forestry - Section Notes(Friday 10/5 and Monday 10/8 1...

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Section Notes (Friday 10/5 and Monday 10/8) 1 Timber Problem Review the relationship between Q ( t ) vs t and Q ( t ) vs t . Let’s try to match up points by joining the graphs up vertically. The relationships between Q ( t ) , Q ( t ) , and Figure 1: Forest Relationship over Time 0 20 40 60 80 100 0 1 2 3 4 5 x 10 4 Stock Time 0 20 40 60 80 100 -500 0 500 1000 Change in Stock Time 0 20 40 60 80 100 0 0.2 0.4 0.6 0.8 1 % Growth in Stock Time Q ( t ) /t are similar to the relationships be- tween total, average, and marginal cost that you may remember from micro. Early on the rate of growth is increasing which means the marginal increase in the stock is positive and growing. A little above 30, the marginal growth reaches its maximum. This is the inflection point on the top graph. Beyond this point, marginal growth is falling. At 75, the stock reaches its maxium. Beyond this point, the stock is falling so the marginal increase is negative. Early on, the average stock size is smaller than the marginal increase in stock. We can see this by noting that the ray is flatter than the slope. Because the marginal increase is above the average stock, average stock must be rising. This continues until we hit 50 where the average stock is maximized. We
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