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# Introductory Microeconomics Resource Allocation and Market Structure ECON 1

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This 13 page Class Notes was uploaded by Isidro Stoltenberg on Monday September 7, 2015. The Class Notes belongs to ECON 1 at University of California - Santa Cruz taught by Staff in Fall. Since its upload, it has received 24 views. For similar materials see /class/182322/econ-1-university-of-california-santa-cruz in Economcs at University of California - Santa Cruz.

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Date Created: 09/07/15

S171 51847Krugman2eiPsich12qxp 91608 922 PM Page S 171 Behind the Supply Curve Inputs and Costs 1 Changes in the prices of key commodities can have a significant impact on a compa ny s bottom line According to a September 27 2007 article in the Wall Street Journal Now with oil gas and electricity prices soaring companies are beginning to realize that saving energy can translate into dramatically lower costs Another Wall Street journal article dated September 9 2007 states Higher grain prices are taking an increasing financial toll Energy is an input into virtually all types of production corn is an input into the production of beef chicken highfructose corn syrup and ethanol the gasoline substitute fuel a Explain how the cost of energy can be both a fixed cost and a variable cost for a company 939 Suppose energy is a fixed cost and energy prices rise What happens to the compa ny s average total cost curve What happens to its marginal cost curve Illustrate your answer with a diagraml 5quot Explain why the cost of corn is a variable cost but not a fixed cost for an ethanol producer a When the cost of corn goes up what happens to the average total cost curve of an ethanol producer What happens to its marginal cost curve Illustrate your answer with a diagraml a Energy required to keep a company operating regardless of how much output is produced represents a fixed cost such as the energy costs of operating office buildings factories and stores that must be maintained independent of the amount of output produced In addition energy is a variable cost because produc ing more output almost always requires using more energy 039 When fixed costs increase so will average total costs The average total cost curve will shift upwardl In panel a of the accompanying diagram this is illustrated by the movement of the average total cost curve from its initial position ATC1 to its new position ATCZI The marginal cost curve is not affected if the variable costs do not change So the marginal cost curve remains at its initial position MCI a A Rise in the Price of Energy b A Rise in the Price of Corn Cast Cast M52 of unit MC ATEZ of unit M51 Arc1 Arc2 Arc1 Quantity Quantity S171 S171 SlS47Krugman2e7PSich12qxp 91608 922 PM Page S 172 CHAPTER 12 BEHIND THE SUPPLY CURVES INPUTS AND COSTS c Since corn is an input into the production of ethanol producing a larger quantity of ethanol requires a larger quantity of corn making corn a variable cost d When variable costs increase so do average total costs and marginal costs Both curves will shift upwardl In panel b of the accompanying diagram the move ment of the average total cost curve is illustrated by the shift from its initial posi tion ATC1 to its new position ATCZT The movement of the marginal cost curve is illustrated by the shift from its initial position MCl to its new position MCZT 2 Marty s Frozen Yogurt is a small shop that sells cups of frozen yogurt in a university townl Marty owns three frozenyogurt machinesl His other inputs are refrigerators frozenyogurt mix cups sprinkle toppings and of course workersl He estimates that his daily production function when he varies the number of workers employed and at the same time of course yogurt mix cups and so on is as shown in the accom panying tablel Quantity of labor Quantity of frozen workers yogurt cups mmbwmno N l o a What are the fixed inputs and variable inputs in the production of cups of frozen yogurt 939 Draw the total product curvel Put the quantity of labor on the horizontal axis and the quantity of frozen yogurt on the vertical axis c What is the marginal product of the first worker The second worker The third worker Why does marginal product decline as the number of workers increases 2 a The fixed inputs are those whose quantities do not change as the quantity of out put changes frozenyogurt