Firm Decisions and Costs Lecture Notes

foreign decisions and we move into the last part of the course where we're going to look at how firms behave and how they make their decisions about costs and setting prices and so forth this is a pivot from what we've been learning so far looking at consumer behavior and firm decisions are an important part of microeconomics on top of that uh they're actually it's the it's a sub specialty in which students find the most difficult to grasp so for the next this video will cover the next three chapters work only coming part of chapter 14 but we're basically covering chapter 12 13 and parts of 14 in in this one week so it is very important that you put in the needed time to read do the practice questions and review this video as often as possible sorry or as often as needed in order to master this material like I said it's first for most students it is the more a difficult uh sometimes most abstract part of microeconomics so let's get started on firm decisions on how firms make their decisions the first thing that we need to do is to look at why we even study the decisions by firms so before we get to the chapter material I want to highlight a few statistics concerning firms in Canada you're not required to learn these statistics but it's best to understand at least putting into context before understanding firm decisions or managers decisions of how firms actually contribute to GDP and to what extent now in Canada industry Canada defines different size of firms in different ways depending on the number of employees that affirm employees a small firm in Canada is considered to have 1 to 99 paid employees medium firms are deemed to have employees between 100 and 499 employees and then large firms uh or any Enterprise that employs 500 or more paid employees you'll hear sometimes uh the word or the acronym smes used you see here at the bottom last point that stands for small and medium Enterprises uh it's a term that industry Canada uses or the government of Canada uses when speaking about small and medium firms so a little bit of fun facts for uh for Canada there are 1.2 million employee businesses in Canada and if you notice the majority of these uh overwhelming majority that is 98 or small businesses only 1.9 percent uh firms in Canada are deemed to be medium-sized so that that is as I mentioned between 100 and 499 employees and uh only 0.2 percent are large Enterprises so when we think of uh you know the Big Bangs like the Royal Bank or Scotiabank or big employees such as Apple uh Walmart Canadian Thai for example these only represents represent 2.2 percent of businesses in in Canada most of Canada's smaller lawyer businesses are concentrated in two provinces uh respectively Ontario and Quebec with just shy of half a million small businesses in Ontario and a quarter million uh small businesses in Quebec we should we should never discount the small business contribution to GDP well over a third so here we have about 37 percent of GDP is generated by small businesses and this is GDP generated by the private sector to be clear large firms do contribute quite a bit about half of private sector GDP comes from large firms but that's not to say that the other half is not imported clearly another half of private sector GDP is generated by smes uh in on top of that of of all the employee businesses in Canada there's about 53 52 663 Lolita statistics of Canadian establishments that export goods outside of Canada and their exported total value of those goods is just over 575 billion dollars so well over half a trillion dollars so quite a bit similar numbers for uh the United States United States has to about 28 million firms same thing small businesses make up 99.7 of all in U.S firms and these particular firms have a tremendous role and effect on on the economy they decide what to produce how to produce how to Market it and the um the price at which to sell their goods and services and then we're going to look at in uh in a mathematical sense How firm from we call it firm managers make these decisions now what we're going to show you when we make these mathematical models the managers of these firms the owners and so forth are not sitting down on a desk actually um creating particular functions for their restaurant or for their massage parlor for their dental clinic or Law Firm um but what we do in economics is we look at the data and look at the behavior and see if we can model it mathematically as long and remember what I said in other videos as long as a model can make reliable predictions it is a valid model so to create our model of uh firm Behavior we have to look at certain parts of that behavior the first part is uh how firms use inputs to create outputs so we start off with our firm production function here we're interested in distinguishing between inputs and outputs so inputs so inputs are any of the resources the scarce resources that we spoke about in the early chapters in chapter one that go into production so raw material physical capital okay and human capital or labor so we have three inputs and with those inputs we specify those quantities in what we call a production function we label the production function Q the reason for Q is for output and quantity of output and so the so Q is a function so f is function of the raw materials the physical capital and the human or labor capital uh what is going to be relevant for the last two chapters that we'll cover next week is that the inputs and outputs are strictly uh um a matter of desirable inputs and outputs these three chapters were not going to talk about outputs that are undesirable such as waste products pollution or waste heat material that are not and these are not included in production function so this is something that's lacking in your general approach to production functions and the modeling of firm Behavior it is usually left these types of negative externalities or unwanted outputs are considered in higher level courses when we deal with environmental economics but strictly speaking the neoclassical approach without considering negative externalities or undesired waste products is what we're covering in these three chapters so like always in economics we're going to do a marginal analysis what means what happens to Output when we change one unit of some input just for convenience only where you know there's could be hundreds of inputs that go into a production function we're going to limit ourselves so that we make a two-dimensional graphical analysis easy we're going to limit ourselves to two inputs capital and labors of physical capital and Laser so this becomes our production function it's just a function of two variables okay we're going to also distinguish production in the short run and in the long run okay [Music] economists operate by the assumption that the supply of capital is inelastic in the short run and elastic in the long run and so thus the firm in the short run the