{"id":6741,"date":"2018-02-16T05:14:35","date_gmt":"2018-02-16T05:14:35","guid":{"rendered":"https:\/\/courses.lumenlearning.com\/wm-microeconomics\/?post_type=chapter&#038;p=6741"},"modified":"2024-04-25T21:46:08","modified_gmt":"2024-04-25T21:46:08","slug":"costs-in-the-short-run","status":"publish","type":"chapter","link":"https:\/\/courses.lumenlearning.com\/wm-microeconomics\/chapter\/costs-in-the-short-run\/","title":{"raw":"Costs in the Short Run","rendered":"Costs in the Short Run"},"content":{"raw":"<div class=\"textbox learning-objectives\">\r\n<h3>Learning Objectives<\/h3>\r\n<ul>\r\n \t<li>Describe the relationship between production and costs, including average and marginal costs<\/li>\r\n \t<li>Analyze short-run costs in terms of fixed cost and variable cost<\/li>\r\n<\/ul>\r\n<\/div>\r\nWe\u2019ve explained that a firm\u2019s total cost of production depends on the quantities of inputs the firm uses to produce its output and the cost of those inputs to the firm. The firm\u2019s production function tells us how much output the firm will produce with given amounts of inputs.\u00a0A production function can be expressed mathematically as\r\n<p style=\"text-align: center;\">[latex]Q=f\\left[L\\text{,}\\stackrel{-}{K}\\right][\/latex]<\/p>\r\nwhere Q is the firm's output, L is the amount of labor employed, and K is the amount of fixed capital.\r\n\r\nSuppose we think about the production function backwards:\r\n<p style=\"text-align: center;\">[latex]L=g\\left[Q\\text{,}\\stackrel{-}K\\right][\/latex],<\/p>\r\nwhere the g just means the function f in reverse. This equation tells us how much labor we need to produce a given level of output, with the fixed capital stock we have.\u00a0If we knew the cost of labor and capital, we could then compute the total cost of producing any level of output.\u00a0It is to this that we next turn.\r\n<p id=\"eip-112\">For every factor of production (or input), there is an associated factor payment.\u00a0<strong>Factor payments<\/strong>\u00a0are what the firm pays for the use of the factors of production. From the firm\u2019s perspective, factor payments are costs. From the owner of each factor\u2019s perspective, factor payments are income. Factor payments include:<\/p>\r\n\r\n\r\n[caption id=\"attachment_6765\" align=\"alignright\" width=\"332\"]<img class=\"wp-image-6765\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/2042\/2018\/02\/16155345\/CNX_Econ2e_C01_002.jpg\" alt=\"The circular flow diagram\u2019s outer arrows represent a goods and services market, and the inner arrows represent a labor market. As illustrated by the outer arrows, in a goods and services market, firms give goods and services to households and, in exchange, households give payment to firms. As illustrated by the inner arrows, in a labor market, households provide labor to firms and, in exchange, firms give wages, salaries, and benefits to households.\" width=\"332\" height=\"229\" \/> <strong>Figure 1.<\/strong> The Circular Flow Diagram is a model of economic activity with firms supplying goods and services (arrow A) to households.\u00a0 In return, households pay for those goods and services (arrow B).\u00a0 The inner circle of arrows shows factors and factor payments.\u00a0 In this figure, household supply labor services (arrow C) to firms, who pay wages, salaries and benefits (arrow D) in return.\u00a0 A more complete model would include all the other factors supplied in arrow C, and the associated factor payments in arrow D.[\/caption]\r\n<ul id=\"eip-185\">\r\n \t<li><em>Raw materials prices<\/em>\u00a0for raw materials<\/li>\r\n \t<li><em>Rent<\/em>\u00a0for land or buildings<\/li>\r\n \t<li><em>Wages and salaries<\/em>\u00a0for labor<\/li>\r\n \t<li><em>Interest and dividends<\/em>\u00a0for the use of financial capital (loans and equity investments)<\/li>\r\n \t<li><em>Profit<\/em>\u00a0<em>for entrepreneurship<\/em>. Profit is the residual, what\u2019s left over from revenues after the firm pays all the other costs. While it may seem odd to treat profit as a \u201ccost\u201d, it is the payment that goes from total revenues to entrepreneurs or taking the risk of starting a business. You can see this correspondence between factors of production and factor payments in the inside loop of the circular flow diagram in Figure 1.<\/li>\r\n<\/ul>\r\nWe now have all the information necessary to determine a firm\u2019s costs.\r\n\r\nA cost function is a mathematical equation that shows the cost of producing different levels of output. Table 1 gives an example, which shows the cost of producing different quantities of widgets.\r\n<table id=\"eip-147\">\r\n<tbody>\r\n<tr style=\"height: 44px;\">\r\n<td style=\"height: 44px; width: 685px;\" colspan=\"5\"><strong>Table 1. Cost Function for Producing Widgets<\/strong><\/td>\r\n<\/tr>\r\n<tr style=\"height: 15px;\">\r\n<td style=\"height: 15px; width: 167px;\"><strong>Q<\/strong><\/td>\r\n<td style=\"height: 15px; width: 115px;\">1<\/td>\r\n<td style=\"height: 15px; width: 140px;\">2<\/td>\r\n<td style=\"height: 15px; width: 124px;\">3<\/td>\r\n<td style=\"height: 15px; width: 139px;\">4<\/td>\r\n<\/tr>\r\n<tr style=\"height: 15px;\">\r\n<td style=\"height: 15px; width: 167px;\"><strong>Cost<\/strong><\/td>\r\n<td style=\"height: 15px; width: 115px;\">$32.50<\/td>\r\n<td style=\"height: 15px; width: 140px;\">$44<\/td>\r\n<td style=\"height: 15px; width: 124px;\">$52<\/td>\r\n<td style=\"height: 15px; width: 139px;\">$90<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<p id=\"eip-340\">What we observe is that the cost increases as the firm produces higher quantities of output. This is pretty intuitive, since producing more output requires greater quantities of inputs, which cost more dollars to acquire.<\/p>\r\n<p id=\"eip-994\">What is the origin of these cost figures? They come from the production function and the factor payments. Suppose the production function for widgets is as shown in Table 2:<\/p>\r\n\r\n<table id=\"eip-549\">\r\n<tbody>\r\n<tr style=\"height: 15px;\">\r\n<td style=\"width: 416px; height: 15px;\" colspan=\"11\"><strong>Table 2. Number of Workers and Widgets Produced<\/strong><\/td>\r\n<\/tr>\r\n<tr style=\"height: 30px;\">\r\n<td style=\"width: 92px; height: 30px;\"><strong>Workers (L)<\/strong><\/td>\r\n<td style=\"width: 32px; height: 30px;\">1<\/td>\r\n<td style=\"width: 32px; height: 30px;\">2<\/td>\r\n<td style=\"width: 32px; height: 30px;\">3<\/td>\r\n<td style=\"width: 40px; height: 30px;\">3.25<\/td>\r\n<td style=\"width: 32px; height: 30px;\">4.4<\/td>\r\n<td style=\"width: 32px; height: 30px;\">5.2<\/td>\r\n<td style=\"width: 32px; height: 30px;\">6<\/td>\r\n<td style=\"width: 32px; height: 30px;\">7<\/td>\r\n<td style=\"width: 40px; height: 30px;\">8<\/td>\r\n<td style=\"width: 20px; height: 30px;\">9<\/td>\r\n<\/tr>\r\n<tr style=\"height: 30px;\">\r\n<td style=\"width: 92px; height: 30px;\"><strong>Widgets (Q)<\/strong><\/td>\r\n<td style=\"width: 32px; height: 30px;\">0.2<\/td>\r\n<td style=\"width: 32px; height: 30px;\">0.4<\/td>\r\n<td style=\"width: 32px; height: 30px;\">0.8<\/td>\r\n<td style=\"width: 40px; height: 30px;\">1<\/td>\r\n<td style=\"width: 32px; height: 30px;\">2<\/td>\r\n<td style=\"width: 32px; height: 30px;\">3<\/td>\r\n<td style=\"width: 32px; height: 30px;\">3.5<\/td>\r\n<td style=\"width: 32px; height: 30px;\">3.8<\/td>\r\n<td style=\"width: 40px; height: 30px;\">3.95<\/td>\r\n<td style=\"width: 20px; height: 30px;\">4<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<p id=\"eip-480\">We can use the information from the production function to determine production costs. What we need to know is how many workers are required to produce any quantity of output. If we flip the order of the rows, we \"invert\" the production function so it shows [latex]L=g\\left(Q\\right)[\/latex].