machines refrigerators and the shop The variable inputs are those whose quantities do change as the quantity of output changes frozenyogurt mix cups sprinkle toppings and workers b The accompanying diagram illustrates the total product curvel Quantity of frozen yogurt CUPS 350 TF 300 250 200 150 100 50 l l l l l l 0 l 2 3 4 5 6 Quantity of labor workers S171 SlS47Krugman2e7PSich12qxp 91608 922 PM Page S 173 CHAPTER 12 BEHIND THE SUPPLY CURVES INPUTS AND COSTS c The marginal product MPL of the first worker is 110 cups The MPL of the sec ond worker is 90 cups The MPL of the third worker is 70 cups The MPL of labor declines as more and more workers are added due to the principle of diminishing returns to labor Since the number of frozenyogurt machines is fixed as workers are added there are fewer and fewer machines for each worker to work with mak ing each additional worker less and less productive 3 The production function for Marty s Frozen Yogurt is given in Problem 2 Marty pays each of his workers 80 per day The cost of his other variable inputs is 0150 per cup of yogurt His fixed cost is 100 per day a What is Marty s variable cost and total cost when he produces 110 cups of yogurt 200 cups Calculate variable and total cost for every level of output given in Problem 21 Draw Marty s variable cost curve On the same diagram draw his total cost curve 939 What is the marginal cost per cup for the first 110 cups of yogurt For the next 90 cups Calculate the marginal cost for all remaining levels of output 5quot 3 a Marty s variable cost VC is his wage cost 80 per worker per day and his other input costs 050 per cupl His total cost TC is the sum of the variable cost and his fixed cost of 100 per day The answers are given in the accompanying tablet Quantity of frozen Quantity yogurt of labor cups workers VC TC MC of cup 0 0 0 100 123 110 1 1 X 80 110 X 05 135 235 139 200 Z Z X 80 200 X 05 260 360 164 270 3 3 X 80 270 X 05 375 475 317 300 4 4 X 80 300 X 05 470 570 450 320 5 5 X 80 320 X 05 560 660 850 330 6 6 X 80 330 X 05 645 745 b The accompanying diagram shows the variable cost and total cost curvesl Cost 800 r5 V5 600 400 200 0 50 100 150 200 250 300 350 Quantity of frozen yogurt cups c Marginal cost MC per cup of frozen yogurt is shown in the table in part a it is the change in total cost divided by the change in quantity of output S171 SlS47Krugman2e7PSich12qxp 91608 922 PM Page S 174 CHAPTER 12 BEHIND THE SUPPLY CURVES INPUTS AND COSTS 4 The production function for Marty s Frozen Yogurt is given in Problem 2 The costs are given in Problem 3quot a For each of the given levels of output calculate the average fixed cost AFC aver age variable cost AVC and average total cost ATC per cup of frozen yogurt b On one diagram draw the AFC AVC and ATC curvesl c What principle explains why the AFC declines as output increases What principle explains why the AVC increases as output increases Explain your answers d How many cups of frozen yogurt are produced when average total cost is minimized 4 a The average fixed cost average variable cost and average total cost per cup of yogurt are given in the accompanying tablet Numbers are rounded Quantity of frozen yogurt cups VC TC AFC of cup AVC of cup ATC of cup 0 0 100 110 135 235 091 123 214 200 260 360 050 130 180 270 375 475 037 139 176 300 470 570 033 157 190 320 560 660 031 175 206 330 645 745 030 195 226 b The accompanying diagram shows the AFC AVC and ATC curvesl Cost of cup 250 ATC 2 00 VIMC 1 50 100 050 AF 0 100 150 200 250 300 350 Quantity of frozen yogurt cups c AFC declines as output increases due to the spreading effect The fixed cost is spread over more and more units of output as output increasesl AVC increases as output increases due to the diminishing returns effectl Due to diminishing returns to labor it costs more to produce each additional unit of output d Average total cost is minimized when 270 cups of yogurt are produced At lower quantities of output the fall attributable to the spreading effect dominates changes in average total cost At higher quantities of output the rise attributable to the diminishing returns effect dominates changes in average total cost S171 S1847Krugman2e7PS7Ch12qxp 91608 922 PM Page S 175 CHAPTER 12 BEHIND THE SUPPLY CURVES INPUTS AND COSTS 5 The accompanying table shows a car manufacturer s total cost of producing cars Quantity of cars TC 0 500000 540000 560000 570000 590000 620000 660000 720000 800000 920000 1100000 loooxnmuwbwmn