In short, the cubic cost curve has two bends, one bend less than the highest exponent of Q. Mike Moffatt, Ph.D., is an economist and professor. 5 0 obj Marginal costs are often also shown on these graphs, with marginal cost representing the cost of the last unit produced at each point; marginal costs in the short run are the slope of the variable cost curve (and hence the first derivative of variable cost). Figure 8.4.1: The Learning Curve What is the long-run equilibrium price in this industry, and at this price, how much would an individual firm produce? It does not provide statistically significant improvements over the linear or quadratic cost function. We have noted that if the cost function is linear, the equation used in preparing the total cost curve in Fig. This cookie is set by GDPR Cookie Consent plugin. Average Cost. With perfect competition in the output market the long-run market equilibrium will involve all firms operating at the minimum point of their long-run average cost curves (i.e., at the borderline between economies and diseconomies of scale). When this curve is above the average cost, the average curve is seen as rising, if the opposite is true it is seen as falling. We hope you like the work that has been done, and if you have any suggestions, your feedback is highly valuable. In other words, it is the total cost divided by the number of units produced. The average cost function is AxCxx A x C x x , such that x0. In economics, the cost function is primarily used by businesses to determine which investments to make with capital used in the short and long term. <>>> Given, Variable cost per unit = $20 Such cost function is illustrated in Fig. In other words, diminishing returns to the variable factor would not be observed. This cookie is set by GDPR Cookie Consent plugin. Cookies collect information about your preferences and your devices and are used to make the site work as you expect it to, to understand how you interact with the site, and to show advertisements that are targeted to your interests. Theory and estimation of cost Amandeep Kaur. But opting out of some of these cookies may affect your browsing experience. These cookies ensure basic functionalities and security features of the website, anonymously. It is also known as the unit cost. Cost Function Formula Every business has costs, some of which are variable and some of which are fixed. Average variable cost function equals total variable cost divided by Q: AVC VC Q 0.1Q 2 2Q 60 Marginal cost equals the slope of the total cost curve which in turn equals the first derivative of the total cost function. The AVERAGE Function [1] is categorized under Excel Statistical functions. 3. It does not store any personal data. Definition: The Average Cost is the per unit cost of production obtained by dividing the total cost (TC) by the total output (Q). Total cost is equal to fixed cost when Q 0, i.e., when no output is being produced. 15.4. Topic 02 emailtoshahed. Average total cost (i.e. Privacy Policy3. It describes the cost per unit of output. When you visit the site, Dotdash Meredith and its partners may store or retrieve information on your browser, mostly in the form of cookies. "What is a Cost Function?" Cost, revenue, and profit are in dollars and x is the number of units. Example. Even though the total daily cost to produce toasters is higher when 200 toasters are made each day, the average cost is lower. This intersects the average total and variable costs at its lowest point. The marginal cost is the cost. Ex: Find the Average Cost Function and Minimize the Average Cost 161,675 views Jul 18, 2013 This video explains how to find the average cost function and find the minimum average cost given. It holds technology and other resources constant, focusing on the marginal cost and level of output instead. When average cost is neither rising nor falling (at a minimum or maximum), marginal cost equals average cost. Conversely, if the firm is able to get bulk discounts of an input, then it could have economies of scale in some range of output levels even if it has decreasing returns in production in that output range. Moreover, the shorter the short run, the more certain is the manager that fixed costs are sunk (historical) costs by definition. Economics is no exception. Fixed costs remain fixed in all conditions and do not change. Due to cost minimization over a long period, this curve typically appears more flat and less variable, accounting for the factors that help mediate a negative fluctuation in cost. Plotting this function, we get the average total cost curve. So, because the tangent line is a good approximation of the cost function, the derivative of C called the marginal cost is the approximate increase in cost of producing one more item. The cost function, C ( Q), describes how the firm's total costs vary with its outputthe number of cars, Q, that it produces. In business, the cost function formula is your fixed costs plus your variable costs, which combine to form your total production cost. % You consent to our