firm will increase production only by increasing labor uh because labor is more elastic you could hire or um lay off employees far more easily than changing your capital capital is far more expensive uh you may be contractually obligated to keep certain capital and this is inclusive building so maybe you cannot get rid of a lease on a building or if you own it in short time right the lease May last another year or it could have a five-year lease so this is why in the short run capital is considered fixed or inelastic however in the long run which is really an ill-defined time frame for economists we'll say five years or longer The Firm can employ more of both more or less of both capital and labor so the supply of capital becomes elastic over time okay and one of the golden rules for this type of marginal analysis in in firm production is the last Point as long as marginal benefits exceed the marginal costs firms should expand production so we'll take a look at what that means graphically using an example so the example that we're going to use is wheat production so we're going to create a production function for wheat and we know that in this production function for wheat foreign function for wheat Q is a function of many inputs natural Capital manufactured Capital right so like um tractors combines you have human capital Farmers uh the helpers and so forth Social Capital Financial capital and so forth um we could specify more details what these inputs are so for example the same production function you could say we have seeds land fertilizer pesticides labor and so forth but we're only going to limit our analysis to uh to two to make it easier for us to grasp the results qualitatively are the same so like I said we have to talk about two types of inputs we have in our production function we have what's called a fixed input okay I fixed is because you cannot change it very easily in the short runs one an example and for this production function the fixed input that cannot be changed there easily would be land okay why because either you own it then you have to sell it or you can't acquire more of it if it's not available or if you've leased the land you can't you have a contract on the lease and you cannot break that contract very easily so any fixed input is a limiting factor that that really constrains the amount of production that can occur especially if you want to increase production at a a lot of land for farming um is fairly fixed you can't add more Farmland unless it is available around you to either be leased or bought but if there's a river or there's a natural park around and then that can't be done then you have a fixed input that is a limiting or constraining factor so what does a production function look like graphically if we say we have one or two inputs very easily it would look something like this and this is the production function Q with respect to only one input as a function of fertilizer holding and so we have that caters paribus condition again holding all other inputs constant so what we see here is that the production function as we increase the input fertilizers we're increasing the the units of fertilizer wheat yield or production increases but it increases at a decreasing rate there's it doesn't increase uh linearly or subtly what each point here indicates is the total amount of wheat for every quantity of input so for one bag of fertilizer per acre the total wheat yield is 80. so that's the total product refer as t p [Music] so the total product and here's the definition is the maximum amount of output that can be produced at different levels of one input assuming that the other input is fixed at a particular level right always the cater is paribus assumption now when we talked about total output we see that it is increasing over time as we increase the input but the amount that increases is is smaller for each additional unit of fertilizer so to be clear one bag of fertilizer we have total output of 80 the increase the X input or fertilizer by one unit the increase here is 30. increase in yield is 30. then if when we go from two to three so another additional bag of fertilizer the yield the total output goes up but this time only by 17. and then we go to we add one more additional unit of input output goes up by only 10. so you see that total output increases but at a decreasing rate okay so that's Point number two here and what we just did is margin we just described marginal product right as marginal product is the change in total product when there's a change in the quantity of input essentially it's the slope of the production function here's another way of calculating well it's the same way if calculate another chart or example of calculating a marginal product right so remember the interpretation marginal product is the change in output for every one unit change in input and it is possible that at a certain point as your output increases you'll get to a point where there is no further increase okay so the marginal product the becomes zero okay so at this point once it becomes zero you should not be adding more input because adding more input is costly and it doesn't change your total output and in fact if you continuously adding continuously add output you may actually have a negative marginal product that would be when the total product curve starts dipping this way right this is total product curve quantitative input versus total product you don't want to go into the negative marginal product you're losing output in that case and you're continuously paying for more input [Music] we could look at a wheat output from another from another perspective this perspective of the labor input instead of [Music] instead of fertilizer input so you could do this for every input holding all the other inputs constant so we see here we have another similar type of total product curve and in fact this is not a quint this is not just a coincidence this is the type of product curves that you'll see for a competitive firm uh they tend to look like this and then decrease this is true for for any business at the beginning you'll see that total product curves uh have an increasing slope so we have what's called increasing marginal returns and then at a certain point of uh input level the curve starts to um slow down in its increases which we have diminishing marginal Returns the marginal product in this case marginal product for labor is still positive right the slope is still positive along this entire line but it becomes closer and becomes smaller and smaller until it eventually becomes zero where the total product for labor is going to be zero and if you continuously add workers to this firm eventually you'll have negative marginal product for labor and you don't want that so you don't want this area here so what is the relationship between the total product curve and the marginal product curse that means when we look at the slope try this I let's try red when we