o a What is this manufacturer s fixed cost b For each level of output calculate the variable cost VC For each level of output except zero output calculate the average variable cost AVC average total cost ATC and average fixed cost AFC What is the minimumcost output c For each level of output calculate this manufacturer s marginal cost MC d On one diagram draw the manufacturer s AVC ATC and MC curves 5 a The manufacturer s fixed cost is 500000 Even when no output is produced the manufacturer has a cost of 500000 b The accompanying table shows VC calculated as TC 7 FC AVC calculated as VCQ ATC calculated as TC Q and AFC calculated as FCQ Numbers are rounded The minimumcost output is 8 cars the level at which ATC is minimized Quantity of cars TC MC of car VC AVC of car ATC of car AFC of car 0 500000 0 40000 1 540000 40000 40000 540000 500000 20000 2 560000 60000 30000 280000 250000 10000 3 570000 70000 23333 190000 166667 20000 4 590000 90000 22500 147500 125000 30000 5 620000 120000 24000 124000 100000 40000 6 660000 160000 26667 110000 83333 60000 7 720000 220000 31429 102857 71429 80000 8 800000 300000 37500 100000 62500 120000 9 920000 420000 46667 102222 55556 180000 10 1100000 600000 60000 110000 50000 c The table also shows MC the additional cost per additional car produced Notice that MC is below ATC for levels of output less than the minimumcost output and above ATC for levels of output greater than the minimumcost output S171 SlS47Krug man2e7PSich12qxp 91608 922 PM Page S 176 S176 CHAPTER 12 BEHIND THE SUPPLY CURVES 6 INPUTS AND COSTS d The AVC ATC and MC curves are shown in the accompanying diagram Cost of car 600000 500000 400000 300000 200000 MC ATE A V 100000 0 l 2 3 4 5 6 7 8 Quantity of cars Labor costs represent a large percentage of total costs for many firms According to a September I 2007 Wall Street journal article US labor costs were up 09 during the preceding three months and 08 over the three months preceding those a When labor costs increase what happens to average total cost and marginal cost Consider a case in which labor costs are only variable costs and a case in which they are both variable and fixed costs An increase in labor productivity means each worker can produce more output Recent data on productivity show that labor productivity in the US nonfarm busi ness sector grew 2 for each of the years 2005 2006 and 2007 Annual growth in labor productivity averaged 15 from the mid1970s to mid1990s 26 in the past decade and 4 for a couple of years in the early 2000s b When productivity growth is positive what happens to the total product curve and the marginal product of labor curve Illustrate your answer with a diagram c When productivity growth is positive what happens to the marginal cost curve and the average total cost curve Illustrate your answer with a diagram 9 If labor costs are rising over time on average why would a company want to adopt equipment and methods that increase labor productivity a When labor costs are a variable cost but not a fixed cost an increase in labor costs leads to an increase in both average total cost and marginal cost When labor costs are a variable cost and a fixed cost the result is the same both the average total cost and the marginal cost increase 039 When productivity growth is positive any given quantity of labor can produce more output causing the total product curve to shift upward Since each unit of labor can produce more output the marginal product of labor will increase and the marginal product of labor curve will shift upward In panel a of the accom panying diagram the upward shift of the total product curve is illustrated by the S171 SlS47Krugman2e7PSich12qxp 91608 922 PM Page S 177 CHAPTER 12 BEHIND THE SUPPLY CURVES INPUTS AND COSTS movement from its initial position TPl to its new position TPZl In panel b the upward shift of the marginal product of labor curve is illustrated by the move ment from its initial position MPLl to its new position MPLZl a Total Product Curves b Marginal Product Curves Quantity Marginal product of TF2 l l T MPL2 MPL1 Quantity of labor Quantity of labor c When productivity growth is positive the marginal cost curve and the average total cost curve will both shift downward assuming labor costs have not changed In the accompanying diagram the movement of the average total cost curve is illustrated by the shift from its initial position ATCl to its new position ATC l The movement of the marginal cost curve is