15Lecture

15Lecture - LECTURE 15 Today is Tuesday The spot price of...

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LECTURE 15 Today is Tuesday, October 12, 2010. The spot price of gold is $1,351.80. It closed at $1,070 per ounce on October 15, 2009. THE SUN-DEVIL MINE PRODUCTION FUNCTION (CONTINUED) Look again at Table 13-1, from which we created Figures 14-1 and 14-2. Also, have Figure 15-1 and 15-2 in front of you while you read through this lecture. Figures 15-1 and 15-2 are smooth, typical , short-run Total Product (TP), Marginal Product (MP), and Average Product (AP) curves that apply to any and all firms operating with at least one fixed input. In our case the fixed input is Land (the mine shaft that we have decided to lease and re-open). Look carefully at Figures 14-1 and 14-2 and compare them to the two graphs depicted on Figure 15-1. Essentially they are identical. The actual graphs look different, but the key features of each set of graphs are identical. In both Figures 14 and Figure 15, as we apply more and more units of the variable input (doses of labor and capital for our mine) to some fixed input (our leased land & mine shaft) TP increases; at first at an increasing rate (the TP curve is concave upward . Then the TP curve reaches an inflection point (the first vertical dashed line in Figure 15-1) at which point the TP curve increases at a decreasing rate (the TP curve is concave downward ). The TP curve continues to increase at a decreasing rate until it reaches a maximum at the second vertical dashed line, where the slope of the TP curve, which has been decreasing since the first vertical dashed line, becomes zero, (the horizontal dashed line at the maximum point of the TP curve). After this point TP begins to decrease. The relationship between total physical product (TP) and the number of units of the variable inputs employed each period (Doses of N & K) is an empirical relationship for any firm, including our mining company. We alter the physical units of labor and capital that we apply to the mine shaft each week and we record the different levels of output, in ounces of gold, that we obtain. The Marginal Product (MP) and Average Product (AP) curves in Figure 14-2 and the bottom portion of Figure 15-1 are derived from the TP function. AP = (TP) / (Doses of N&K) Equation 15-1
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Where AP is average product per dose of labor and capital, measured in ounces per week; TP is total product, measured in ounces per week; and Doses of N&K is the number of doses of the variable inputs employed each week. MP = ( TP) / ( 1 Equation 15- 2 Where MP is marginal product per dose of labor and capital, measured in ounces per week, and is defined as the change in TP brought about by a one unit change in the number of doses employed. Both in the top and bottom portions of Figure 15-1, note there are three
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15Lecture - LECTURE 15 Today is Tuesday The spot price of...

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