look at the slope at every point along the total product curve okay we see that the slope as I said earlier is positive then it's zero at this point we're at zero you go if you were to plot the slope so this is the marginal product which is the slope the total product curve if you're going to plot the slope against the same input we see that here it's zero because the slope at the total product curve is zero here we have an increasing slope so it increases here at which point here we have a decreasing still positive a decreasing slope so here it's still positive but getting closer and closer to zero remember this is zero and then finally here the slope is negative right if you take the slope but at this point it's negative so this is why we have a negative slope below zero there okay so this is the relationship between a total product curve and a marginal product curve so in essence uh we've just described three stages of production we have increasing constant and decreasing returns this is your a stylized total product curve not all businesses necessarily go through three stages uh but most of them do and um I mean you could have it again you could have businesses that experienced just this type of curve or businesses could experience this type of curve as we saw in the previous PowerPoint slide but generally speaking at least two of these uh three stages are are there so in the stylized version we talk about the three three stages we have increasing we have constant marginal returns and then decreasing marginal returns you could you could jump a business can have its own particular production function that goes from uh increase the marginal returns so decreasing marginal terms without a range of constant margin returns that's possible and um the curves are not static over time so as you can see with these red arrows here production functions can shift up or down due to changes in different types of inputs or different types of Technology Now we move to uh production costs we look at the production curve now we're going to look at what type of costs a firm has to undertake there are two types of costs there are fixed costs and there are variable costs just like there are fixed inputs and there are variable inputs labor would be a variable input land would be a fixed input so in the same manner we have fixed costs and and variable costs and then definitions are the same right a fixed cost is one in which it cannot be changed over the short term and they don't and very very important as part of the definition of a fixed cost they do not generally vary with production volume right so if you take a bakery as an example the bakery has to pay uh say it buys out it buys ovens it has to make monthly payments on those ovens now whether you use the ovens to bake bread or not you're you still have to pay the cost because you bought them same thing if you either rent or bought out your bakery the building in which you have your bakery you still have to pay rent or mortgage costs regardless of how many loaves of bread one bakes but when we talk about variable costs now these are costs that are um are born depending on how much is produced so if you bake more bread you're going to pay more electricity if you bake less bread you pay less electricity so the utilities would be a variable cost same thing with wages the more Bakers you hire the higher your wage costs less Bakers to make less bread then you have a lower wage cost so we have to be able to distinguish between these two types of costs so why is it important to understand costs well it's important because when we model firm uh decisions we find that the break-even point which is if we look here the number of units or dollars at which total revenue equals total costs um determines whether a firm should should continue operating uh or not so we we need to use costs both fixed costs and variable costs in order to understand whether or what the relationship happens to be with respect to total revenue and for competitive firms marginal Costcos which will describe shortly actually derives the supply curve so understanding costs is incredibly important in order to understand the supply curve for firms and to determine a firm's break-even point sure so let's look at the short run costs so in the um in the short run we have both six and variable costs in the long run we only have variable cause there's no fixed cost so we're in the moment for the moment we're only going to consider the short run so we have fixed costs and variable costs the sum of total fixed costs and full variable costs is equal to tal cost right you don't need some students get confused by this you don't necessarily need to put total fixed costs but what we mean is all fixed cost plus all variable costs equals total cost so if you want you can rewrite the last Point that's total cost of a firm is equal to fixed costs plus variable cost this is a very easy um uh relationship but firms are not interested just in total costs and uh fixed costs or variable costs but they're really looking at is average cost that means what is the cost for the total amount of output that's being produced what is the the um the cost on a uh for all my baked bread right so this just takes us to average cost this is very a far more important concept than just total cost so the baker the law firm the dental firm a dental clinic these businesses are all interested in average fixed costs variable costs and then their average total cost so you notice what I do here I take my fixed costs take my fixed cost I divided by quantity produced or output and I do that for each of the three types of costs as we saw in the previous slide I'll just rewrite here total cost is equal to average I'm sorry not average total cost is equal to tal fixed costs plus total variable cost and I'm dividing both sides by my output to Q and what does this give me total cost divided by Q is average total cost equal to and this this is technically divided by big Q so if you just remember your math you could distribute so you'll get confused here this is the same as writing what I had earlier oops [Music] I don't want to make the assumption that you're all following [Music] very quickly so I'm just so I step back and make sure that you understand what I just did there so I divided both sides by Q which is equivalent to dividing each of the total fixed and total variable costs separately so total fixed cost divided by Q is average fixed cost and total variable cost divided by Q is average variable cost okay so these are um the equations that you need to know again they're very simple we started off with total cost is equal to Total fixed cost Plus total variable cost and then we divide everything by Q to get our three average costs the last one that's important uh is the marginal cost again in in economics we always need to look at marginal cost and it is the increase in total cost from producing one more unit of output should be of output