<\/p>\r\n\r\n<table id=\"eip-353\">\r\n<tbody>\r\n<tr>\r\n<td style=\"width: 295px;\" colspan=\"11\"><strong>Table 3. Widgets Produced by Workers<\/strong><\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"width: 81px;\"><strong>Widgets (Q)<\/strong><\/td>\r\n<td style=\"width: 21px;\">0.2<\/td>\r\n<td style=\"width: 21px;\">0.4<\/td>\r\n<td style=\"width: 21px;\">0.8<\/td>\r\n<td style=\"width: 29px;\">1<\/td>\r\n<td style=\"width: 21px;\">2<\/td>\r\n<td style=\"width: 21px;\">3<\/td>\r\n<td style=\"width: 21px;\">3.5<\/td>\r\n<td style=\"width: 21px;\">3.8<\/td>\r\n<td style=\"width: 29px;\">3.95<\/td>\r\n<td style=\"width: 9px;\">4<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"width: 81px;\"><strong>Workers (L)<\/strong><\/td>\r\n<td style=\"width: 21px;\">1<\/td>\r\n<td style=\"width: 21px;\">2<\/td>\r\n<td style=\"width: 21px;\">3<\/td>\r\n<td style=\"width: 29px;\">3.25<\/td>\r\n<td style=\"width: 21px;\">4.4<\/td>\r\n<td style=\"width: 21px;\">5.2<\/td>\r\n<td style=\"width: 21px;\">6<\/td>\r\n<td style=\"width: 21px;\">7<\/td>\r\n<td style=\"width: 29px;\">8<\/td>\r\n<td style=\"width: 9px;\">9<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<p id=\"eip-623\">Now focus on the whole number quantities of output. We\u2019ll eliminate the fractions (or partial widgets) from the table:<\/p>\r\n\r\n<table id=\"eip-935\">\r\n<tbody>\r\n<tr style=\"height: 43px;\">\r\n<td style=\"width: 308px; height: 43px;\" colspan=\"5\"><strong>Table 4. Number of Widgets Produced\u00a0<\/strong><\/td>\r\n<\/tr>\r\n<tr style=\"height: 15px;\">\r\n<td style=\"width: 130px; height: 15px;\"><strong>Widgets (Q)<\/strong><\/td>\r\n<td style=\"width: 56px; height: 15px;\">1<\/td>\r\n<td style=\"width: 45px; height: 15px;\">2<\/td>\r\n<td style=\"width: 45px; height: 15px;\">3<\/td>\r\n<td style=\"width: 32px; height: 15px;\">4<\/td>\r\n<\/tr>\r\n<tr style=\"height: 15px;\">\r\n<td style=\"width: 130px; height: 15px;\"><strong>Workers (L)<\/strong><\/td>\r\n<td style=\"width: 56px; height: 15px;\">3.25<\/td>\r\n<td style=\"width: 45px; height: 15px;\">4.4<\/td>\r\n<td style=\"width: 45px; height: 15px;\">5.2<\/td>\r\n<td style=\"width: 32px; height: 15px;\">9<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\nSuppose widget workers receive $10 per hour. Multiplying the Workers row by $10 (and eliminating the blanks) gives us the cost of producing different levels of output.\r\n<table id=\"eip-236\">\r\n<tbody>\r\n<tr>\r\n<td style=\"width: 638px;\" colspan=\"5\"><strong>Table 5. Cost of Producing Widgets<\/strong><\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"width: 260px;\"><strong>Widgets (Q)<\/strong><\/td>\r\n<td style=\"width: 95px;\">1.00<\/td>\r\n<td style=\"width: 87px;\">2.00<\/td>\r\n<td style=\"width: 92px;\">3.00<\/td>\r\n<td style=\"width: 104px;\">4.00<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"width: 260px;\"><strong>Workers (L)<\/strong><\/td>\r\n<td style=\"width: 95px;\">3.25<\/td>\r\n<td style=\"width: 87px;\">4.4<\/td>\r\n<td style=\"width: 92px;\">5.2<\/td>\r\n<td style=\"width: 104px;\">9<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"width: 260px;\"><strong>\u00d7 Wage Rate per hour<\/strong><\/td>\r\n<td style=\"width: 95px;\">$10<\/td>\r\n<td style=\"width: 87px;\">$10<\/td>\r\n<td style=\"width: 92px;\">$10<\/td>\r\n<td style=\"width: 104px;\">$10<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"width: 260px;\"><strong>= Cost<\/strong><\/td>\r\n<td style=\"width: 95px;\">$32.50<\/td>\r\n<td style=\"width: 87px;\">$44.00<\/td>\r\n<td style=\"width: 92px;\">$52.00<\/td>\r\n<td style=\"width: 104px;\">$90.00<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<p id=\"eip-164\">This is same cost function with which we began (shown in\u00a0Table 1).\u00a0Figure 2 shows the graph of the cost function.<\/p>\r\n\r\n\r\n[caption id=\"attachment_7362\" align=\"aligncenter\" width=\"591\"]<img class=\"wp-image-7362 size-full\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/2042\/2018\/02\/26192531\/Screen-Shot-2018-03-26-at-10.48.50-AM.png\" alt=\"Upward sloping line showing the total cost curve.\" width=\"591\" height=\"400\" \/> <strong>Figure 2.<\/strong> <strong>The Total Cost curve for Widgets.<\/strong> This shows cost increasing at an increasing rate as the firm produces more output.[\/caption]\r\n\r\n<div class=\"textbox tryit\">\r\n<h3>Try It<\/h3>\r\nhttps:\/\/assess.lumenlearning.com\/practice\/fa9c4a2e-7423-46cf-98a1-4ed61756a718\r\n\r\n<\/div>\r\n<p id=\"eip-302\">Now that we have the basic idea of the cost origins and how they are related to production, let\u2019s drill down into the details, by examining average, marginal, fixed, and variable costs.<\/p>\r\n\r\n<section id=\"eip-363\">\r\n<h2>Average and Marginal Costs<\/h2>\r\n<p id=\"eip-398\">The cost of producing a firm\u2019s output depends on how much labor and capital the firm uses. A list of the costs involved in producing cars will look very different from the costs involved in producing computer software or haircuts or fast-food meals.<\/p>\r\n<p id=\"eip-343\">We can measure costs in a variety of ways. Each way provides its own insight into costs. Sometimes firms need to look at their cost per unit of output, not just their total cost. There are two ways to measure per unit costs. The most intuitive way is average cost. <strong>Average cost<\/strong> is the cost on average of producing a given quantity. We define\u00a0average cost\u00a0as total cost divided by the quantity of output produced.<\/p>\r\n<p style=\"text-align: center;\">[latex]AC=TC\/Q[\/latex]<\/p>\r\n<p style=\"text-align: left;\">If producing two widgets costs a total of $44, the average cost per widget is<\/p>\r\n<p style=\"text-align: center;\">[latex]$44\/2=$22[\/latex]<\/p>\r\nper widget. The other way of measuring cost per unit is marginal cost. If average cost is the cost of the average unit of output produced, marginal cost is the cost of each individual unit produced. More formally, <strong>marginal cost<\/strong> is the cost of producing one more unit (or a few more units) of output. Mathematically,\u00a0marginal cost\u00a0is the change in total cost divided by the change in output:\r\n<p style=\"text-align: center;\">[latex]MC=\\Delta TC\/\\Delta Q[\/latex].<\/p>\r\n<p style=\"text-align: left;\">If the cost of the first widget is $32.50 and the cost of two widgets is $44, the marginal cost of the second widget is<\/p>\r\n<p style=\"text-align: center;\">[latex]$44-$32.50=$11.50[\/latex]<\/p>\r\n<p style=\"text-align: left;\">We can see the Widget Cost table redrawn below with average and marginal cost added.<\/p>\r\n\r\n<table id=\"eip-672\" summary=\"This table illustrates the extended cost function. For one widget, the cost is 32.50, and the average and marginal costs are the same value. For two widgets, the cost is 44.00; the average cost is 22.00, and the marginal costs is 11.50. For three widgets the total costs is 52.00. The average cost is 17.33 and the marginal cost is 8.00. For four widgets, the cost is 90.00; the average cost is 22.50 and the marginal cost is 38.00.