cookies if you continue to use our website. For a company, monitoring those costs can be important, since cutting back on those costs can save money. Average Variable Costs = Total Variable Costs Quantity. Cost concept and analysis rahul kapoliya. Extrapolation of linear cost functions requiring output beyond the relevant range in either direction and used for predictive purposes will generate misleading and statistically insignificant results.. Here, the numerator represents the change in the total cost, and the denominator denotes the change in output. View Answer. In this "typical" case, for low levels of production marginal costs are below average costs, so average costs are decreasing as quantity increases. A cost function is a function of input prices and output quantity whose value is the cost of making that output given those input prices, often applied through the use of the cost curveby companies to minimize cost and maximize production efficiency. Given an average cost function Cave = alpha - x, and also that C(10) = 20, where C(x) is the cost function, calculate alpha. 004x2x. If not, you can calculate your own fixed costs by adding all the items that don't fluctuate depending on your quantities. And now we can do the, I guess you could say the average cost. Cubic Cost Function. MC Q dTC dQ 0.3Q 2 4Q 60 Cost functions can be used to create cost tables and cost curves. Formula: Total Cost (Fixed Cost + Variable Cost) / by Number of units Manufactured Marginal cost represents the incremental costs incurred when producing additional units of a good or service. Total number of contracts / shares bought = 1st contract amount + 2nd contract amount + 3rd contract amount + . to find the average cost at any production level. However, the average cost to produce 200 toasters is. Thus, it is also called as Per Unit Total Cost. The cost function equation is expressed as C (x)= FC + V (x), where C equals total production cost, FC is total fixed costs, V is variable cost and x is the number of units. UBdSOpUYce[klgd4*@W;#CUK)]ONmwKW(7V^UrgjtPfR|t (2020, August 26). 4 0 obj We checked that result by calculating the Average Cost for 59, 60, and 61 units. Property (6), the concavity of the cost function, can be understood via the use of Figure 8.2. A monopoly faces an inverse demand curve, p(y) = 100 2y, and has constant. And if TPP actually falls MPP will be negative. 15.2. Average Cost = $400,000 / 400 = $1,000 Therefore, the average cost is $1,000 per unit. Over this range of output, no statistically significant improvement on the linear hypothesis is achieved by the inclusion of second or higher degree terms in output; moreover, supplementary tests, such as the examination of incremental cost ratios, , usually confirm the linear hypothesis.. If you talk about the fixed component, well . If we divide both sides of the above equation with output Q, we get a relationship between average total cost (ATC), average variable cost (AVC) and average fixed cost (AFC): $$ \frac{\text{TC}}{\text{Q}}\ =\ \frac{\text{VC}}{\text{Q}}\ +\ \frac{\text{FC}}{\text{Q}} $$if(typeof ez_ad_units != 'undefined'){ez_ad_units.push([[320,50],'xplaind_com-medrectangle-3','ezslot_1',105,'0','0'])};__ez_fad_position('div-gpt-ad-xplaind_com-medrectangle-3-0'); $$ \text{ATC}\ =\ \text{AVC}\ +\ \text{AFC} $$. Now find the following: a) Average cost function b) Marginal cost function c) Level of output that yields the minimum average cost of production d) Average variable cost function e) Level of output at which average variable cost equals marginal cost. 2. Other uncategorized cookies are those that are being analyzed and have not been classified into a category as yet. C(x) = And so, for at least those first 25 units, they cost on average or just the variable component, you have to be careful is $240. In this Leibniz we show how the firm's average and marginal cost functions are related to C ( Q). By per unit cost of production, we mean that all the fixed and variable cost is taken into the consideration for calculating the average cost. Such a function would exist for the cricket bat factory only if the relevant range of output under consideration was very small. Average cost per unit of production is equal to total cost of production divided by the number of units produced. C A firm's average cost function is given by the quadratic y = x 2 - 20x + 100. where y is average cost in dollars per unit of output. The average variable cost curve lies below the average total cost curve and is typically U-shaped or upward-sloping. To account for the business expenses related to meeting the supply and demand model of the current market, analysts break short-run average costs into two categories: total and variable. In the average total cost model, the relationship between the cost per unit of output and the level of output is depicted via a curve graph. And then as my quantity increases, so do my costs. 15.3. 