Okay so what does that mean well marginal cost is equal to the change in total cost divided by the change in output okay so if if the baker decides to increase um [Music] so increase the number of uh muffins that he or she bakes uh the marginal cost is the change in total cost that the baker experiences when output or muffins increases by one so hopefully that those those Concepts um makes sense and I have some questions and exercises that I'm going to go through uh with you for production and costs of production so here is the example I'm going to use basically I'm going to ask you to complete the table the answers on the following slide so I'm going to go through a couple of these boxes and then you should do the rest by yourself don't look at the answers try it out first so uh the problem states that every fourth of July a stitch in time is the name of the company prints t-shirts for visitors to the small town of Liberty this production process involves both fixed cost fixed and variable costs fixed costs of printing these shirts is ten dollars that means it's fixed that's the definition of fixed code they don't it doesn't change and so the following table describes some of these costs all right so let's work out a few of them so I'm just going to move this across Okay so fixed costs are always ten dollars that's that's important to note and we know that oops we know that total costs are going to be the sum of this column total variable Clause plus the fixed costs right so if if we look at one unit of output total cost is equal two eight dollars plus the fixed costs ten dollars so this would be 18. I can't do anything for output 2 so I'll move to Output 3. so if total cost is 28 and I know my fixed costs are 10 remember our formula right total cost is equal to Total fixed cost plus total variable cost so I know that this is 28 this is 10 so this must be there you go 18. same thing here 32 plus 10 42 and this would be oops 60 4. okay now let's look at average variable cost [Music] so average variable cost would be total variable cost divided by total output well in in in the first output there's zero so if you can't divide any of these by zero so everything here is going to be undefined right the only thing you have when you have zero output is the total fixed costs right so at that point total fixed cost is equal to the total cost because there are no variable costs when you're not producing anything [Music] so as we move down to this the second row where we have one unit of output or one t-shirt the total variable cost we said is eight total um cost is 18. so the average variable cost would be the total variable cost divided by average variable cost divided by oops let's try that again average variable cost my brain's thinking faster than my head average variable cost is equal to tal variable cost divided by Q this is true for the entire column so what is TVC divided by Q well in this cell here it is eight divided by one let's go with eight what else can I fill out well here 18 um divided by three is six okay and you continue down the column same thing so if you notice this would be 32 divided by 5 should give you six point 4. okay if you're wondering 54 divided by 7 is 7 point 7 2. average total cost remember average total cost is equal to the total cost divided by Q and so if you have the total cost and you divide by Q at 18. and the total cost here divide by Q for this one here you get oops you get six oh sorry it was 28 my mistake 28 28 divided by 3 would be 9.33 if my brain works as well as a calculator hopefully it does not that old yet and so um there we have it and then you continue filling in the blanks I'll leave it to you and then I'll I'll do a couple for marginal costs remember what marginal cost implies marginal costs is the change in total cost divided by the change in Q now the change in Q for each one this is easy for each one the change in Q is always one right you're going for one to two two to three three to four is always it's always one all we have to note here is the change in total cost so here the change in total cost for this one here we're going to look at this is the change it's 8 divided by one which is equal to eight uh what's another one where we have another change um well here we could actually do the opposite so this is equal to change in total cost divided by change in Q we know that the change in Q is one so the change in total cost must be 10. so 42 to this is a difference of 10. so this number must be 52. so that's how we would go and continue filling out this chart so I I've done a half for you so try the other half make sure you answer the other questions how to graph and solve forth and then you'll see that the answers will follow on this and [Music] in this slide okay you will notice that cost curves are very particular so I I'll jump here to the summary of cost curves again what we try to do in economics is try to model our functions and we economists have discovered that firm decisions are performed behavior is based on on cost curves that are represented uh as such a given one one variable so all average total cost curves dip in this manner and dip down and then back up in a parabola-like fashion average cost curves do the same thing but there's they're lower than the average total cost because they don't include fixed costs that's why the total cost is always higher than the very the variable cost and the marginal cost curves always look like this green line as well and what's important to note specifically is that and this is a rule and the marginal cost Curve will always decline always decline reach a minimum and then increase and will always intersect the average and total cost curves at their minimum point so this is the minimum point of the average total cost curves minimum point for the average variable cost curve and the marginal cost Curve will always do that remember these are the costs so on the y-axis we have MC marginal cost average total cost and average variable cost and then here we have any one input that you would like there does it matter which out sorry not input a quantity of output and all firms will experience in the competitive market I should be clear about that all firms will experience this type of behavior in their cost curves okay so there's this is a general or rule so everybody should learn how to draw these these curves remember if you want two smiley faces and something like this a check mark that goes through check mark is the marginal cost curve the average total cost curve is above the average variable cost curve and this is where it intersects at the minimum of each of those curves [Music] thank you

