course Mth 173 assignment #027??????Ux?x????{+??Calculus I
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20:51:39 These interpretations are a little more detailed and subtle than you would expect, but as you observe at the end of the assigment, calculus is very applicable to a wide variety of situations. In fact our whole technological society, as well as most of our economic policy, is for the most part solidly based on it.
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RESPONSE --> okay
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20:57:40 Comment from another student: I have taken Microeconomics and Macroeconomics in college, but I never thought about how well this could be used with calculus. I am starting to see the importance of calculus more and more in real life situations.
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RESPONSE --> calculus is seems, is mathematically interperting nearly everything and graphing that and then interperting that and possibly interperting that again. Maybe this is just the analytical geometery part of the course but graphically analysing everything really makes alot things easier to understand.
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21:37:44 Query 4.4.8 (was problem 3 p 268) C(q) total cost of production monotone incr C' incr then decr then incr Ws the meaning of C'(0) (explain why)?
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RESPONSE --> C'(0) is C' at t=0 so it is the rate at which the cost / unit changes.
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21:39:25 ** C'(0) is the rate at which cost is increasing, with respect to the number of items produced, when the number of items being produced is zero. That is, it is the marginal cost (the additional cost per additional item produced) when q = 0. **
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RESPONSE --> Yes it is when the number of items produced is 0 so q=0 not t=0.
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21:44:08 In terms of economics explain the concavity of the graph.
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RESPONSE --> when the cost is concave down the rate at which the cost / unit decreases so it costs less to produce an item, when the cost is cancave up, the rate at which the cost / unit increases, meaning for each addtional unit it costs more to produce it.
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21:49:28 ** The slope of the graph indicates the rate at which cost changes, i.e., the marginal cost. The rate at which the slope changes, which is closely related to the concavity, tells you the rate at which the marginal cost is changing. If the graph is concave up, then the marginal cost--i.e., the cost per additional item produced--is increasing, as might happen for example if we are pushing the capacity of a production line or if at a certain level the cost of materials increases. If the graph is concave down, the marginal cost is decreasing, perhaps because of an improving economy of scale. **
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RESPONSE --> okay
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21:57:14 Explain the economic significance of the point at which concavity changes.
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RESPONSE --> The point at which the concavity changes is when the marginal cost ""balances out.""
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22:08:31 ** The concavity changes from concave down, where marginal cost is decreasing, to concave up, where marginal cost is increasing. For this graph, this is the point where marginal cost starts going back up.. **
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RESPONSE --> before the cost is decreasing, and after the cost is increasing.
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22:25:02 Query 4.4.15 (was prob 9 p 269 ) C(q) as in previous Explain why ave cost is slope of line from the origin to the point (q, C(q)).
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RESPONSE --> If the cost of production is given by C(q) then the fluxuations of that line above and below the average line would average out to the average line. Basically for every part that the cost goes above average it must also come back down that far, and vica versa. Since the slope is representative of the cost / unit then the average slope would be the average cost / unit.
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22:25:58 ** The average cost per item is total cost C(q) divided by number q of items produced, i.e., C(q) / q. From the origin to the point (q, C(q) ) the rise is C(q), the run is q so the slope is indeed C(q) / q, the average cost per item. **
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RESPONSE --> okay
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22:34:23 Where on the curve should P be to make the slope a minimum?
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RESPONSE --> P should be where the minima of the cost graph is.
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22:35:10 ** Imagine running a line from the origin to the graph. For awhile the slope of this line keeps decreasing, with its angle to the x axis continuously decreasing. The minimum slope occurs when the slope of this line stops decreasing, which will occur at the instant the line becomes tangent to the curve. So a line from the origin, and tangent to the curve, will show you the point at which average cost is minimized. **
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RESPONSE --> So by drawing this tangent line from the origin to the curve you can easily tell the minima point.
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22:45:04 Explain why at the point where ave cost is minimized the ave and marginal costs are equal.
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RESPONSE --> Because the most effecient point is where the tangent line comes from the origin to the minima the average and marginal costs (represented by the graph it self) are equal at that point.
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22:46:22 ** Marginal cost is represented by the slope of the graph. At the point where the average cost is minimized, the line from the origin to the graph is tangent to the graph, so the slope of the graph is equal to the slope of this line. Since the slope of the line is the average cost, and the slope of the graph is the marginal cost, the two must be equal. ** COMMON MISCONCEPTION: The point where the average cost is minimized is also the point where the profit function is maximized. The marginal revenue and marginal costs are equal at this point. At this point the cost and revenue functions are increasing at the same rate. Just before this point, revenue will be going up faster than costs, just after this point cost will be going up faster than revenue. EXPLANATION: ** You are talking about an important idea when applied to both the revenue and cost functions, specifically to the difference between those functions. However the profit function depends on much more than the cost graph. All we can talk about based on this graph is the cost function and things like marginal cost and average cost. **
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RESPONSE --> okay
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22:47:00 Query Add comments on any surprises or insights you experienced as a result of this assignment.
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RESPONSE --> This is simliar to optimazation, where you are evalutating how the different functions react with each other.
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