\"><caption>Table 6. Extended Cost Function for Producing Widgets<\/caption>\r\n<tbody>\r\n<tr>\r\n<td>Q<\/td>\r\n<td>1<\/td>\r\n<td>2<\/td>\r\n<td>3<\/td>\r\n<td>4<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Total Cost<\/td>\r\n<td>$32.50<\/td>\r\n<td>$44.00<\/td>\r\n<td>$52.00<\/td>\r\n<td>$90.00<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Average Cost<\/td>\r\n<td>$32.50<\/td>\r\n<td>$22.00<\/td>\r\n<td>$17.33<\/td>\r\n<td>$22.50<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Marginal Cost<\/td>\r\n<td>$32.50<\/td>\r\n<td>$11.50<\/td>\r\n<td>$8.00<\/td>\r\n<td>$38.00<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<p id=\"eip-270\">Note that the marginal cost of the first unit of output is always the same as total cost.\u00a0Figures 3a and 3b show the graphs of average and marginal cost respectively.\u00a0 The typical shape of each is a U-shape, with average\/marginal cost falling at low levels of output and rising at higher levels of output.<\/p>\r\n\r\n\r\n[caption id=\"attachment_7366\" align=\"alignnone\" width=\"857\"]<img class=\"wp-image-7366\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/2042\/2018\/02\/26200502\/Screen-Shot-2018-03-26-at-3.04.32-PM.png\" alt=\"Figure a shows an average cost curve, which starts high, slopes down and then rises slightly. Figure b shows the marginal cost curve, which is a larger u-shape and starts high, the slopes down and back up.\" width=\"857\" height=\"303\" \/> <strong>Figure 3. Average and Marginal Cost Curves.<\/strong> Figure 3a shows the average cost of producing widgets based on the data in Table 6. Figure 3b shows the marginal cost of producing widgets. Both average and marginal cost curves typically are U-shaped.[\/caption]\r\n\r\n<\/section>\r\n<div class=\"textbox tryit\">\r\n<h3>Try It<\/h3>\r\nhttps:\/\/assess.lumenlearning.com\/practice\/507c0243-3c76-43f0-b438-1a7b828bb16c\r\n\r\nhttps:\/\/assess.lumenlearning.com\/practice\/74022a71-7f3b-4daa-99af-4e015cd097f9\r\n\r\n<\/div>\r\n<h2>Fixed and Variable Costs<\/h2>\r\nRemember, we explained earlier that fixed inputs are those that cannot be easily adjusted, like a building lease, and variable inputs are those that can be changed easily, like pizza ingredients. We can apply these same terms to costs.\u00a0<strong>Fixed costs<\/strong> are the costs of the fixed inputs. Fixed costs do not change regardless of the level of production, at least not in the short term. Whether you produce a lot or a little, the fixed costs are the same. One example is the rent on a factory or a retail space. Once you sign the lease, the rent is the same regardless of how much you produce, at least until the lease runs out.\r\n\r\nFixed costs can take many other forms: for example, the cost of machinery or equipment to produce the product, research and development costs to develop new products, even an expense like advertising to popularize a brand name. The level of fixed costs varies according to the specific line of business: for instance, manufacturing computer chips requires an expensive factory, but a local moving and hauling business can get by with almost no fixed costs at all if it rents trucks by the day when needed.\r\n\r\n<strong>Variable costs<\/strong>, on the other hand, are the costs of the variable inputs; they\u00a0are incurred in the act of producing\u2014the more you produce, the greater the variable cost. Labor is treated as a variable cost, since producing a greater quantity of a good or service typically requires more workers or more work hours. Variable costs would also include raw materials.\r\n\r\nAs a concrete example of fixed and variable costs, consider a barber shop called \"The Clip Joint.\" The data for output and costs are shown in Table 7. The fixed costs of operating the barber shop, including the space and equipment, are $160 per day. The variable costs are the costs of hiring barbers, which in our example is $80 per barber each day. The first two columns of the table show the quantity of haircuts the barbershop can produce as it hires additional barbers. The third column shows the fixed costs, which do not change regardless of the level of production. The fourth column shows the variable costs at each level of output. These are calculated by taking the amount of labor hired and multiplying by the wage. For example, two barbers cost: 2 \u00d7 $80 = $160. Adding together the fixed costs in the third column and the variable costs in the fourth column produces the total costs in the fifth column. So, for example, with two barbers the total cost is: $160 + $160 = $320.\r\n<table>\r\n<thead>\r\n<tr>\r\n<th style=\"width: 410px;\" colspan=\"5\">Table 7. Output and Total Costs<\/th>\r\n<\/tr>\r\n<tr>\r\n<th style=\"width: 54px;\">Labor<\/th>\r\n<th style=\"width: 73px;\">Quantity<\/th>\r\n<th style=\"width: 89px;\">Fixed Cost<\/th>\r\n<th style=\"width: 108px;\">Variable Cost<\/th>\r\n<th style=\"width: 86px;\">Total Cost<\/th>\r\n<\/tr>\r\n<\/thead>\r\n<tbody>\r\n<tr>\r\n<td style=\"width: 54px;\">1<\/td>\r\n<td style=\"width: 73px;\">16<\/td>\r\n<td style=\"width: 89px;\">$160<\/td>\r\n<td style=\"width: 108px;\">$80<\/td>\r\n<td style=\"width: 86px;\">$240<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"width: 54px;\">2<\/td>\r\n<td style=\"width: 73px;\">40<\/td>\r\n<td style=\"width: 89px;\">$160<\/td>\r\n<td style=\"width: 108px;\">$160<\/td>\r\n<td style=\"width: 86px;\">$320<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"width: 54px;\">3<\/td>\r\n<td style=\"width: 73px;\">60<\/td>\r\n<td style=\"width: 89px;\">$160<\/td>\r\n<td style=\"width: 108px;\">$240<\/td>\r\n<td style=\"width: 86px;\">$400<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"width: 54px;\">4<\/td>\r\n<td style=\"width: 73px;\">72<\/td>\r\n<td style=\"width: 89px;\">$160<\/td>\r\n<td style=\"width: 108px;\">$320<\/td>\r\n<td style=\"width: 86px;\">$480<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"width: 54px;\">5<\/td>\r\n<td style=\"width: 73px;\">80<\/td>\r\n<td style=\"width: 89px;\">$160<\/td>\r\n<td style=\"width: 108px;\">$400<\/td>\r\n<td style=\"width: 86px;\">$560<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"width: 54px;\">6<\/td>\r\n<td style=\"width: 73px;\">84<\/td>\r\n<td style=\"width: 89px;\">$160<\/td>\r\n<td style=\"width: 108px;\">$480<\/td>\r\n<td style=\"width: 86px;\">$640<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"width: 54px;\">7<\/td>\r\n<td style=\"width: 73px;\">82<\/td>\r\n<td style=\"width: 89px;\">$160<\/td>\r\n<td style=\"width: 108px;\">$560<\/td>\r\n<td style=\"width: 86px;\">$720<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\nThe relationship between the quantity of output being produced and the cost of producing that output is shown graphically in the Figure 4. The fixed costs are always shown as the vertical intercept of the total cost curve; that is, they are the costs incurred when output is zero so there are no variable costs. You can see from the graph that once production starts, total costs and variable costs rise. While variable costs may initially increase at a decreasing rate, at some point they begin increasing at an increasing rate. This is caused by diminishing marginal returns, which is easiest to see with an example. As the number of barbers increases from zero to one in the table, output increases from 0 to 16 for a marginal gain of 16; as the number rises from one to two barbers, output increases from 16 to 40, a marginal gain of 24. From that point on, though, the marginal gain in output diminishes as each additional barber is added.