14Lecture - LECTURE 14 SUN DEVIL MINING COMPANY Shaft 212...

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LECTURE 14 SUN DEVIL MINING COMPANY Shaft # 212 THE PRODUCTION FUNCTION, CONTINUED AGAIN, OUR GOAL IS TO MAXIMIZE PROFIT EACH WEEK THAT WE OPERATE THE MINE. THIS IS THE ONLY GOAL THAT WE HAVE, AND THE ONLY REASON THAT WE DECIDED TO OPERATE OUR ARIZONA GOLD MINE. We create our production function empirically. We hire doses of labor and capital (N&K) and set them to work mining gold. One dose of N&K is one worker, plus the optimum physical amount of capital the worker needs to efficiently mine gold from our mine shaft, working one four-hour shift per week. One dose of K&N costs $90. First, we apply one dose of K&N to our fixed mine shaft each week, to determine the output of gold produced. The result is .375 ounces of gold per week (3/8 of one ounce). Mathematically, to produce one ounce of gold per week should take 2 2/3 doses of K&N per week. When we apply 2 2/3 doses of K&N per week to our mine shaft, we produce one ounce of gold per week. We then tell our crew, "Apply increasing doses of K&N to our mine shaft each week until production is running at 2 ounces per week; then 3 ounces per week; then 4 ounces per week, and so on. Keep increasing weekly output by increasing our variable inputs, K&N, until we produce 14 ounces of gold per week. And be sure to record your data." The first two columns of Table 13-1, below, (which was first discussed in Lecture 13) record our production data, and, empirically, show our production function. The first two columns, (1) "Output in ounces per week", and the (2) "Labor and capital required to produce those levels of output", again, are empirical propositions. We simply apply varying amounts of K&N to our fixed mine shaft until we observe the desired levels of output. 1 1 There are no restrictions. We could have asked our crews to produce and record half-ounces, or quarter- ounces of gold produced each week, and recorded the necessary doses of K&N required. For simplicity we will use whole ounces.
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TABLE 13-1 Production Data for Your Competitive Gold Mine (1) (2) (3) (4) (5) Output N & K Average Product Marginal Product (Oz./wk) (Doses Required) Per Dose (Oz./wk) Per Dose (Oz./wk) 0 0 0 0 +2.67 1 2.67 .375 .375 +2.11 2 4.78 .418 .474 +2.66 3 7.44 .403 .376 +3.23 4 10.67 .375 .310 +4.33 5 15 .333 .231 +5.44 6 20.44 .293 .184 +6.56 7 27 .259 .153 +7.67 8 34.67 .231 .130 +8.77 9 43.44 .207 .114 +9.89 10 53.33 .188 .101 +11 11 64.33 .171 .091 +12.11 12 76.44 .157 .083 +15.12 13 91.56 .142 .066 +20.11 14 111.67 .125 .050 1 Dose of Labor & Capital (K&N) = 1 worker, with an optimum supply of capital, working one four-hour shift per week. 1 Dose of K&N costs $90. Note the most important data contained in the first two columns. When we go from producing zero ounces of gold per week to one ounce per week, it requires 2.67 doses of K&N to produce the first ounce of gold. When we go from one ounce of gold per week to two ounces per week, it requires 2.11 additional doses of K&N . (The total doses required to produce one ounce per week is 2.67 doses. The total doses required to produce two ounces per
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week is 4.78 doses. The difference, which results in the second ounce of gold being produced, is 2.11 doses.) Column (3), with the "plus" signs, shows the extra doses of K&N needed to increase output by one ounce of gold per week.
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