foreign decisions and we move into the last part of the course where we&#39;re going to look at how firms behave and how they make their decisions about costs and setting prices and so forth this is a pivot from what we&#39;ve been learning so far looking at consumer behavior and firm decisions are an important part of microeconomics on top of that uh they&#39;re actually it&#39;s the it&#39;s a sub specialty in which students find the most difficult to grasp so for the next this video will cover the next three chapters work only coming part of chapter 14 but we&#39;re basically covering chapter 12 13 and parts of 14 in in this one week so it is very important that you put in the needed time to read do the practice questions and review this video as often as possible sorry or as often as needed in order to master this material like I said it&#39;s first for most students it is the more a difficult uh sometimes most abstract part of microeconomics so let&#39;s get started on firm decisions on how firms make their decisions the first thing that we need to do is to look at why we even study the decisions by firms so before we get to the chapter material I want to highlight a few statistics concerning firms in Canada you&#39;re not required to learn these statistics but it&#39;s best to understand at least putting into context before understanding firm decisions or managers decisions of how firms actually contribute to GDP and to what extent now in Canada industry Canada defines different size of firms in different ways depending on the number of employees that affirm employees a small firm in Canada is considered to have 1 to 99 paid employees medium firms are deemed to have employees between 100 and 499 employees and then large firms uh or any Enterprise that employs 500 or more paid employees you&#39;ll hear sometimes uh the word or the acronym smes used you see here at the bottom last point that stands for small and medium Enterprises uh it&#39;s a term that industry Canada uses or the government of Canada uses when speaking about small and medium firms so a little bit of fun facts for uh for Canada there are 1.2 million employee businesses in Canada and if you notice the majority of these uh overwhelming majority that is 98 or small businesses only 1.9 percent uh firms in Canada are deemed to be medium-sized so that that is as I mentioned between 100 and 499 employees and uh only 0.2 percent are large Enterprises so when we think of uh you know the Big Bangs like the Royal Bank or Scotiabank or big employees such as Apple uh Walmart Canadian Thai for example these only represents represent 2.2 percent of businesses in in Canada most of Canada&#39;s smaller lawyer businesses are concentrated in two provinces uh respectively Ontario and Quebec with just shy of half a million small businesses in Ontario and a quarter million uh small businesses in Quebec we should we should never discount the small business contribution to GDP well over a third so here we have about 37 percent of GDP is generated by small businesses and this is GDP generated by the private sector to be clear large firms do contribute quite a bit about half of private sector GDP comes from large firms but that&#39;s not to say that the other half is not imported clearly another half of private sector GDP is generated by smes uh in on top of that of of all the employee businesses in Canada there&#39;s about 53 52 663 Lolita statistics of Canadian establishments that export goods outside of Canada and their exported total value of those goods is just over 575 billion dollars so well over half a trillion dollars so quite a bit similar numbers for uh the United States United States has to about 28 million firms same thing small businesses make up 99.7 of all in U.S firms and these particular firms have a tremendous role and effect on on the economy they decide what to produce how to produce how to Market it and the um the price at which to sell their goods and services and then we&#39;re going to look at in uh in a mathematical sense How firm from we call it firm managers make these decisions now what we&#39;re going to show you when we make these mathematical models the managers of these firms the owners and so forth are not sitting down on a desk actually um creating particular functions for their restaurant or for their massage parlor for their dental clinic or Law Firm um but what we do in economics is we look at the data and look at the behavior and see if we can model it mathematically as long and remember what I said in other videos as long as a model can make reliable predictions it is a valid model so to create our model of uh firm Behavior we have to look at certain parts of that behavior the first part is uh how firms use inputs to create outputs so we start off with our firm production function here we&#39;re interested in distinguishing between inputs and outputs so inputs so inputs are any of the resources the scarce resources that we spoke about in the early chapters in chapter one that go into production so raw material physical capital okay and human capital or labor so we have three inputs and with those inputs we specify those quantities in what we call a production function we label the production function Q the reason for Q is for output and quantity of output and so the so Q is a function so f is function of the raw materials the physical capital and the human or labor capital uh what is going to be relevant for the last two chapters that we&#39;ll cover next week is that the inputs and outputs are strictly uh um a matter of desirable inputs and outputs these three chapters were not going to talk about outputs that are undesirable such as waste products pollution or waste heat material that are not and these are not included in production function so this is something that&#39;s lacking in your general approach to production functions and the modeling of firm Behavior it is usually left these types of negative externalities or unwanted outputs are considered in higher level courses when we deal with environmental economics but strictly speaking the neoclassical approach without considering negative externalities or undesired waste products is what we&#39;re covering in these three chapters so like always in economics we&#39;re going to do a marginal analysis what means what happens to Output when we change one unit of some input just for convenience only where you know there&#39;s could be hundreds of inputs that go into a production function we&#39;re going to limit ourselves so that we make a two-dimensional graphical analysis easy we&#39;re going to limit ourselves to two inputs capital and labors of physical capital and Laser so this becomes our production function it&#39;s just a function of two variables okay we&#39;re going to also distinguish production in the short run and in the long run okay [Music] economists operate by the assumption that the supply of capital is inelastic in the short run and elastic in the long run and so thus the firm in the short run the firm will increase production only by increasing labor uh because labor is more elastic you could hire or um lay off employees far more easily than changing your capital capital is far more expensive uh you may be contractually obligated