\r\n\r\n[caption id=\"\" align=\"aligncenter\" width=\"390\"]<img src=\"https:\/\/textimgs.s3.amazonaws.com\/DE\/microecon\/ku26-goeqtg7i#fixme#fixme#fixme\" alt=\"The graph shows how costs increase with output. It shows a cost curve that starts a 0 with a total cost around $180, then as output increases, so does the total cost, until at an output of 90, the cost is $650.\" width=\"390\" height=\"261\" \/> <strong>Figure 4. \"The Clip Joint\" Total Costs.\u00a0<\/strong>At zero production, the fixed costs of $160 are still present. As production increases, variable costs are added to fixed costs, and the total cost is the sum of the two.[\/caption]\r\n\r\nFor example, as the number of barbers rises from two to three, the marginal output gain is only 20; and as the number rises from three to four, the marginal gain is only 12. To understand the reason behind this pattern, consider that a one-man barber shop is a very busy operation. The single barber needs to do everything: say hello to people entering, answer the phone, cut hair, sweep up, and run the cash register. A second barber reduces the level of disruption from jumping back and forth between these tasks, and allows a greater division of labor and specialization. The result can be greater increasing marginal returns. However, as other barbers are added, the advantage of each additional barber is less, since the specialization of labor can only go so far. The addition of a sixth or seventh or eighth barber just to greet people at the door will have less impact than the second one did. This is the pattern of diminishing marginal returns. At some point, you may even see negative returns as the additional barbers begin bumping elbows and getting in each other's way. In this case, the addition of still more barbers would actually cause output to decrease, as shown in the last row of Table 1. As a result, the total costs of production will begin to rise more rapidly as output increases.\r\n\r\nThis pattern of <strong>diminishing marginal returns<\/strong> is common in production. As another example, consider the problem of irrigating a crop on a farmer's field. The plot of land is the fixed factor of production, while the water that can be added to the land is the key variable cost. As the farmer adds water to the land, output increases. But adding more and more water brings smaller and smaller increases in output, until at some point the water floods the field and actually reduces output. Diminishing marginal returns occur because, at a given level of fixed costs, each additional input contributes less and less to overall production.\r\n<div class=\"textbox tryit\">\r\n<h3>Try It<\/h3>\r\nhttps:\/\/assess.lumenlearning.com\/practice\/a605d396-dd0e-41d7-a6c5-a4c402e74288\r\n\r\n<\/div>\r\n<div class=\"textbox examples\">\r\n<h3>Watch It<\/h3>\r\nWatch this clip to review and assess your ability to identify the variable, fixed, total, and marginal costs.\r\n\r\n<iframe src=\"\/\/plugin.3playmedia.com\/show?mf=2649001&amp;p3sdk_version=1.10.1&amp;p=20361&amp;pt=375&amp;video_id=ucJBO9UTmwo&amp;video_target=tpm-plugin-0o04cv3y-ucJBO9UTmwo\" width=\"800px\" height=\"450px\" frameborder=\"0\" marginwidth=\"0px\" marginheight=\"0px\"><\/iframe>\r\n\r\n<\/div>\r\n<div class=\"textbox tryit\">\r\n<h3>Try It<\/h3>\r\nThese questions allow you to get as much practice as you need, as you can click the link at the top of the first question (\u201cTry another version of these questions\u201d) to get a new set of questions. Practice until you feel comfortable doing the questions.\r\n\r\n[ohm_question height=\"1000\"]276566[\/ohm_question]\r\n\r\n<\/div>\r\n<div class=\"textbox learning-objectives\">\r\n<h3>Glossary<\/h3>\r\n<dl>\r\n \t<dt>factor payments:<\/dt>\r\n \t<dd>what the firm pays for the use of the factors of production-includes raw materials, rent, wages and salaries, interest and dividends, and profit for entrepreneurship<\/dd>\r\n<\/dl>\r\n<dl>\r\n \t<dt>fixed cost:<\/dt>\r\n \t<dd>cost of the fixed inputs; expenditure that a firm must make before production starts and that does not change regardless of the production level<\/dd>\r\n<\/dl>\r\n<dl>\r\n \t<dt>marginal cost:<\/dt>\r\n \t<dd>the additional cost of producing one more unit; mathematically, [latex]MC=\\Delta TC\/\\Delta Q[\/latex].<\/dd>\r\n<\/dl>\r\n<dl>\r\n \t<dt>total cost:<\/dt>\r\n \t<dd>the sum of fixed and variable costs of production<\/dd>\r\n<\/dl>\r\n<dl>\r\n \t<dt>variable cost:<\/dt>\r\n \t<dd>cost of production that increases with the quantity produced; the cost of the variable inputs<\/dd>\r\n<\/dl>\r\n<\/div>","rendered":"<div class=\"textbox learning-objectives\">\n<h3>Learning Objectives<\/h3>\n<ul>\n<li>Describe the relationship between production and costs, including average and marginal costs<\/li>\n<li>Analyze short-run costs in terms of fixed cost and variable cost<\/li>\n<\/ul>\n<\/div>\n<p>We\u2019ve explained that a firm\u2019s total cost of production depends on the quantities of inputs the firm uses to produce its output and the cost of those inputs to the firm. The firm\u2019s production function tells us how much output the firm will produce with given amounts of inputs.\u00a0A production function can be expressed mathematically as<\/p>\n<p style=\"text-align: center;\">[latex]Q=f\\left[L\\text{,}\\stackrel{-}{K}\\right][\/latex]<\/p>\n<p>where Q is the firm&#8217;s output, L is the amount of labor employed, and K is the amount of fixed capital.<\/p>\n<p>Suppose we think about the production function backwards:<\/p>\n<p style=\"text-align: center;\">[latex]L=g\\left[Q\\text{,}\\stackrel{-}K\\right][\/latex],<\/p>\n<p>where the g just means the function f in reverse. This equation tells us how much labor we need to produce a given level of output, with the fixed capital stock we have.\u00a0If we knew the cost of labor and capital, we could then compute the total cost of producing any level of output.\u00a0It is to this that we next turn.<\/p>\n<p id=\"eip-112\">For every factor of production (or input), there is an associated factor payment.\u00a0<strong>Factor payments<\/strong>\u00a0are what the firm pays for the use of the factors of production. From the firm\u2019s perspective, factor payments are costs. From the owner of each factor\u2019s perspective, factor payments are income. Factor payments include:<\/p>\n<div id=\"attachment_6765\" style=\"width: 342px\" class=\"wp-caption alignright\"><img loading=\"lazy\" decoding=\"async\" aria-describedby=\"caption-attachment-6765\" class=\"wp-image-6765\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/2042\/2018\/02\/16155345\/CNX_Econ2e_C01_002.jpg\" alt=\"The circular flow diagram\u2019s outer arrows represent a goods and services market, and the inner arrows represent a labor market. As illustrated by the outer arrows, in a goods and services market, firms give goods and services to households and, in exchange, households give payment to firms. As illustrated by the inner arrows, in a labor market, households provide labor to firms and, in exchange, firms give wages, salaries, and benefits to households.\" width=\"332\" height=\"229\" \/><\/p>\n<p id=\"caption-attachment-6765\" class=\"wp-caption-text\"><strong>Figure 1.<\/strong> The Circular Flow Diagram is a model of economic activity with firms supplying goods and services (arrow A) to households.