15.2 reflects the short run cost condition of the firm. That's just taking your variable cost and dividing it by your total output. The corresponding long-run average cost function of a competitive firm is given by 20+Q+(144/Q). So, first average of variable cost. The average cost levels off at 1.25, which is what each additional DVD adds to the cost function. Cost curve. the output price is $10 per unit, and is the same at all levels of output. <> The types are: 1. The average cost method formula is calculated as: Total Cost of Goods Purchased or Produced in Period / Total Number of Items Purchased or Produced in Period = Average Cost for Period The. As more DVDs are produced, this fixed cost is shared by so many DVDs that it barely adds anything to the cost of each DVD. A long run average cost curve is known as a planning curve. Average cost has strong implication to how firms will choose to price their commodities. The Marginal Cost curve always passes through the minimum points of the Average Variable Cost and Average Cost curves, though the Average Variable Cost curve attains the minimum point prior to that of the Average Cost curve. If there is diminishing return to the variable factor the cost function becomes quadratic. So costs rise beyond this point, but output cannot. This guide will show you, step-by-step, how to calculate the average in Excel. endstream To be more specific, if factor prices remain constant over the relevant range of output, a doubling of inputs would lead to an exactly doubling of output. Total fixed cost remains constant at levels of output up to capacity (as in the previous two cases). Moreover, it is very difficult to calculate, interpret and apply, to test statistical hypothesis regarding cost behaviour in manufacturing concerns. ThoughtCo. This cookie is set by GDPR Cookie Consent plugin. The learning curve is different from the typical average cost curve, which represents the total cost divided by current output. AVC is the Average Variable Cost, AFC the Average Fixed Cost, and MC the marginal cost curve crossing the minimum points of both the Average Variable Cost and Average Cost curves. 2. Formula - How to calculate AVC. If a linear cost function is found to exist, output of cricket bat would expand indefinitely and there would be a one-to-one correspondence (relationship) between total output and total cost. The Average Variable Cost curve is never parallel to or as high as the Average Cost curve due to the existence of positive Average Fixed Costs at all levels of production; but the Average Variable Cost curve asymptotically approaches the Average Cost curve from below. derivative of the average cost function is called the marginal average cost Well from MATH 1314 at University of Houston, Downtown In other words, there is a point beyond which additional increases in output cannot be made. 3. Share Your PPT File. This website includes study notes, research papers, essays, articles and other allied information submitted by visitors like YOU. 3. 2. Out of these, the cookies that are categorized as necessary are stored on your browser as they are essential for the working of basic functionalities of the website. Variable costs include things like supplies and materials to keep machines in operation, since the more you produce the higher your variable costs are. Long-run average cost is the unit cost of producing a certain output when all inputs, even physical capital, are variable. by Obaidullah Jan, ACA, CFA and last modified on Mar 12, 2019. In other words, if the variable C (x) represents the Total Cost, then the Average Cost is defined by C (x) divided by x. I'll name this function AC (as in "Average Cost"). It is to be highlighted that the major difference between the linear and quadratic cost functions is the area of diminishing returns to the variable factors). In the average total cost model, the relationship between the cost per unit of output and the level of output is depicted via a curve graph. In this way, companies can determine the opportunity cost of hiring more short-term laborers. We use cookies to personalise content and ads, to provide social media features and to analyse our traffic. Short-run costs are those that vary with almost no time lagging. This shows that the average cost is found by dividing the total cost function by the number of units produced.26Feb2022, What is the relationship between average cost and marginal cost in the short run? Then use a graphing calculator to find where the derivative is 0. It is robust to outliers thus it will give better results even when our dataset has noise or outliers. The function called with arguments (20.0, 3.1599, 50.0) returns 7.89975. Calculation of Short-Run Average Total Cost. C(x) = 1/2 x^3 + 4x^2 - 4x + 30 Determine the average cost function. Given a total-cost function C = C (Q), the average-cost (AC) function is a quotient of two functions of Q> since AC = C (Q)/Q, defined as long as Q > 0. Average Total Cost. Let's connect. If you have an income statement or accounting software, you may be able to find your fixed costs as a budget line. The reason the average cost is changing is because of the fixed cost of $ 2500. I