to keep certain capital and this is inclusive building so maybe you cannot get rid of a lease on a building or if you own it in short time right the lease May last another year or it could have a five-year lease so this is why in the short run capital is considered fixed or inelastic however in the long run which is really an ill-defined time frame for economists we&#39;ll say five years or longer The Firm can employ more of both more or less of both capital and labor so the supply of capital becomes elastic over time okay and one of the golden rules for this type of marginal analysis in in firm production is the last Point as long as marginal benefits exceed the marginal costs firms should expand production so we&#39;ll take a look at what that means graphically using an example so the example that we&#39;re going to use is wheat production so we&#39;re going to create a production function for wheat and we know that in this production function for wheat foreign function for wheat Q is a function of many inputs natural Capital manufactured Capital right so like um tractors combines you have human capital Farmers uh the helpers and so forth Social Capital Financial capital and so forth um we could specify more details what these inputs are so for example the same production function you could say we have seeds land fertilizer pesticides labor and so forth but we&#39;re only going to limit our analysis to uh to two to make it easier for us to grasp the results qualitatively are the same so like I said we have to talk about two types of inputs we have in our production function we have what&#39;s called a fixed input okay I fixed is because you cannot change it very easily in the short runs one an example and for this production function the fixed input that cannot be changed there easily would be land okay why because either you own it then you have to sell it or you can&#39;t acquire more of it if it&#39;s not available or if you&#39;ve leased the land you can&#39;t you have a contract on the lease and you cannot break that contract very easily so any fixed input is a limiting factor that that really constrains the amount of production that can occur especially if you want to increase production at a a lot of land for farming um is fairly fixed you can&#39;t add more Farmland unless it is available around you to either be leased or bought but if there&#39;s a river or there&#39;s a natural park around and then that can&#39;t be done then you have a fixed input that is a limiting or constraining factor so what does a production function look like graphically if we say we have one or two inputs very easily it would look something like this and this is the production function Q with respect to only one input as a function of fertilizer holding and so we have that caters paribus condition again holding all other inputs constant so what we see here is that the production function as we increase the input fertilizers we&#39;re increasing the the units of fertilizer wheat yield or production increases but it increases at a decreasing rate there&#39;s it doesn&#39;t increase uh linearly or subtly what each point here indicates is the total amount of wheat for every quantity of input so for one bag of fertilizer per acre the total wheat yield is 80. so that&#39;s the total product refer as t p [Music] so the total product and here&#39;s the definition is the maximum amount of output that can be produced at different levels of one input assuming that the other input is fixed at a particular level right always the cater is paribus assumption now when we talked about total output we see that it is increasing over time as we increase the input but the amount that increases is is smaller for each additional unit of fertilizer so to be clear one bag of fertilizer we have total output of 80 the increase the X input or fertilizer by one unit the increase here is 30. increase in yield is 30. then if when we go from two to three so another additional bag of fertilizer the yield the total output goes up but this time only by 17. and then we go to we add one more additional unit of input output goes up by only 10. so you see that total output increases but at a decreasing rate okay so that&#39;s Point number two here and what we just did is margin we just described marginal product right as marginal product is the change in total product when there&#39;s a change in the quantity of input essentially it&#39;s the slope of the production function here&#39;s another way of calculating well it&#39;s the same way if calculate another chart or example of calculating a marginal product right so remember the interpretation marginal product is the change in output for every one unit change in input and it is possible that at a certain point as your output increases you&#39;ll get to a point where there is no further increase okay so the marginal product the becomes zero okay so at this point once it becomes zero you should not be adding more input because adding more input is costly and it doesn&#39;t change your total output and in fact if you continuously adding continuously add output you may actually have a negative marginal product that would be when the total product curve starts dipping this way right this is total product curve quantitative input versus total product you don&#39;t want to go into the negative marginal product you&#39;re losing output in that case and you&#39;re continuously paying for more input [Music] we could look at a wheat output from another from another perspective this perspective of the labor input instead of [Music] instead of fertilizer input so you could do this for every input holding all the other inputs constant so we see here we have another similar type of total product curve and in fact this is not a quint this is not just a coincidence this is the type of product curves that you&#39;ll see for a competitive firm uh they tend to look like this and then decrease this is true for for any business at the beginning you&#39;ll see that total product curves uh have an increasing slope so we have what&#39;s called increasing marginal returns and then at a certain point of uh input level the curve starts to um slow down in its increases which we have diminishing marginal Returns the marginal product in this case marginal product for labor is still positive right the slope is still positive along this entire line but it becomes closer and becomes smaller and smaller until it eventually becomes zero where the total product for labor is going to be zero and if you continuously add workers to this firm eventually you&#39;ll have negative marginal product for labor and you don&#39;t want that so you don&#39;t want this area here so what is the relationship between the total product curve and the marginal product curse that means when we look at the slope try this I let&#39;s try red when we look at the slope at every point along the total product curve okay we see that the slope as I