\u00a0 In return, households pay for those goods and services (arrow B).\u00a0 The inner circle of arrows shows factors and factor payments.\u00a0 In this figure, household supply labor services (arrow C) to firms, who pay wages, salaries and benefits (arrow D) in return.\u00a0 A more complete model would include all the other factors supplied in arrow C, and the associated factor payments in arrow D.<\/p>\n<\/div>\n<ul id=\"eip-185\">\n<li><em>Raw materials prices<\/em>\u00a0for raw materials<\/li>\n<li><em>Rent<\/em>\u00a0for land or buildings<\/li>\n<li><em>Wages and salaries<\/em>\u00a0for labor<\/li>\n<li><em>Interest and dividends<\/em>\u00a0for the use of financial capital (loans and equity investments)<\/li>\n<li><em>Profit<\/em>\u00a0<em>for entrepreneurship<\/em>. Profit is the residual, what\u2019s left over from revenues after the firm pays all the other costs. While it may seem odd to treat profit as a \u201ccost\u201d, it is the payment that goes from total revenues to entrepreneurs or taking the risk of starting a business. You can see this correspondence between factors of production and factor payments in the inside loop of the circular flow diagram in Figure 1.<\/li>\n<\/ul>\n<p>We now have all the information necessary to determine a firm\u2019s costs.<\/p>\n<p>A cost function is a mathematical equation that shows the cost of producing different levels of output. Table 1 gives an example, which shows the cost of producing different quantities of widgets.<\/p>\n<table id=\"eip-147\">\n<tbody>\n<tr style=\"height: 44px;\">\n<td style=\"height: 44px; width: 685px;\" colspan=\"5\"><strong>Table 1. Cost Function for Producing Widgets<\/strong><\/td>\n<\/tr>\n<tr style=\"height: 15px;\">\n<td style=\"height: 15px; width: 167px;\"><strong>Q<\/strong><\/td>\n<td style=\"height: 15px; width: 115px;\">1<\/td>\n<td style=\"height: 15px; width: 140px;\">2<\/td>\n<td style=\"height: 15px; width: 124px;\">3<\/td>\n<td style=\"height: 15px; width: 139px;\">4<\/td>\n<\/tr>\n<tr style=\"height: 15px;\">\n<td style=\"height: 15px; width: 167px;\"><strong>Cost<\/strong><\/td>\n<td style=\"height: 15px; width: 115px;\">$32.50<\/td>\n<td style=\"height: 15px; width: 140px;\">$44<\/td>\n<td style=\"height: 15px; width: 124px;\">$52<\/td>\n<td style=\"height: 15px; width: 139px;\">$90<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p id=\"eip-340\">What we observe is that the cost increases as the firm produces higher quantities of output. This is pretty intuitive, since producing more output requires greater quantities of inputs, which cost more dollars to acquire.<\/p>\n<p id=\"eip-994\">What is the origin of these cost figures? They come from the production function and the factor payments. Suppose the production function for widgets is as shown in Table 2:<\/p>\n<table id=\"eip-549\">\n<tbody>\n<tr style=\"height: 15px;\">\n<td style=\"width: 416px; height: 15px;\" colspan=\"11\"><strong>Table 2. Number of Workers and Widgets Produced<\/strong><\/td>\n<\/tr>\n<tr style=\"height: 30px;\">\n<td style=\"width: 92px; height: 30px;\"><strong>Workers (L)<\/strong><\/td>\n<td style=\"width: 32px; height: 30px;\">1<\/td>\n<td style=\"width: 32px; height: 30px;\">2<\/td>\n<td style=\"width: 32px; height: 30px;\">3<\/td>\n<td style=\"width: 40px; height: 30px;\">3.25<\/td>\n<td style=\"width: 32px; height: 30px;\">4.4<\/td>\n<td style=\"width: 32px; height: 30px;\">5.2<\/td>\n<td style=\"width: 32px; height: 30px;\">6<\/td>\n<td style=\"width: 32px; height: 30px;\">7<\/td>\n<td style=\"width: 40px; height: 30px;\">8<\/td>\n<td style=\"width: 20px; height: 30px;\">9<\/td>\n<\/tr>\n<tr style=\"height: 30px;\">\n<td style=\"width: 92px; height: 30px;\"><strong>Widgets (Q)<\/strong><\/td>\n<td style=\"width: 32px; height: 30px;\">0.2<\/td>\n<td style=\"width: 32px; height: 30px;\">0.4<\/td>\n<td style=\"width: 32px; height: 30px;\">0.8<\/td>\n<td style=\"width: 40px; height: 30px;\">1<\/td>\n<td style=\"width: 32px; height: 30px;\">2<\/td>\n<td style=\"width: 32px; height: 30px;\">3<\/td>\n<td style=\"width: 32px; height: 30px;\">3.5<\/td>\n<td style=\"width: 32px; height: 30px;\">3.8<\/td>\n<td style=\"width: 40px; height: 30px;\">3.95<\/td>\n<td style=\"width: 20px; height: 30px;\">4<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p id=\"eip-480\">We can use the information from the production function to determine production costs. What we need to know is how many workers are required to produce any quantity of output. If we flip the order of the rows, we &#8220;invert&#8221; the production function so it shows [latex]L=g\\left(Q\\right)[\/latex].<\/p>\n<table id=\"eip-353\">\n<tbody>\n<tr>\n<td style=\"width: 295px;\" colspan=\"11\"><strong>Table 3. Widgets Produced by Workers<\/strong><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 81px;\"><strong>Widgets (Q)<\/strong><\/td>\n<td style=\"width: 21px;\">0.2<\/td>\n<td style=\"width: 21px;\">0.4<\/td>\n<td style=\"width: 21px;\">0.8<\/td>\n<td style=\"width: 29px;\">1<\/td>\n<td style=\"width: 21px;\">2<\/td>\n<td style=\"width: 21px;\">3<\/td>\n<td style=\"width: 21px;\">3.5<\/td>\n<td style=\"width: 21px;\">3.8<\/td>\n<td style=\"width: 29px;\">3.95<\/td>\n<td style=\"width: 9px;\">4<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 81px;\"><strong>Workers (L)<\/strong><\/td>\n<td style=\"width: 21px;\">1<\/td>\n<td style=\"width: 21px;\">2<\/td>\n<td style=\"width: 21px;\">3<\/td>\n<td style=\"width: 29px;\">3.25<\/td>\n<td style=\"width: 21px;\">4.4<\/td>\n<td style=\"width: 21px;\">5.2<\/td>\n<td style=\"width: 21px;\">6<\/td>\n<td style=\"width: 21px;\">7<\/td>\n<td style=\"width: 29px;\">8<\/td>\n<td style=\"width: 9px;\">9<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p id=\"eip-623\">Now focus on the whole number quantities of output. We\u2019ll eliminate the fractions (or partial widgets) from the table:<\/p>\n<table id=\"eip-935\">\n<tbody>\n<tr style=\"height: 43px;\">\n<td style=\"width: 308px; height: 43px;\" colspan=\"5\"><strong>Table 4. Number of Widgets Produced\u00a0<\/strong><\/td>\n<\/tr>\n<tr style=\"height: 15px;\">\n<td style=\"width: 130px; height: 15px;\"><strong>Widgets (Q)<\/strong><\/td>\n<td style=\"width: 56px; height: 15px;\">1<\/td>\n<td style=\"width: 45px; height: 15px;\">2<\/td>\n<td style=\"width: 45px; height: 15px;\">3<\/td>\n<td style=\"width: 32px; height: 15px;\">4<\/td>\n<\/tr>\n<tr style=\"height: 15px;\">\n<td style=\"width: 130px; height: 15px;\"><strong>Workers (L)<\/strong><\/td>\n<td style=\"width: 56px; height: 15px;\">3.25<\/td>\n<td style=\"width: 45px; height: 15px;\">4.4<\/td>\n<td style=\"width: 45px; height: 15px;\">5.2<\/td>\n<td style=\"width: 32px; height: 15px;\">9<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>Suppose widget workers receive $10 per hour. Multiplying the Workers row by $10 (and eliminating the blanks) gives us the cost of producing different levels of output.