Dominick Salvatore Schaums Outline of Microeconomics, 4th edition Schaums Outline Series 2006

168 COSTS OF PRODUCTION [CHAP. 7
(b)
curve is greater than the slope of a line from the origin to the LTC curve. Thus, LMC is greater than or is
above LAC.
If the LTC curve had been a straight line through the origin, the LAC curve would be horizontal throughout (at
the constant value of the slope of the LTC curve) and would coincide with the LMC curve throughout its
entire length. For the LAC curve to look like the one in Problem 7.14(a), a portion of the LTC must coincide
or be tangent to a portion of a ray from the origin to the LTC curve. In that case, the LMC curve would
coincide with the horizontal portion of the LAC curve.
7.19 Using Fig. 7-17, (a) explain the relationship between the SAC 1 curve and the LAC curve in Fig. 7-16
and (b) explain the relationship between the SMC 1 curve and the LMC curve.
(a) For outputs which are either smaller or larger than two units, the slope of a ray from the origin to the STC 1
curve (i.e., SAC) exceeds the slope of a ray from the origin to the LTC curve (i.e., LAC) at the same level of
output (see Fig. 7-17). Thus, the SAC 1 curve is above the corresponding LAC curve for outputs smaller and
larger than two units (see Fig. 7-16). At the output level of two units, the slope of a ray from the origin to the
STC 1 curve is the same as the slope of a ray from the origin to the LTC curve. Thus, at two units of output,
SAC ¼ LAC and the SAC 1 curve is tangent to the corresponding LAC curve. The relationship between the
SAC 3 and SAC 4 curves and the LAC curve in Fig. 7-16 can be explained in an exactly analogous fashion from
the relationship between the STC 3 and STC 4 curves and the corresponding LTC curve in Fig. 7-17.
(b) For outputs smaller than two units, the slope of the STC 1 curve (i.e., SMC) is smaller than the slope of the
LTC curve (i.e., LMC) at the same level of output (see Fig. 7-17). Thus the SMC 1 curve is below the corresponding
LMC curve for outputs smaller than two units (see Fig. 7-16). For outputs greater than two units, the
exact opposite is true. At the output level of two units, the STC 1 curve is tangent to the LTC curve and so their
slopes are equal. Thus, SMC ¼ LMC and the LMC intersects the SMC 1 curve at the lowest point on the SMC 1
curve at two units of output. The relationship between the SMC 3 and SMC 4 curves and the corresponding
LMC curve can be explained analogously from the relationship between the STC 3 and STC 4 curves and
the corresponding LTC curve. Note once again that at the lowest point on the LAC curve, LAC ¼ LMC ¼
SAC ¼ SMC (see point F in Fig. 7-16). This is always true.
PRODUCTION FUNCTIONS AND COST CURVES
7.20 (a) State the relationship between production functions and cost curves. (b) Explain how we can derive
the TP, AP, and MP curves for a factor of production from an isoquant diagram. (c) Explain how we
derive the TVC curve from a TP curve. (d) State the relationship between the AVC and MC curves
and the corresponding AP and MP curves.
(a) On Problem 6.17 we saw how a firm should combine inputs in order to minimize the cost of producing various
levels of output. The production function of a firm together with the prices that the firm must pay for its factors
of production or inputs determine the firm’s cost curves.
(b) Suppose that we have only two factors of production, say labor and capital, and we keep the amount of capital
used (per time period) fixed at a particular level (and are thus dealing with the short run). Then, by increasing
the amount of labor used per time period, we reach higher and higher isoquants or levels of output (up to a
maximum). If we plot the output that we get with different quantities of labor used per unit of time (with the
fixed amounts of capital), we get the TP L function or curve. From this TP L curve we can derive the AP L and
the MP L curves (see Problem 7.21).
(c) For each level of the TP L , we can get the corresponding TVC by multiplying the price per unit of labor times
the quantity of labor required to produce the specified level of output. Thus, from the TP L curve we can get the
corresponding TVC curve. Then from the TVC curve we can derive the AVC and the MC curves (see Problem
7.22).
(d ) The AVC curve we get is the monetized reciprocal of the corresponding AP curve, and the MC curve is the
monetized reciprocal of the corresponding MP curve (see Problem 7.23). Note that from an isoquant-isocost
diagram we can also obtain the LTC and the LAC curves and show the relation between LTC and STC and
between LAC and SAC (see Problem 7.24). Thus, Problems 7.21 to 7.24 summarize the relationship between
production functions and cost curves.