said earlier is positive then it&#39;s zero at this point we&#39;re at zero you go if you were to plot the slope so this is the marginal product which is the slope the total product curve if you&#39;re going to plot the slope against the same input we see that here it&#39;s zero because the slope at the total product curve is zero here we have an increasing slope so it increases here at which point here we have a decreasing still positive a decreasing slope so here it&#39;s still positive but getting closer and closer to zero remember this is zero and then finally here the slope is negative right if you take the slope but at this point it&#39;s negative so this is why we have a negative slope below zero there okay so this is the relationship between a total product curve and a marginal product curve so in essence uh we&#39;ve just described three stages of production we have increasing constant and decreasing returns this is your a stylized total product curve not all businesses necessarily go through three stages uh but most of them do and um I mean you could have it again you could have businesses that experienced just this type of curve or businesses could experience this type of curve as we saw in the previous PowerPoint slide but generally speaking at least two of these uh three stages are are there so in the stylized version we talk about the three three stages we have increasing we have constant marginal returns and then decreasing marginal returns you could you could jump a business can have its own particular production function that goes from uh increase the marginal returns so decreasing marginal terms without a range of constant margin returns that&#39;s possible and um the curves are not static over time so as you can see with these red arrows here production functions can shift up or down due to changes in different types of inputs or different types of Technology Now we move to uh production costs we look at the production curve now we&#39;re going to look at what type of costs a firm has to undertake there are two types of costs there are fixed costs and there are variable costs just like there are fixed inputs and there are variable inputs labor would be a variable input land would be a fixed input so in the same manner we have fixed costs and and variable costs and then definitions are the same right a fixed cost is one in which it cannot be changed over the short term and they don&#39;t and very very important as part of the definition of a fixed cost they do not generally vary with production volume right so if you take a bakery as an example the bakery has to pay uh say it buys out it buys ovens it has to make monthly payments on those ovens now whether you use the ovens to bake bread or not you&#39;re you still have to pay the cost because you bought them same thing if you either rent or bought out your bakery the building in which you have your bakery you still have to pay rent or mortgage costs regardless of how many loaves of bread one bakes but when we talk about variable costs now these are costs that are um are born depending on how much is produced so if you bake more bread you&#39;re going to pay more electricity if you bake less bread you pay less electricity so the utilities would be a variable cost same thing with wages the more Bakers you hire the higher your wage costs less Bakers to make less bread then you have a lower wage cost so we have to be able to distinguish between these two types of costs so why is it important to understand costs well it&#39;s important because when we model firm uh decisions we find that the break-even point which is if we look here the number of units or dollars at which total revenue equals total costs um determines whether a firm should should continue operating uh or not so we we need to use costs both fixed costs and variable costs in order to understand whether or what the relationship happens to be with respect to total revenue and for competitive firms marginal Costcos which will describe shortly actually derives the supply curve so understanding costs is incredibly important in order to understand the supply curve for firms and to determine a firm&#39;s break-even point sure so let&#39;s look at the short run costs so in the um in the short run we have both six and variable costs in the long run we only have variable cause there&#39;s no fixed cost so we&#39;re in the moment for the moment we&#39;re only going to consider the short run so we have fixed costs and variable costs the sum of total fixed costs and full variable costs is equal to tal cost right you don&#39;t need some students get confused by this you don&#39;t necessarily need to put total fixed costs but what we mean is all fixed cost plus all variable costs equals total cost so if you want you can rewrite the last Point that&#39;s total cost of a firm is equal to fixed costs plus variable cost this is a very easy um uh relationship but firms are not interested just in total costs and uh fixed costs or variable costs but they&#39;re really looking at is average cost that means what is the cost for the total amount of output that&#39;s being produced what is the the um the cost on a uh for all my baked bread right so this just takes us to average cost this is very a far more important concept than just total cost so the baker the law firm the dental firm a dental clinic these businesses are all interested in average fixed costs variable costs and then their average total cost so you notice what I do here I take my fixed costs take my fixed cost I divided by quantity produced or output and I do that for each of the three types of costs as we saw in the previous slide I&#39;ll just rewrite here total cost is equal to average I&#39;m sorry not average total cost is equal to tal fixed costs plus total variable cost and I&#39;m dividing both sides by my output to Q and what does this give me total cost divided by Q is average total cost equal to and this this is technically divided by big Q so if you just remember your math you could distribute so you&#39;ll get confused here this is the same as writing what I had earlier oops [Music] I don&#39;t want to make the assumption that you&#39;re all following [Music] very quickly so I&#39;m just so I step back and make sure that you understand what I just did there so I divided both sides by Q which is equivalent to dividing each of the total fixed and total variable costs separately so total fixed cost divided by Q is average fixed cost and total variable cost divided by Q is average variable cost okay so these are um the equations that you need to know again they&#39;re very simple we started off with total cost is equal to Total fixed cost Plus total variable cost and then we divide everything by Q to get our three average costs the last one that&#39;s important uh is the marginal cost again in in economics we always need to look at marginal cost and it is the increase in total cost from producing one more unit