course Mth 173 4/28 10 Question: `qQuery 4.4.8 (was problem 3 p 268) C(q) total cost of production monotone incr C' incr then decr then incr
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Given Solution: `a** 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. ** &&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&& Self-critique (if necessary): OK ------------------------------------------------ Self-critique rating #$&* 3 ********************************************* Question: `qIn terms of economics explain the concavity of the graph. YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY Your solution: The concavity shows a rate of cost change and therefore explains the graph economically. The two are pretty much directly proportional. confidence rating #$&* 3 ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
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Given Solution: `a** 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. ** &&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&& Self-critique (if necessary): As common sense would tell me, the graph and the economic period aren’t always directly proportional, like if costs go down the economy might be rising. ------------------------------------------------ Self-critique rating #$&* 3 ********************************************* Question: `qExplain the economic significance of the point at which concavity changes. YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY Your solution: This changes the economy one way or another. Whether it be a change for rising costs means a lowering economy, or a temporary decrease in costs means a temporary economic struggle (ex. war). confidence rating #$&* 3 ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
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Given Solution: `a** 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.. ** &&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&& Self-critique (if necessary): OK ------------------------------------------------ Self-critique rating #$&* 3 ********************************************* Question: `qQuery 4.4.15 (was prob 9 p 269 ) C(q) as in previous Explain why ave cost is slope of line from the origin to the point (q, C(q)). YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY Your solution: Slope is rise/run, so the slope of a line represents ave cost because the total cost between the origin and a point divided by the time covered is exactly that. confidence rating #$&* 3 ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
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Given Solution: `a** 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. ** &&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&& Self-critique (if necessary): OK ------------------------------------------------ Self-critique rating #$&* 3 ********************************************* Question: `qWhere on the curve should P be to make the slope a minimum? YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY Your solution: P should be directly before the slope begins to increase, or at the lowest pt (or flat pt) you might say. confidence rating #$&* 3 ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
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Given Solution: `a** 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. ** &&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&& Self-critique (if necessary): OK ------------------------------------------------ Self-critique rating #$&* 3 ********************************************* Question: `qExplain why at the point where ave cost is minimized the ave and marginal costs are equal. YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY Your solution: When the ave cost is minimized, the two costs are equal because both are at their lowest points. The lowest point of ave cost means that the marginal cost (or profit) is also equally low. confidence rating #$&* 3 ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
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Given Solution: `a** 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. ** &&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&& Self-critique (if necessary): Yes, the two costs are directly proportional. ------------------------------------------------ Self-critique rating #$&* 3 ********************************************* Question: `qQuery Add comments on any surprises or insights you experienced as a result of this assignment. &&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&& Self-critique (if necessary): N/A ------------------------------------------------ Self-critique rating #$&* 3 "