You can think of the result in any one game as being Paolo's marginal free-throw percentage. Based on your previous answer, you can deduce that when Paolo's marginal free-throw percentage is below the average, the average must be You can now apply this analysis to production costs. For a U-shaped average total cost (ATC) curve, when the marginal cost curve is below the average total cost curve, the average total cost must be Also, when the marginal cost curve is above the average total cost curve, the average Therefore, the marginal cost curve intersects the average total cost curve total cost must be

Introduction to Calculus in Economics (continued): In the previous Problem Set question, we started looking at the cost function C (æ), the cost of a firm producing z items. An important microeconomics concept is the marginal cost, defined in (non- mathematical introductory) economics as the cost of producing one additional item. If the current production level is æ items with cost C (z), then the cost of computing h additionial (C(z+h)-C(z)) items is C (z + h). The average cost of those h items is . As we analyze the cost of just the last item produced, this can be made into a mathematical model by taking the limit as h → 0, i.e. the derivative C' (z). Use this function in the model below for the Marginal Cost function MC (x). Problem Set question: The cost, in dollars, of producing z units of a certain item is given by C (z) = 0.02a3 – 10z + 450. (a) Find the marginal cost function. MC (z) (b) Find the marginal cost when 50 units of the item are produced. The marginal cost when 50…

Back to Assignment Attempts: Keep the Highest: 1/4 3. The relationship between marginal and average costs Consider the following scenario to understand the relationship between marginal and average values. Suppose Edison is a professional basketball player, and his game log for free throws can be summarized in the following table. Fill in the columns with Edison's free-throw percentage for each game and his overall free-throw average after each game. Game Game Result Total Game Free-Throw Percentage Average Free-Throw Percentage 3/3 3/3 100 100 3/5 6/8 80 3 2/8 8/16 4 2/4 10/20 5/5 15/25 On the following graph, use the orange points (square symbol) to plot Edison's free-throw percentage for each game individually, and use the green points (triangle symbol) to plot his overall average free-throw percentage after each game. Note: Plot your points in the order in which you would like them connected. Line segments will connect the points automatically. 100 T

Q.4 Marginal Cost is closely related to: (a) Total variable cost (b) Total cost (c) Total fixed cost (d) All of the above

can you explain how they got M=y^2/2 and L=2y^2 from part b of this question