<\/p>\n<table id=\"eip-236\">\n<tbody>\n<tr>\n<td style=\"width: 638px;\" colspan=\"5\"><strong>Table 5. Cost of Producing Widgets<\/strong><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 260px;\"><strong>Widgets (Q)<\/strong><\/td>\n<td style=\"width: 95px;\">1.00<\/td>\n<td style=\"width: 87px;\">2.00<\/td>\n<td style=\"width: 92px;\">3.00<\/td>\n<td style=\"width: 104px;\">4.00<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 260px;\"><strong>Workers (L)<\/strong><\/td>\n<td style=\"width: 95px;\">3.25<\/td>\n<td style=\"width: 87px;\">4.4<\/td>\n<td style=\"width: 92px;\">5.2<\/td>\n<td style=\"width: 104px;\">9<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 260px;\"><strong>\u00d7 Wage Rate per hour<\/strong><\/td>\n<td style=\"width: 95px;\">$10<\/td>\n<td style=\"width: 87px;\">$10<\/td>\n<td style=\"width: 92px;\">$10<\/td>\n<td style=\"width: 104px;\">$10<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 260px;\"><strong>= Cost<\/strong><\/td>\n<td style=\"width: 95px;\">$32.50<\/td>\n<td style=\"width: 87px;\">$44.00<\/td>\n<td style=\"width: 92px;\">$52.00<\/td>\n<td style=\"width: 104px;\">$90.00<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p id=\"eip-164\">This is same cost function with which we began (shown in\u00a0Table 1).\u00a0Figure 2 shows the graph of the cost function.<\/p>\n<div id=\"attachment_7362\" style=\"width: 601px\" class=\"wp-caption aligncenter\"><img loading=\"lazy\" decoding=\"async\" aria-describedby=\"caption-attachment-7362\" class=\"wp-image-7362 size-full\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/2042\/2018\/02\/26192531\/Screen-Shot-2018-03-26-at-10.48.50-AM.png\" alt=\"Upward sloping line showing the total cost curve.\" width=\"591\" height=\"400\" \/><\/p>\n<p id=\"caption-attachment-7362\" class=\"wp-caption-text\"><strong>Figure 2.<\/strong> <strong>The Total Cost curve for Widgets.<\/strong> This shows cost increasing at an increasing rate as the firm produces more output.<\/p>\n<\/div>\n<div class=\"textbox tryit\">\n<h3>Try It<\/h3>\n<p>\t<iframe id=\"assessment_practice_fa9c4a2e-7423-46cf-98a1-4ed61756a718\" class=\"resizable\" src=\"https:\/\/assess.lumenlearning.com\/practice\/fa9c4a2e-7423-46cf-98a1-4ed61756a718?iframe_resize_id=assessment_practice_id_fa9c4a2e-7423-46cf-98a1-4ed61756a718\" frameborder=\"0\" style=\"border:none;width:100%;height:100%;min-height:300px;\"><br \/>\n\t<\/iframe><\/p>\n<\/div>\n<p id=\"eip-302\">Now that we have the basic idea of the cost origins and how they are related to production, let\u2019s drill down into the details, by examining average, marginal, fixed, and variable costs.<\/p>\n<section id=\"eip-363\">\n<h2>Average and Marginal Costs<\/h2>\n<p id=\"eip-398\">The cost of producing a firm\u2019s output depends on how much labor and capital the firm uses. A list of the costs involved in producing cars will look very different from the costs involved in producing computer software or haircuts or fast-food meals.<\/p>\n<p id=\"eip-343\">We can measure costs in a variety of ways. Each way provides its own insight into costs. Sometimes firms need to look at their cost per unit of output, not just their total cost. There are two ways to measure per unit costs. The most intuitive way is average cost. <strong>Average cost<\/strong> is the cost on average of producing a given quantity. We define\u00a0average cost\u00a0as total cost divided by the quantity of output produced.<\/p>\n<p style=\"text-align: center;\">[latex]AC=TC\/Q[\/latex]<\/p>\n<p style=\"text-align: left;\">If producing two widgets costs a total of $44, the average cost per widget is<\/p>\n<p style=\"text-align: center;\">[latex]$44\/2=$22[\/latex]<\/p>\n<p>per widget. The other way of measuring cost per unit is marginal cost. If average cost is the cost of the average unit of output produced, marginal cost is the cost of each individual unit produced. More formally, <strong>marginal cost<\/strong> is the cost of producing one more unit (or a few more units) of output. Mathematically,\u00a0marginal cost\u00a0is the change in total cost divided by the change in output:<\/p>\n<p style=\"text-align: center;\">[latex]MC=\\Delta TC\/\\Delta Q[\/latex].<\/p>\n<p style=\"text-align: left;\">If the cost of the first widget is $32.50 and the cost of two widgets is $44, the marginal cost of the second widget is<\/p>\n<p style=\"text-align: center;\">[latex]$44-$32.50=$11.50[\/latex]<\/p>\n<p style=\"text-align: left;\">We can see the Widget Cost table redrawn below with average and marginal cost added.<\/p>\n<table id=\"eip-672\" summary=\"This table illustrates the extended cost function. For one widget, the cost is 32.50, and the average and marginal costs are the same value. For two widgets, the cost is 44.00; the average cost is 22.00, and the marginal costs is 11.50. For three widgets the total costs is 52.00. The average cost is 17.33 and the marginal cost is 8.00. For four widgets, the cost is 90.00; the average cost is 22.50 and the marginal cost is 38.00.\">\n<caption>Table 6. Extended Cost Function for Producing Widgets<\/caption>\n<tbody>\n<tr>\n<td>Q<\/td>\n<td>1<\/td>\n<td>2<\/td>\n<td>3<\/td>\n<td>4<\/td>\n<\/tr>\n<tr>\n<td>Total Cost<\/td>\n<td>$32.50<\/td>\n<td>$44.00<\/td>\n<td>$52.00<\/td>\n<td>$90.00<\/td>\n<\/tr>\n<tr>\n<td>Average Cost<\/td>\n<td>$32.50<\/td>\n<td>$22.00<\/td>\n<td>$17.33<\/td>\n<td>$22.50<\/td>\n<\/tr>\n<tr>\n<td>Marginal Cost<\/td>\n<td>$32.50<\/td>\n<td>$11.50<\/td>\n<td>$8.00<\/td>\n<td>$38.00<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p id=\"eip-270\">Note that the marginal cost of the first unit of output is always the same as total cost.\u00a0Figures 3a and 3b show the graphs of average and marginal cost respectively.\u00a0 The typical shape of each is a U-shape, with average\/marginal cost falling at low levels of output and rising at higher levels of output.<\/p>\n<div id=\"attachment_7366\" style=\"width: 867px\" class=\"wp-caption alignnone\"><img loading=\"lazy\" decoding=\"async\" aria-describedby=\"caption-attachment-7366\" class=\"wp-image-7366\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/2042\/2018\/02\/26200502\/Screen-Shot-2018-03-26-at-3.04.32-PM.png\" alt=\"Figure a shows an average cost curve, which starts high, slopes down and then rises slightly. Figure b shows the marginal cost curve, which is a larger u-shape and starts high, the slopes down and back up.\" width=\"857\" height=\"303\" \/><\/p>\n<p id=\"caption-attachment-7366\" class=\"wp-caption-text\"><strong>Figure 3. Average and Marginal Cost Curves.<\/strong> Figure 3a shows the average cost of producing widgets based on the data in Table 6. Figure 3b shows the marginal cost of producing widgets. Both average and marginal cost curves typically are U-shaped.<\/p>\n<\/div>\n<\/section>\n<div class=\"textbox tryit\">\n<h3>Try It<\/h3>\n<p>\t<iframe id=\"assessment_practice_507c0243-3c76-43f0-b438-1a7b828bb16c\" class=\"resizable\" src=\"https:\/\/assess.lumenlearning.com\/practice\/507c0243-3c76-43f0-b438-1a7b828bb16c?iframe_resize_id=assessment_practice_id_507c0243-3c76-43f0-b438-1a7b828bb16c\" frameborder=\"0\" style=\"border:none;width:100%;height:100%;min-height:300px;\"><br \/>\n\t<\/iframe><\/p>\n<p>\t<iframe id=\"assessment_practice_74022a71-7f3b-4daa-99af-4e015cd097f9\" class=\"resizable\" src=\"https:\/\/assess.lumenlearning.com\/practice\/74022a71-7f3b-4daa-99af-4e015cd097f9?iframe_resize_id=assessment_practice_id_74022a71-7f3b-4daa-99af-4e015cd097f9\" frameborder=\"0\" style=\"border:none;width:100%;height:100%;min-height:300px;\"><br \/>\n\t<\/iframe><\/p>\n<\/div>\n<h2>Fixed and Variable Costs<\/h2>\n<p>Remember, we explained earlier that fixed inputs are those that cannot be easily adjusted, like a building lease, and variable inputs are those that can be changed easily, like pizza ingredients. We can apply these same terms to costs.