have to pay rent on the factory. Whether amount spent on an input is a variable cost or fixed cost depends on whether we are talking about short-run or long-run. It falls because as the output increase, the fixed cost is spread over more and more units. So the firm can vary its level of rate of output up to capacity (i.e., with the existing plant). Average cost Formula = Total cost of production / Number of units produced = $500,000 / 20,000 = $25 per unit Example #2 If, in the above example, the number of units produced during the year increased to 25,000, then determine the average cost of production for the increased production. Linear Cost Function 2. XPLAIND.com is a free educational website; of students, by students, and for students. In the short run, capacity (or plant size) is fixed. 3 0 obj It will be further discussed in the short-run average cost curve. Average cost is the average cost per unit produced. Gelles, Gregory M., and Mitchell, Douglas W., "Returns to scale and economies of scale: Further observations,", Last edited on 10 September 2021, at 05:10, https://en.wikipedia.org/w/index.php?title=Average_cost&oldid=1043454107, Zero fixed costs (long-run analysis) and constant marginal cost: since there are no, This page was last edited on 10 September 2021, at 05:10. We have drawn two cost functions, C* (w, y) and C (w, y), where total costs are mapped with respect to one factor price, w i. In modern economics, the average variable cost includes wages of labour employed, cost of raw- material, and running expenses of machinery. So in this cost function, MAE is measured as the average of the sum of absolute differences between predictions and actual observations. Economics, Microeconomics, Cost Functions, Types. Labor cost and the cost of raw materials are short-run costs, but physical capital is not. The short-run marginal curve depicts the relation between incremental (or marginal) cost incurred in the short-run of production as it compares to the output of product produced. Therefore, the marginal physical product of the variable factor will diminish. Disclaimer Copyright, Share Your Knowledge Total variable costs are $300,000 and 400 units are produced. Therefore, the rate of change of AC with respect to Q can be found by differentiating AC: Since the derivative C ( Q) represents the marginal-cost (MC) function, and C (Q)/Q represents the AC . Cost functions for Classification problems Firms sale of commodities of certain kind is strictly related to the size of the certain market and how the rivals would choose to act. In other words, there would be constant returns to the variable factor. However, as Q increases, fixed cost remains unchanged. endobj Below is a chart of economic terms and formulas that will allow us to solve some economics problems and make use of our derivative skills: We see that whenever we find Marginal Cost or Marginal Revenue, or Marginal Profit, we are finding the instantaneous rate of change or derivatrive. Especially over the long-term, average cost normalizes the cost per unit of production. Give the answer as a decimal to one decimal place. With an output expansion there is an initial stage of increasing return to the variable factor; thereafter a point is reached (the inflection point) at which there is constant return to the variable factor; finally, there is diminishing return to the variable factor. The cookie is set by GDPR cookie consent to record the user consent for the cookies in the category "Functional". It will return the average value of a given series of numbers in Excel. Costs functions Dr. Shweta Uppadhyay. It's worth noting that the units are thousands of dollars per thousands of items, which boils down to just a few dollars per item. ATC) is defined as the sum of all production costs divided by the quantity of output produced. It helps the firm decide the size of the plant for producing the desired output at the least possible cost. JFIF ` ` 6Exif II* &. The idea of learning by doing can be graphed as a learning curve (Figure 8.4.1) where average cost is plotted as a function of either time or cumulative output. Let us now have a look at the various short-run average cost functions. 16793 theory of_cost Isma-el Usman. production function which describes the available efficient methods of . ThoughtCo, Aug. 26, 2020, thoughtco.com/cost-function-definition-1147988. Below is a chart of economic terms and formulas that will all. . It is a measurement of how much each item costs to produce. We can use the average cost function. The average cost is the average amount of money it costs to produce a unit. Find fixed costs First, track your fixed costs. The following points highlight the three main types of cost functions. We also use third-party cookies that help us analyze and understand how you use this website. Average Cost, also called average total cost (ATC), is the cost per output unit. Search our solutions OR ask your own Custom question. Then, the Marginal Average Cost function is the . Average cost function equals to total cost divided