of output should be of output Okay so what does that mean well marginal cost is equal to the change in total cost divided by the change in output okay so if if the baker decides to increase um [Music] so increase the number of uh muffins that he or she bakes uh the marginal cost is the change in total cost that the baker experiences when output or muffins increases by one so hopefully that those those Concepts um makes sense and I have some questions and exercises that I&#39;m going to go through uh with you for production and costs of production so here is the example I&#39;m going to use basically I&#39;m going to ask you to complete the table the answers on the following slide so I&#39;m going to go through a couple of these boxes and then you should do the rest by yourself don&#39;t look at the answers try it out first so uh the problem states that every fourth of July a stitch in time is the name of the company prints t-shirts for visitors to the small town of Liberty this production process involves both fixed cost fixed and variable costs fixed costs of printing these shirts is ten dollars that means it&#39;s fixed that&#39;s the definition of fixed code they don&#39;t it doesn&#39;t change and so the following table describes some of these costs all right so let&#39;s work out a few of them so I&#39;m just going to move this across Okay so fixed costs are always ten dollars that&#39;s that&#39;s important to note and we know that oops we know that total costs are going to be the sum of this column total variable Clause plus the fixed costs right so if if we look at one unit of output total cost is equal two eight dollars plus the fixed costs ten dollars so this would be 18. I can&#39;t do anything for output 2 so I&#39;ll move to Output 3. so if total cost is 28 and I know my fixed costs are 10 remember our formula right total cost is equal to Total fixed cost plus total variable cost so I know that this is 28 this is 10 so this must be there you go 18. same thing here 32 plus 10 42 and this would be oops 60 4. okay now let&#39;s look at average variable cost [Music] so average variable cost would be total variable cost divided by total output well in in in the first output there&#39;s zero so if you can&#39;t divide any of these by zero so everything here is going to be undefined right the only thing you have when you have zero output is the total fixed costs right so at that point total fixed cost is equal to the total cost because there are no variable costs when you&#39;re not producing anything [Music] so as we move down to this the second row where we have one unit of output or one t-shirt the total variable cost we said is eight total um cost is 18. so the average variable cost would be the total variable cost divided by average variable cost divided by oops let&#39;s try that again average variable cost my brain&#39;s thinking faster than my head average variable cost is equal to tal variable cost divided by Q this is true for the entire column so what is TVC divided by Q well in this cell here it is eight divided by one let&#39;s go with eight what else can I fill out well here 18 um divided by three is six okay and you continue down the column same thing so if you notice this would be 32 divided by 5 should give you six point 4. okay if you&#39;re wondering 54 divided by 7 is 7 point 7 2. average total cost remember average total cost is equal to the total cost divided by Q and so if you have the total cost and you divide by Q at 18. and the total cost here divide by Q for this one here you get oops you get six oh sorry it was 28 my mistake 28 28 divided by 3 would be 9.33  if my brain works as well as a calculator hopefully it does not that old yet and so um there we have it and then you continue filling in the blanks I&#39;ll leave it to you and then I&#39;ll I&#39;ll do a couple for marginal costs remember what marginal cost implies marginal costs is the change in total cost divided by the change in Q now the change in Q for each one this is easy for each one the change in Q is always one right you&#39;re going for one to two two to three three to four is always it&#39;s always one all we have to note here is the change in total cost so here the change in total cost for this one here we&#39;re going to look at this is the change it&#39;s 8 divided by one which is equal to eight uh what&#39;s another one where we have another change um well here we could actually do the opposite so this is equal to change in total cost divided by change in Q we know that the change in Q is one so the change in total cost must be 10. so 42 to this is a difference of 10. so this number must be 52. so that&#39;s how we would go and continue filling out this chart so I I&#39;ve done a half for you so try the other half make sure you answer the other questions how to graph and solve forth and then you&#39;ll see that the answers will follow on this and [Music] in this slide okay you will notice that cost curves are very particular so I I&#39;ll jump here to the summary of cost curves again what we try to do in economics is try to model our functions and we economists have discovered that firm decisions are performed behavior is based on on cost curves that are represented uh as such a given one one variable so all average total cost curves dip in this manner and dip down and then back up in a parabola-like fashion average cost curves do the same thing but there&#39;s they&#39;re lower than the average total cost because they don&#39;t include fixed costs that&#39;s why the total cost is always higher than the very the variable cost and the marginal cost curves always look like this green line as well and what&#39;s important to note specifically is that and this is a rule and the marginal cost Curve will always decline always decline reach a minimum and then increase and will always intersect the average and total cost curves at their minimum point so this is the minimum point of the average total cost curves minimum point for the average variable cost curve and the marginal cost Curve will always do that remember these are the costs so on the y-axis we have MC marginal cost average total cost and average variable cost and then here we have any one input that you would like there does it matter which out sorry not input a quantity of output and all firms will experience in the competitive market I should be clear about that all firms will experience this type of behavior in their cost curves okay so there&#39;s this is a general or rule so everybody should learn how to draw these these curves remember if you want two smiley faces and something like this a check mark that goes through check mark is the marginal cost curve the average total cost curve is above the average variable cost curve and this is where it intersects at the minimum of each of those curves [Music] thank you

Transcript for:Firm Decisions and Costs Lecture Notes

Transcript for:
Firm Decisions and Costs Lecture Notes