\u00a0<strong>Fixed costs<\/strong> are the costs of the fixed inputs. Fixed costs do not change regardless of the level of production, at least not in the short term. Whether you produce a lot or a little, the fixed costs are the same. One example is the rent on a factory or a retail space. Once you sign the lease, the rent is the same regardless of how much you produce, at least until the lease runs out.<\/p>\n<p>Fixed costs can take many other forms: for example, the cost of machinery or equipment to produce the product, research and development costs to develop new products, even an expense like advertising to popularize a brand name. The level of fixed costs varies according to the specific line of business: for instance, manufacturing computer chips requires an expensive factory, but a local moving and hauling business can get by with almost no fixed costs at all if it rents trucks by the day when needed.<\/p>\n<p><strong>Variable costs<\/strong>, on the other hand, are the costs of the variable inputs; they\u00a0are incurred in the act of producing\u2014the more you produce, the greater the variable cost. Labor is treated as a variable cost, since producing a greater quantity of a good or service typically requires more workers or more work hours. Variable costs would also include raw materials.<\/p>\n<p>As a concrete example of fixed and variable costs, consider a barber shop called &#8220;The Clip Joint.&#8221; The data for output and costs are shown in Table 7. The fixed costs of operating the barber shop, including the space and equipment, are $160 per day. The variable costs are the costs of hiring barbers, which in our example is $80 per barber each day. The first two columns of the table show the quantity of haircuts the barbershop can produce as it hires additional barbers. The third column shows the fixed costs, which do not change regardless of the level of production. The fourth column shows the variable costs at each level of output. These are calculated by taking the amount of labor hired and multiplying by the wage. For example, two barbers cost: 2 \u00d7 $80 = $160. Adding together the fixed costs in the third column and the variable costs in the fourth column produces the total costs in the fifth column. So, for example, with two barbers the total cost is: $160 + $160 = $320.<\/p>\n<table>\n<thead>\n<tr>\n<th style=\"width: 410px;\" colspan=\"5\">Table 7. Output and Total Costs<\/th>\n<\/tr>\n<tr>\n<th style=\"width: 54px;\">Labor<\/th>\n<th style=\"width: 73px;\">Quantity<\/th>\n<th style=\"width: 89px;\">Fixed Cost<\/th>\n<th style=\"width: 108px;\">Variable Cost<\/th>\n<th style=\"width: 86px;\">Total Cost<\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr>\n<td style=\"width: 54px;\">1<\/td>\n<td style=\"width: 73px;\">16<\/td>\n<td style=\"width: 89px;\">$160<\/td>\n<td style=\"width: 108px;\">$80<\/td>\n<td style=\"width: 86px;\">$240<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 54px;\">2<\/td>\n<td style=\"width: 73px;\">40<\/td>\n<td style=\"width: 89px;\">$160<\/td>\n<td style=\"width: 108px;\">$160<\/td>\n<td style=\"width: 86px;\">$320<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 54px;\">3<\/td>\n<td style=\"width: 73px;\">60<\/td>\n<td style=\"width: 89px;\">$160<\/td>\n<td style=\"width: 108px;\">$240<\/td>\n<td style=\"width: 86px;\">$400<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 54px;\">4<\/td>\n<td style=\"width: 73px;\">72<\/td>\n<td style=\"width: 89px;\">$160<\/td>\n<td style=\"width: 108px;\">$320<\/td>\n<td style=\"width: 86px;\">$480<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 54px;\">5<\/td>\n<td style=\"width: 73px;\">80<\/td>\n<td style=\"width: 89px;\">$160<\/td>\n<td style=\"width: 108px;\">$400<\/td>\n<td style=\"width: 86px;\">$560<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 54px;\">6<\/td>\n<td style=\"width: 73px;\">84<\/td>\n<td style=\"width: 89px;\">$160<\/td>\n<td style=\"width: 108px;\">$480<\/td>\n<td style=\"width: 86px;\">$640<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 54px;\">7<\/td>\n<td style=\"width: 73px;\">82<\/td>\n<td style=\"width: 89px;\">$160<\/td>\n<td style=\"width: 108px;\">$560<\/td>\n<td style=\"width: 86px;\">$720<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>The relationship between the quantity of output being produced and the cost of producing that output is shown graphically in the Figure 4. The fixed costs are always shown as the vertical intercept of the total cost curve; that is, they are the costs incurred when output is zero so there are no variable costs. You can see from the graph that once production starts, total costs and variable costs rise. While variable costs may initially increase at a decreasing rate, at some point they begin increasing at an increasing rate. This is caused by diminishing marginal returns, which is easiest to see with an example. As the number of barbers increases from zero to one in the table, output increases from 0 to 16 for a marginal gain of 16; as the number rises from one to two barbers, output increases from 16 to 40, a marginal gain of 24. From that point on, though, the marginal gain in output diminishes as each additional barber is added.<\/p>\n<div style=\"width: 400px\" class=\"wp-caption aligncenter\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/textimgs.s3.amazonaws.com\/DE\/microecon\/ku26-goeqtg7i#fixme#fixme#fixme\" alt=\"The graph shows how costs increase with output. It shows a cost curve that starts a 0 with a total cost around $180, then as output increases, so does the total cost, until at an output of 90, the cost is $650.\" width=\"390\" height=\"261\" \/><\/p>\n<p class=\"wp-caption-text\"><strong>Figure 4. &#8220;The Clip Joint&#8221; Total Costs.\u00a0<\/strong>At zero production, the fixed costs of $160 are still present. As production increases, variable costs are added to fixed costs, and the total cost is the sum of the two.<\/p>\n<\/div>\n<p>For example, as the number of barbers rises from two to three, the marginal output gain is only 20; and as the number rises from three to four, the marginal gain is only 12. To understand the reason behind this pattern, consider that a one-man barber shop is a very busy operation. The single barber needs to do everything: say hello to people entering, answer the phone, cut hair, sweep up, and run the cash register. A second barber reduces the level of disruption from jumping back and forth between these tasks, and allows a greater division of labor and specialization. The result can be greater increasing marginal returns. However, as other barbers are added, the advantage of each additional barber is less, since the specialization of labor can only go so far. The addition of a sixth or seventh or eighth barber just to greet people at the door will have less impact than the second one did. This is the pattern of diminishing marginal returns. At some point, you may even see negative returns as the additional barbers begin bumping elbows and getting in each other&#8217;s way. In this case, the addition of still more barbers would actually cause output to decrease, as shown in the last row of Table 1. As a result, the total costs of production will begin to rise more rapidly as output increases.