. Rather, to vary its output level in the short run, the firm will be forced to use sub-optimal input combinations; i.e., MPTr MPLw Using the definition of STC0, it is possible to derive a number of special cost relations which are also functions of the level of output. Short-run average fixed cost is the short-run fixed cost per unit of output produced: SAFC0 = SFC0 / Q . Short-run average variable cost is the short-run variable cost per unit of output produced: SAVC0 = SVC0 / Q . Short-run average total cost is the short-run total cost per unit of output produced: SATC0 = STC0 / Q . Since STC0 = SFC0 + SVC0, SATC0 = SAFC0 + SAVC0 . Short-run marginal cost is the change in short-run total cost resulting from the production of an additional unit of output: SMC0 = STC0 / Q . Since STC0 = SFC0 + SVC0 and SFC0 = 0, SMC0 = SVC0 / Q . Since the STC0 curve is a vertical translation of the SVC0 curve, they have the same slope at every output level so that SMC0 can be derived from either curve. Since SFC0 is a constant, SAFC0 decreases as Q increases (the same amount of money is distributed over more units of output). Since the difference between SATC0 and SAVC0 is SAFC0, the former two curves get closer together as Q increases.
The assumption implicitly being made in representing the TPL by a stylized "S"-shaped curve is that initially the MPL is rising as labour is added to the production process. Since there is a fixed input of land, it is initially "underutilized" and labour's MP rises as the number of person-hours employed increases. Thus, SVC rises less rapidly as output expands. Beyond the point of inflection, the MPL begins to decline so that SVC rises more rapidly as output expands.
Respectively, the shape and position of the STC0 curve are determined solely by the shape of SVC0 and the position of SFC0. It is important to understand that the costs given by STC0 are not necessarily the minimal required outlays for producing the various feasible output levels. Since land input is fixed in the short run, the firm does not have the flexibility in input choice that was assumed in the discussion of profit maximization above. Rather, to vary its output level in the short run, the firm will be forced to use sub-optimal input combinations; i.e., MPTr MPLw Using the definition of STC0, it is possible to derive a number of special cost relations which are also functions of the level of output. Short-run average fixed cost is the short-run fixed cost per unit of output produced: SAFC0 = SFC0 / Q . Short-run average variable cost is the short-run variable cost per unit of output produced: SAVC0 = SVC0 / Q . Short-run average total cost is the short-run total cost per unit of output produced: SATC0 = STC0 / Q . Since STC0 = SFC0 + SVC0, SATC0 = SAFC0 + SAVC0 . Short-run marginal cost is the change in short-run total cost resulting from the production of an additional unit of output: SMC0 = STC0 / Q . Since STC0 = SFC0 + SVC0 and SFC0 = 0, SMC0 = SVC0 / Q . Since the STC0 curve is a vertical translation of the SVC0 curve, they have the same slope at every output level so that SMC0 can be derived from either curve. Since SFC0 is a constant, SAFC0 decreases as Q increases (the same amount of money is distributed over more units of output). Since the difference between SATC0 and SAVC0 is SAFC0, the former two curves get closer together as Q increases.
Respectively, the shape and position of the STC0 curve are determined solely by the shape of SVC0 and the position of SFC0.
It is important to understand that the costs given by STC0 are not necessarily the minimal required outlays for producing the various feasible output levels. Since land input is fixed in the short run, the firm does not have the flexibility in input choice that was assumed in the discussion of profit maximization above. Rather, to vary its output level in the short run, the firm will be forced to use sub-optimal input combinations; i.e.,
Using the definition of STC0, it is possible to derive a number of special cost relations which are also functions of the level of output. Short-run average fixed cost is the short-run fixed cost per unit of output produced:
Short-run average variable cost is the short-run variable cost per unit of output produced:
Short-run average total cost is the short-run total cost per unit of output produced:
Since STC0 = SFC0 + SVC0,
Short-run marginal cost is the change in short-run total cost resulting from the production of an additional unit of output:
Since STC0 = SFC0 + SVC0 and SFC0 = 0,
Since the STC0 curve is a vertical translation of the SVC0 curve, they have the same slope at every output level so that SMC0 can be derived from either curve.
Since SFC0 is a constant, SAFC0 decreases as Q increases (the same amount of money is distributed over more units of output). Since the difference between SATC0 and SAVC0 is SAFC0, the former two curves get closer together as Q increases.