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# Answers - 266 COST CURVES(Ch 21 Chapter 21 NAME Cost Curves...

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Chapter 21 NAME Cost Curves Introduction. Here you continue to work on cost functions. Total cost can be divided into fixed cost, the part that doesn’t change as output changes, and variable cost. To get the average (total) cost, average fixed cost, and average variable cost, just divide the appropriate cost function by y , the level of output. The marginal cost function is the derivative of the total cost function with respect to output—or the rate of increase in cost as output increases, if you don’t know calculus. Remember that the marginal cost curve intersects both the average cost curve and the average variable cost curve at their minimum points. So to find the minimum point on the average cost curve, you simply set marginal cost equal to average cost and similarly for the minimum of average variable cost. Example: A firm has the total cost function C ( y ) = 100 + 10 y . Let us find the equations for its various cost curves. Total fixed costs are 100, so the equation of the average fixed cost curve is 100 /y . Total variable costs are 10 y , so average variable costs are 10 y/y = 10 for all y . Marginal cost is 10 for all y . Average total costs are (100 + 10 y ) /y = 10 + 10 /y . Notice that for this firm, average total cost decreases as y increases. Notice also that marginal cost is less than average total cost for all y . 21.1 (0) Mr. Otto Carr, owner of Otto’s Autos, sells cars. Otto buys autos for \$ c each and has no other costs. (a) What is his total cost if he sells 10 cars? 10 c . What if he sells 20 cars? 20 c . Write down the equation for Otto’s total costs assuming he sells y cars: TC ( y ) = cy . (b) What is Otto’s average cost function? AC ( y ) = c . For every additional auto Otto sells, by how much do his costs increase? c . Write down Otto’s marginal cost function: MC ( y ) = c . (c) In the graph below draw Otto’s average and marginal cost curves if c = 20. 266 COST CURVES (Ch. 21) 0 10 20 30 40 10 20 30 40 AC, MC Red line AC=MC=20 Output (d) Suppose Otto has to pay \$ b a year to produce obnoxious television commercials. Otto’s total cost curve is now TC ( y ) = cy + b , his average cost curve is now AC ( y ) = c + b/y , and his marginal cost curve is MC ( y ) = c . (e) If b = \$100, use red ink to draw Otto’s average cost curve on the graph above. 21.2 (0) Otto’s brother, Dent Carr, is in the auto repair business. Dent recently had little else to do and decided to calculate his cost conditions. He found that the total cost of repairing s cars is TC ( s ) = 2 s 2 + 10. But Dent’s attention was diverted to other things . . . and that’s where you come in. Please complete the following: Dent’s Total Variable Costs: 2 s 2 . Total Fixed Costs: 10 . Average Variable Costs: 2 s .

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