illustrated by the shift from its initial position MCl to its new position MCZl Cost 751 of unit 2 ATCl ATCZ Quantity d Rising labor costs will shift the average total cost and marginal cost curves upwardl Productivity growth will counteract this shifting the average total cost and marginal cost curves downwardl 7 Magnificent Blooms is a florist specializing in floral arrangements for weddings graduations and other events Magnificent Blooms has a fixed cost associated with space and equipment of 100 per day Each worker is paid 50 per day The daily production function for Magnificent Blooms is shown in the accompanying tablel Quantity of labor Quantity of floral workers arrangements 0 0 1 5 2 9 3 12 4 14 5 15 S171 SlS47Krugman2e7PSich12qxp 91608 922 PM Page S 178 S178 CHAPTER 12 7 a BEHIND THE SUPPLY CURVES INPUTS AND COSTS Calculate the marginal product of each worker What principle explains why the marginal product per worker declines as the number of workers employed increases Calculate the marginal cost of each level of output What principle explains why the marginal cost per floral arrangement increases as the number of arrangements increases MPL shown in the accompanying table for the five workers is the change in out put resulting from the employment of one additional worker per day MPL falls as the quantity of labor increases due to the principle of diminishing returns Quantity of labor L workers 0 1 2 Quantity of floral arrangements 0 Marginal product of labor Variable MPL cost AllAL VC loral number arrangements of workers per worker X wage rate 0 5 50 4 100 3 150 Z 200 1 250 Marginal cost of flora Total cost arrangement T C FC VC ATCAll 100 1000 505 150 1250 504 200 1667 503 250 2500 502 300 5000 501 350 b The marginal cost MC of floral arrangements is the change in total cost divided by the change in output So to compute MC we first need to compute total cost TC PC VC as shown in the table MC per floral arrangement is also shown in the table MC increases as output increases due again to the principle of diminish ing returns 8 You have the information shown in the accompanying table about a firm s costsl Complete the missing data Quantity 0 1 2 TC MC 20 a A TC A VC 7 a a a a a a a a a S171 SlS47Krug man2e7PSich12qxp 91608 922 PM Page S 179 CHAPTER 12 BEHIND THE SUPPLY CURVES INPUTS AND COSTS 8 The accompanying table contains the complete cost data The total cost of producing one unit of output is the total cost of producing zero units of output plus the mar ginal cost of increasing output from zero to one and so forth The average total cost is just the total cost divided by output Since the total cost of producing zero output is 20 the variable cost is TC 7 20 The average variable cost is then just the vari able cost divided by output Quantity TC MC of unit ATC of unit AVC of unit 0 2000 2000 1 4000 4000 2000 1000 2 5000 2500 1500 1600 3 6600 2200 1533 2000 4 8600 2150 1650 2400 5 11000 2200 1800 9 Evaluate each of the following statements If a statement is true explain why if it is false identify the mistake and try to correct it a A decreasing marginal product tells us that marginal cost must be rising b An increase in fixed cost increases the minimumcost outputl c An increase in fixed cost increases marginal cost d When marginal cost is above average total cost average total cost must be falling 9 a True If each additional unit of the input adds less to output than the previous unit decreasing marginal product then in order to produce additional output the firm needs to use increasingly more of the input that is the marginal cost of production increases 939 True As the fixed cost rises the average fixed cost also rises that is the spreading effect is now largerl It is the spreading effect that causes average total cost to decline Since this effect is now larger it dominates the diminishing returns effect over a greater quantity of output that is average total cost decreases over a greater quantity of output c False An increase in fixed cost does not change marginal cost Marginal cost is the additional cost of producing an additional unit of output Fixed cost does not change as output is increased and so the additional cost of producing an addi tional unit of output is independent of the fixed cost d False When marginal cost is above average total cost average total cost must be rising If the additional cost of producing one more unit of output is greater than what it costs to produce each unit