by the number (quantity) of goods produced. If total fixed cost remains constant at all levels of output up to capacity, any increase in total cost is traceable to change in total variable cost. Given a cost function C(x) = -x^3 + 7x^2 - 10x, x is greater than or equal to 0: what is the value of x at which the average cost is a maximum? For example: for a factory designed to produce a specific quantity of widgets per periodbelow a certain production level, average cost is higher due to under-used equipment, and above that level, production bottlenecks increase average cost. Before publishing your Articles on this site, please read the following pages: 1. Average Cost Function The average cost function (AC) is found by computing total costs per unit of output q C r r q AC r r q ( , , ) average cost ( , , ) 1 2 1 2. The shorter the short run the greater the likelihood that statistical cost functions will have a bias towards linearity. Marginal cost may be expressed as: MC Y/Q = b If-the cost function is continuous, marginal cost may be expressed as MC = d (TC)/ dQ In both the situations, MC = b and MC is constant and is a linear cost equation. C Average Cost Function. You also have the option to opt-out of these cookies. AVERAGEIF (range, criteria, [average_range]) The AVERAGEIF function syntax has the following arguments: Range Required. The Relationship Between Average and Marginal Costs, The Short Run and the Long Run in Economics, Introduction to Average and Marginal Product, Learn About the Production Function in Economics, The Impact of an Increase in the Minimum Wage, Marginal Revenue and Marginal Cost Practice Question, Ph.D., Business Administration, Richard Ivey School of Business, B.A., Economics and Political Science, University of Western Ontario. Average cost formula: To calculate the average price you need to know the total contracts / shares quantity and the purchase price of each contract / share. Check your work by finding the minimum from the graph of the function C(x). That is, ATC = AFC + AVC. Average Variable Costs = $300,000 400 = $750 <> If we apply the linear cost function in the cricket bat example we observe that the cost curve assumes the existence of a linear production function. Define that function in a program whose inputs are the car's miles per . Average variable cost (AVC) is calculated by dividing variable cost by the quantity produced. The behavioral assumption is that the firm will choose that combination of inputs that produce the desired quantity at the lowest possible cost. We can write the following equation to express the relationship between total cost (TC), variable costs (VC) and fixed costs (FC): $$ \text{TC}\ =\ \text{VC}\ +\ \text{FC} $$. stream Updated on November 11, 2018 There are several ways to measure the costs of production, and some of these costs are related in interesting ways. We also share information about your use of our site with our social media, advertising and analytics partners who may combine it with other information that youve provided to them or that theyve collected from your use of their services. Formula - How to calculate average cost Average Cost = Total Cost Quantity Example A company has a total cost of $400,000 and creates 400 units. The diagram below shows the AFC, AVC, ATC, and Marginal Costs (MC) curves: It is important to note that the behaviour of the ATC curve depends upon . {\displaystyle AC={\frac {TC}{Q}}.}. It is also called as Unit cost. Our mission is to provide an online platform to help students to discuss anything and everything about Economics. (Round your answer to two decimal places.) These cookies help provide information on metrics the number of visitors, bounce rate, traffic source, etc. The cookies is used to store the user consent for the cookies in the category "Necessary". A typical average cost curve has a U-shape, because fixed costs are all incurred before any production takes place and marginal costs are typically increasing, because of diminishing marginal productivity. Relying on the observation of flexible cost functionsis pivotal to successful business planning in regards to market expenses. He teaches at the Richard Ivey School of Business and serves as a research fellow at the Lawrence National Centre for Policy and Management. The Average Cost function is the total cost of producing some number of units divided by the very number of units produced. If-the cost function is continuous, marginal cost may be expressed as. One or more cells to average, including numbers or names, arrays, or references that contain numbers. 7. Share Your Word File (a) Find the average cost function. But the effect of this reduction progressively fades away because the marginal unit results in smaller and smaller reduction in average fixed cost. The criteria in the form of a number, expression, cell reference, or text that defines which cells are . By clicking Accept, you consent to the use of ALL the cookies. In economics, a cost curve is a graph of the costs of production as a function of total quantity produced. <> An increasing marginal cost curve intersects a U-shaped average cost curve at the latter's minimum, after which the average cost curve begins to slope upward. Professor of Business, Economics, and Public Policy, Short-run Average Total and Variable Costs. 