<\/p>\n<p>This pattern of <strong>diminishing marginal returns<\/strong> is common in production. As another example, consider the problem of irrigating a crop on a farmer&#8217;s field. The plot of land is the fixed factor of production, while the water that can be added to the land is the key variable cost. As the farmer adds water to the land, output increases. But adding more and more water brings smaller and smaller increases in output, until at some point the water floods the field and actually reduces output. Diminishing marginal returns occur because, at a given level of fixed costs, each additional input contributes less and less to overall production.<\/p>\n<div class=\"textbox tryit\">\n<h3>Try It<\/h3>\n<p>\t<iframe id=\"assessment_practice_a605d396-dd0e-41d7-a6c5-a4c402e74288\" class=\"resizable\" src=\"https:\/\/assess.lumenlearning.com\/practice\/a605d396-dd0e-41d7-a6c5-a4c402e74288?iframe_resize_id=assessment_practice_id_a605d396-dd0e-41d7-a6c5-a4c402e74288\" frameborder=\"0\" style=\"border:none;width:100%;height:100%;min-height:300px;\"><br \/>\n\t<\/iframe><\/p>\n<\/div>\n<div class=\"textbox examples\">\n<h3>Watch It<\/h3>\n<p>Watch this clip to review and assess your ability to identify the variable, fixed, total, and marginal costs.<\/p>\n<p><iframe loading=\"lazy\" src=\"\/\/plugin.3playmedia.com\/show?mf=2649001&amp;p3sdk_version=1.10.1&amp;p=20361&amp;pt=375&amp;video_id=ucJBO9UTmwo&amp;video_target=tpm-plugin-0o04cv3y-ucJBO9UTmwo\" width=\"800px\" height=\"450px\" frameborder=\"0\" marginwidth=\"0px\" marginheight=\"0px\"><\/iframe><\/p>\n<\/div>\n<div class=\"textbox tryit\">\n<h3>Try It<\/h3>\n<p>These questions allow you to get as much practice as you need, as you can click the link at the top of the first question (\u201cTry another version of these questions\u201d) to get a new set of questions. Practice until you feel comfortable doing the questions.<\/p>\n<p><iframe loading=\"lazy\" id=\"ohm276566\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=276566&theme=oea&iframe_resize_id=ohm276566&show_question_numbers\" width=\"100%\" height=\"1000\"><\/iframe><\/p>\n<\/div>\n<div class=\"textbox learning-objectives\">\n<h3>Glossary<\/h3>\n<dl>\n<dt>factor payments:<\/dt>\n<dd>what the firm pays for the use of the factors of production-includes raw materials, rent, wages and salaries, interest and dividends, and profit for entrepreneurship<\/dd>\n<\/dl>\n<dl>\n<dt>fixed cost:<\/dt>\n<dd>cost of the fixed inputs; expenditure that a firm must make before production starts and that does not change regardless of the production level<\/dd>\n<\/dl>\n<dl>\n<dt>marginal cost:<\/dt>\n<dd>the additional cost of producing one more unit; mathematically, [latex]MC=\\Delta TC\/\\Delta Q[\/latex].<\/dd>\n<\/dl>\n<dl>\n<dt>total cost:<\/dt>\n<dd>the sum of fixed and variable costs of production<\/dd>\n<\/dl>\n<dl>\n<dt>variable cost:<\/dt>\n<dd>cost of production that increases with the quantity produced; the cost of the variable inputs<\/dd>\n<\/dl>\n<\/div>\n\n\t\t\t <section class=\"citations-section\" role=\"contentinfo\">\n\t\t\t <h3>Candela Citations<\/h3>\n\t\t\t\t\t <div>\n\t\t\t\t\t\t <div id=\"citation-list-6741\">\n\t\t\t\t\t\t\t <div class=\"licensing\"><div class=\"license-attribution-dropdown-subheading\">CC licensed content, Original<\/div><ul class=\"citation-list\"><li>Modification, adaptation, and original content. <strong>Provided by<\/strong>: Lumen Learning. <strong>License<\/strong>: <em><a target=\"_blank\" rel=\"license\" href=\"https:\/\/creativecommons.org\/licenses\/by\/4.0\/\">CC BY: Attribution<\/a><\/em><\/li><\/ul><div class=\"license-attribution-dropdown-subheading\">CC licensed content, Shared previously<\/div><ul class=\"citation-list\"><li>Costs in the Short Run. <strong>Provided by<\/strong>: OpenStax College. <strong>Located at<\/strong>: <a target=\"_blank\" href=\"https:\/\/cnx.org\/contents\/XAl2LLVA@7.23:kDmsPrPJ@13\/Costs-in-the-Short-Run\">https:\/\/cnx.org\/contents\/XAl2LLVA@7.23:kDmsPrPJ@13\/Costs-in-the-Short-Run<\/a>. <strong>License<\/strong>: <em><a target=\"_blank\" rel=\"license\" href=\"https:\/\/creativecommons.org\/licenses\/by\/4.0\/\">CC BY: Attribution<\/a><\/em>. <strong>License Terms<\/strong>: Download for free at http:\/\/cnx.org\/contents\/bc498e1f-efe9-43a0-8dea-d3569ad09a82@4.4<\/li><\/ul><div class=\"license-attribution-dropdown-subheading\">All rights reserved content<\/div><ul class=\"citation-list\"><li>Costs of Production. <strong>Provided by<\/strong>: ACDC Leadership. <strong>Located at<\/strong>: <a target=\"_blank\" href=\"https:\/\/www.youtube.com\/watch?v=ucJBO9UTmwo\">https:\/\/www.youtube.com\/watch?v=ucJBO9UTmwo<\/a>. <strong>License<\/strong>: <em>Other<\/em>. <strong>License Terms<\/strong>: Standard YouTube License<\/li><\/ul><\/div>\n\t\t\t\t\t\t <\/div>\n\t\t\t\t\t <\/div>\n\t\t\t <\/section>","protected":false},"author":29,"menu_order":7,"template":"","meta":{"_candela_citation":"[{\"type\":\"cc\",\"description\":\"Costs in the Short Run\",\"author\":\"\",\"organization\":\"OpenStax College\",\"url\":\"https:\/\/cnx.org\/contents\/XAl2LLVA@7.23:kDmsPrPJ@13\/Costs-in-the-Short-Run\",\"project\":\"\",\"license\":\"cc-by\",\"license_terms\":\"Download for free at http:\/\/cnx.org\/contents\/bc498e1f-efe9-43a0-8dea-d3569ad09a82@4.4\"},{\"type\":\"copyrighted_video\",\"description\":\"Costs of Production\",\"author\":\"\",\"organization\":\"ACDC Leadership\",\"url\":\"https:\/\/www.youtube.com\/watch?v=ucJBO9UTmwo\",\"project\":\"\",\"license\":\"other\",\"license_terms\":\"Standard YouTube License\"},{\"type\":\"original\",\"description\":\"Modification, adaptation, and original content\",\"author\":\"\",\"organization\":\"Lumen Learning\",\"url\":\"\",\"project\":\"\",\"license\":\"cc-by\",\"license_terms\":\"\"}]","CANDELA_OUTCOMES_GUID":"18f967cc-ace7-4db0-b827-c6d39f41d3bf, afa3be45-7cd3-4ddf-94ae-5e97fced22f3, c993845a-4d42-4955-9dd5-60398ab0e1f6","pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":""},"chapter-type":[],"contributor":[],"license":[],"class_list":["post-6741","chapter","type-chapter","status-publish","hentry"],"part":6395,"_links":{"self":[{"href":"https:\/\/courses.lumenlearning.com\/wm-microeconomics\/wp-json\/pressbooks\/v2\/chapters\/6741","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/courses.lumenlearning.com\/wm-microeconomics\/wp-json\/pressbooks\/v2\/chapters"}],"about":[{"href":"https:\/\/courses.lumenlearning.com\/wm-microeconomics\/wp-json\/wp\/v2\/types\/chapter"}],"author":[{"embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/wm-microeconomics\/wp-json\/wp\/v2\/users\/29"}],"version-history":[{"count":49,"href":"https:\/\/courses.lumenlearning.com\/wm-microeconomics\/wp-json\/pressbooks\/v2\/chapters\/6741\/revisions"}],"predecessor-version":[{"id":10162,"href":"https:\/\/courses.lumenlearning.com\/wm-microeconomics\/wp-json\/pressbooks\/v2\/chapters\/6741\/revisions\/10162"}],"part":[{"href":"https:\/\/courses.lumenlearning.com\/wm-microeconomics\/wp-json\/pressbooks\/v2\/parts\/6395"}],"metadata":[{"href":"https:\/\/courses.lumenlearning.com\/wm-microeconomics\/wp-json\/pressbooks\/v2\/chapters\/6741\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/courses.lumenlearning.com\/wm-microeconomics\/wp-json\/wp\/v2\/media?parent=6741"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/wm-microeconomics\/wp-json\/pressbooks\/v2\/chapter-type?post=6741"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/wm-microeconomics\/wp-json\/wp\/v2\/contributor?post=6741"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/wm-microeconomics\/wp-json\/wp\/v2\/license?post=6741"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}