of output on average then producing that one more unit of output must increase the average total cost S171 SlS47Krugman2e7PSich12qxp 91608 922 PM Page S 180 CHAPTER 12 BEHIND THE SUPPLY CURVES INPUTS AND COSTS 10 Mark and Jeff operate a small company that produces souvenir footballsl Their fixed cost is 2000 per month They can hire workers for 1000 per worker per month Their monthly production function for footballs is as given in the accompanying ta e1 Quantity of labor workers Quantity of footballs 0 0 1 300 2 800 3 1200 4 1400 5 1500 a For each quantity of labor calculate average variable cost AVC average fixed cost AFC average total cost ATC and marginal cost MCT b On one diagram draw the AVC ATC and MC curvesl c At what level of output is Mark and Jeff s average total cost minimized 10 a The AVC AFC ATC TC and MC are given in the accompanying tablel Quantity of labor uantity of AVC of AFC of ATC of TC of MC of workers footballs football football football footballs football 0 0 200000 333 1 300 333 667 1000 300000 200 2 800 250 250 500 400000 250 3 1200 250 167 417 500000 500 4 1400 286 143 429 600000 1000 5 1500 333 133 467 700000 b The accompanying diagram shows the AVC ATC and MC curvesl t of football 10 8 200 400 600 800 1000 1200 1400 1600 uantity of footballs c According to the table Mark and Jeff s average total cost is minimized at 1200 footballs per month where the ATC is 4117 S171 51847Krugman2eiPsich12qxp 91608 922 PM Page S 181 CHAPTER 12 BEHIND THE SUPPLY CURVES INPUTS AND COSTS 1 1 You produce widgetsl Currently you produce 4 widgets at a total cost of 40 a What is your average total cost b Suppose you could produce one more the fifth widget at a marginal cost of 5 If you do produce that fifth widget what will your average total cost be Has your average total cost increased or decreased Why c Suppose instead that you could produce one more the fifth widget at a marginal cost of 20 If you do produce that fifth widget what will your average total cost be Has your average total cost increased or decreased Why 11 9 Your average total cost is 404 10 per Widget 039 If you produce one more widget you are producing five widgets at a total cost of 40 5 45l Your average total cost is therefore 455 9l Your average total cost has decreased because the marginal cost of the additional widget is below the average total cost before you produced the additional Widget 5quot If you produce one more widget you are producing five widgets at a total cost of 40 20 60 Your average total cost is therefore 605 12l Your average total cost has increased because the marginal cost of the additional widget is above the average total cost before you produced the additional widgetl 12 In your economics class each homework problem set is graded on the basis of a maximum score of 100 You have completed 9 out of 10 of the problem sets for the term and your current average grade is 88 What range of grades for your 10th prob lem set will raise your overall average What range will lower your overall average Explain your answer 12 Any grade for your 10th problem set greater than 88 will raise your overall average any grade lower than 88 will lower it This is the same principle at work as that for average total cost and marginal cost If the marginal cost curve the 10th grade is above the average total cost curve the average over the first 9 grades then the aver age total cost is rising that is the average over the 10 sets is greater than the average over the 9 sets And if the marginal cost curve the 10th grade is below the average total cost curve the average over the first 9 grades then the average total cost is falling that is the average over the 10 sets is lower than the average over the 9 sets To see this arithmetically note that your current average 88 is found by Sum of grades9for first 9 sets 88 Average over rst 9 sets Hence Sum of grades for first 9 sets 88 x 9 792 So your overall grade the grade over all 10 problem sets is 792 Grade for 10th set 7 W f 7 Overall average If your 10th grade is 90 then your overall grade is 792 90 W 5 792 90 882 S171 SlS47Krugman2e7PSich12qxp 91608 922 PM Page S 182 CHAPTER 12 BEHIND THE SUPPLY CURVES INPUTS AND COSTS which is greater than 88 And if your 10th grade is 86 then your overall grade is 792 867 W t i 792 86 78718 which is less than 88 13 Don owns a small concretemixing company His fixed cost is the cost of the concrete batching machinery and his mixer trucks His variable cost