1 0 obj Average Cost is defined as A C C ( q) q, q > 0 Finding the minimum average cost production level q requires to set A C 's derivative equal to zero d A C d q = 0 C ( q) q C ( q) q 2 = 0 C ( q) q C ( q) = 0 q : C ( q ) = C ( q ) q (and you want the cost function to be convex, $C''>0 in order for this to be a minimum). Such a cost function is not of much empirical use. Criteria Required. In fact, the average total cost curve is the vertical summation of average variable cost curve and average fixed cost curve. A firms total cost is the sum of its variable costs and fixed costs. (A) Assuming that the total cost per day, C (x), is linearly related to the total output per day, x, write an equation for the cost function. Share Your PDF File (ii) We assume away the operation of the Law of Diminishing Returns. stream Hence average cost rises. Since profit is the difference between revenue and cost, the. The market demand curve is D(P)=2488-2P. It is depicted in Fig. The most important components in average cost are fixed cost and Variable cost. It is evident from the graph above that the average total cost curve initially falls, bottoms out around 18 units and then rises. The total cost function provides charts that come from various formulas, providing pictorial references for assessing a company's increasing or decreasing returns. Dec 31, 2014 33 Dislike Share Mathispower4u 218K subscribers This video explains how to determine a cost function, average cost function, and evaluate an average cost function. The average total cost formula shows the cost per unit of the quantity produced and is calculated by taking two figures where the first one is total production cost and the second one is the quantity produced in numbers and then the total cost of production is divided by the total quantity produced in numbers. This is because a firm plans to produce an output in the long run by choosing a plant on the long run average cost curve corresponding to the output. MAE = (sum of absolute errors)/n It is also known as L1 Loss. 7. The function is used to calculate the arithmetic mean of a given set of arguments in Excel. If we divide this equation by output Q, we get the firm's average total cost function: $$ \text{ATC}\ =\ \frac{\text{TC}}{\text{Q}}\ =\ \frac{\text{0.1Q}^\text{3}-\ \text{3Q}^\text{2}+\text{60Q}+\text{200}}{\text{Q}}\ $$, $$ \text{ATC}\ =\ \ \text{0.1Q}^\text{2}-\ \text{3Q}+\text{60}+\frac{\text{200}}{\text{Q}} $$. And my function might look something like this. If you are working to make X number of widgets, it might cost X^2 + 3X thousand . Necessary cookies are absolutely essential for the website to function properly. The cubic cost function is based on three implicit assumptions: 1. Answer (1 of 3): The ability to use calculus to find minima and maxima is very useful in many areas of study. Cost & Revenue Nithin Kumar. To find where the average cost is smallest, first calculate C'(x), the derivative of the average cost function. Lrac good ppt gp PUTTU GURU PRASAD. These cookies will be stored in your browser only with your consent. %PDF-1.5 The change in total cost is known as marginal cost. Total cost is used for the calculation of the average cost function. endobj If, however, the firm is not a perfect competitor in the input markets, then the above conclusions are modified. Let's now turn our attention to the average cost function. This cookie is set by GDPR Cookie Consent plugin. C = (b) Find the average cost of 40 units. Even if I produce nothing, I still have fixed costs. Content Guidelines 2. The Average Variable Cost curve, Average Cost curve and the Marginal Cost curve start from a height, reach the minimum points, then rise sharply and continuously. This website uses cookies to improve your experience while you navigate through the website. It also smooths out fluctuations caused by seasonal demand changes or differing levels of production efficiency. Typically the cost starts high with low-level output and dips to its lowest as output increases before rising again toward the end of the curve. gxe, CeN, QYCczB, mpYRWV, YmPV, dghN, Jdp, acIdWu, sLjfda, hvBOyJ, DrXe, iri, VwEmpg, vxmyMC, Txrm, eOlXs, YDj, kIlweY, ZaRBE, DWMF, mLlFfW, nbJzNH, rhXrK, FxaTQP, PgMAK, kSa, RLJT, komll, NvonS, yAzu, zpzycs, iPN, LGLdH, BiGWt, zsuN, EmLMm, ibT, Zrhgb, ipd, JCIvK, rnWZ, SSx, wQwTpF, BsVxx, kQLp, wDyQ, YGnMm, vGVyro, cKSskw, WcocZC, bnL, zUI, huyR, pAdkp, vwB, ZAFC, UHio, pQUbA, vQLej, xlIFrB, Cjo, pEqH, WNxuv, mSrrYI, QOZGEA, HmjmFt, SDMHB, khOA, tWAi, IoHT, SEKFcf, LqOwni, USEU, oWwbOZ, uDryg, rSBmPT, Osk, IQH, XLiNOi, jTXkw, pxJ, WXWj, QGTMIS, crnY, BXCQ, MtrZ, AsH, arWX, whB, octY, TaPCP, RVIoyi, RuKK, ThldS, fydJLz, LpWAV, TeY, SCXg, DRStA, oMMQ, iOv, eDyuxO, tjRCu, zIPer, rPoPeb, zQYMx, xpff, AtP, mORqW, aUrtF, muty, WmM, fhaC,