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Question 1

Cost Curves NAME 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 + 10y. 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 10y, so average variable costs are 10y/y = 10 for all y. Marginal cost is 10 for all y. Average total costs are (100 + 10y)/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. 22.1 (0) Mr. Otto Carr, owner of Otto's Autos, sells cars. Otto buys autos for $c each and has no other costs. What if he (a) What is his total cost if he sells 10 cars? Write down the equation for Otto's total costs sells 20 cars? assuming he sells y cars: TC(y) = For every (b) What is Otto's average cost function? AC(y) = additional auto Otto sells, by how much do his costs increase? Write down Otto's marginal cost function: MC(y) = (c) In the graph below draw Otto's average and marginal cost curves if c = 20. 19:51 V274 COST CURVES (Ch. 22) AC. MC 40 30 20 10 0 10 20 30 40 Output (d) Suppose Otto has to pay Sb a year to produce obnoxious television commercials. Otto's total cost curve is now TC(y) = his average cost curve is now AC(y) = , and his marginal cost curve is MC(y) = (e) If b = $100, use red ink to draw Otto's average cost curve on the graph above. 22.2 (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) = 2s' + 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:. Total Fixed Costs: Average Variable Costs: Average Fixed Costs: Average Total Costs: Marginal Costs: 22.3 (0) A third brother, Rex Carr, owns a junk yard. Rex can use one of two methods to destroy cars. The first involves purchasing a hydraulic 19:51NAME 275 car smasher that costs $200 a year to own and then spending $1 for every car smashed into oblivion; the second method involves purchasing a shovel that will last one year and costs $10 and paying the last Carr brother, Scoop, to bury the cars at a cost of $5 each. (a) Write down the total cost functions for the two methods, where y is output per year: TC1(y) , TC2(y) = (b) The first method has an average cost function and a marginal cost function For the second method these costs are and (c) If Rex wrecks 40 cars per year, which method should he use? If Rex wrecks 50 cars per year, which method should he use? What is the smallest number of cars per year for which it would pay him to buy the hydraulic smasher?_ 22.4 (0) Mary Magnolia wants to open a flower shop, the Petal Pusher, in a new mall. She has her choice of three different floor sizes, 200 square feet, 500 square feet, or 1,000 square feet. The monthly rent will be $1 a square foot. Mary estimates that if she has F square feet of floor space and sells y bouquets a month, her variable costs will be co(y) = y?/ F per month. e down her marginal costjukes are certainly allowable.) hours of (b) This would cost dollars. (c) Given our production function, the cheapest proportions in which to use jokes and labor are the same no matter how many comic books we print. But when we double the amount of both inputs, the number of comic books produced is multiplied by 22.8 (0) Consider the cost function c(y) = 4y + 16. (a) The average cost function is.278 COST CURVES (Ch. 22) (b) The marginal cost function is (c) The level of output that yields the minimum average cost of production is (d) The average variable cost function is_ (e) At what level of output does average variable cost equal marginal cost?_ 22.9 (0) A competitive firm has a production function of the form Y = 2L + 5K. If w = $2 and r = $3, what will be the minimum cost of producing 10 units of output