is the cost of the sand gravel and other inputs for producing concrete the gas and maintenance for the machinery and trucks and his workers He is trying to decide how many mixer trucks to purchase He has estimated the costs shown in the accompanying table based on estimates of the number of orders his company will receive per week VC Quantity 20 40 60 of trucks FC orders orders orders 2 6000 2000 5000 12000 3 7000 1800 3800 10800 4 8000 1200 3600 8400 a For each level of fixed cost calculate Don s total cost for producing 20 40 and 60 orders per wee l b If Don is producing 20 orders per week how many trucks should he purchase and what will his average total cost be Answer the same questions for 40 and 60 orders per week 13 a The answers are given in the accompanying table TC Quantity m of trucks orders orders orders 2 8000 11000 18000 3 8800 10800 17800 4 9200 11600 16400 Don should choose the number of trucks that minimizes average total cost for each level of output Given this Don should buy two trucks if he is producing 20 orders per week His average total cost per order will be 400 He should buy three trucks if he is producing 40 orders per week His average total cost per order will then be 270 He should buy four trucks if he is producing 60 orders per week His average total cost per order will then be 273 939 14 Consider Don s concretemixing business described in Problem 13 Assume that Don purchased 3 trucks expecting to produce 40 orders per week a Suppose that in the short run business declines to 20 orders per week What is Don s average total cost per order in the short run What will his average total cost per order in the short run be if his business booms to 60 orders per week b What is Don s longrun average total cost for 20 orders per week Explain why his shortrun average total cost of producing 20 orders per week when the number of trucks is fixed at 3 is greater than his longrun average total cost of producing 20 orders per week S171 SlS47Krug man2e7PSich12qxp 91608 922 PM Page S 183 CHAPTER 12 BEHIND THE SUPPLY CURVES INPUTS AND COSTS c Draw Don s longrun average total cost curve Draw his shortrun average total cost curve if he owns 3 trucksl 14 a In the short run producing 20 orders per week with 3 trucks Don s average total cost per order will be 7000 180020 440 If he instead produces 60 orders per week with three trucks his average total cost per order will be 297I P39 The longrun average total cost of producing 20 orders per week is 400 because Don would choose the number of trucks 2 trucks that minimizes the total cost of producing 20 orders His shortrun average total cost is greater than the long run minimum because using 3 trucks the level of the fixed input is greater than he needs to optimally produce 20 orders per week c The accompanying diagram shows Don s LRATC and ATCI 15 True or False Explain your reasoning a The shortrun average total cost can never be less than the longrun average total cost 939 The shortrun average variable cost can never be less than the longrun average total cost c In the long run choosing a higher level of fixed cost shifts the longrun average total cost curve upwardl 15 a True The longrun average total cost is the average total cost you get by choosing the most favorable level of fixed cost in the long run that is it is the lowest aver age total cost that is possible when you can adjust how much of the fixed input you use In other words the longrun average total cost of producing a certain level of output is the lowest average total cost with which that level of output can be produced 939 False The longrun average total cost is the lowest average total cost possible But average variable cost will always be less than average total cost it is lower than the average total cost by just the amount of the average fixed cost So shortrun average variable cost can be lower than longrun average total cost 5quot False In the long run choosing a higher level of fixed cost allows you to move along and to the right on the longrun average total cost curve In the long run if you want to produce a larger quantity of output you would optimally increase the level of fixed cost this will decrease the average variable cost You will do this in such a way as to spend the lowest possible average total cost that is you will be on the longrun average total cost curve but farther to the right at a larger quan tity of output

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