Intermed Micro Theory
Intermed Micro Theory ECN 100
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This 3 page Class Notes was uploaded by Madie Schinner on Tuesday September 8, 2015. The Class Notes belongs to ECN 100 at University of California - Davis taught by Marianne Page in Fall. Since its upload, it has received 63 views. For similar materials see /class/191873/ecn-100-university-of-california-davis in Economcs at University of California - Davis.
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Date Created: 09/08/15
University of CalifomiaDavis TA Jason Lee ECN lOOSpring 2008 Quarter Email jawleeucdavisedu Handout 5 I The Production Function A Production Function We have seen how we derive the demand curve with the section on consumer choice Now we turn our attention to the producer choice and how we derive the supply curve We start with a concept of the production function You can think of a production function as a situation where a producer chooses inputs such as labor capital and land and combines these inputs with some type of technology to produce output Mathematically economists generally express a production lnction as Q FKL Where Q the amount of output generated F is the production function and K and L is the amount of capital and labor respectively The main decision faced by producers is to decide how many units of inputs principally capital and labor to employ given a resource constraint In making that decision the producers must consider whether they are making the decision over the shortrun or the longrun We define short run as the period of time over which one or more of the inputs used in the production process is fixed We define long run as the period of time which all inputs are variable can be changed B Production with one input that is variable To start our analysis we make some simplifying assumptions 1 We assume that the producer can only choose the level of one input In this case we assume that capital is fixed and the producer can only choose labor In other words we are assuming that the producer is making his decision in the short run 3 We assume that labor is homogeneous That is that labor is interchangeable in the sense that one worker is as good as another The production would therefore look like Q FL where only L determines the amount of output produced Definitions you should know Average product of Labor APL Average product of labor is defined as the total output divided by the total number of workers employed AM 2 2 z FL L L Marginal Product of Labor MPL The marginal product of labor is de ned as the extra output produced by an extra unit of labor hired MPL E AL Law of diminishing returns The idea that the marginal product of an input eventually declines as its numbers increased holding all other inputs xed For a simple example consider a pizza place that has two brick ovens but only 1 employee If the owner of the pizza place hires an additional worker the marginal product will most certainly go up But consider if the owner keeps hiring workers while the number of brick ovens still stays the same At some point workers will start bumping into each other and get into each other s way Marginal product will start declining Relationship between Marginal Product and Average Product Intuitively you already know how this relationship between marginal and average works But to further illustrate the concept let s use a baseball analogy Suppose that in a baseball player has a 250 batting average which means that 25 of the time the player gets a base hit This is his average product Now further imagine that in a given game he has a great night and gets 4 hits in 4 atbats His marginal product for that game is 100 What would happen to his batting average His batting average would increase 0 When the marginal product is above the average product the average will increase Imagine instead that the baseball player goes hitless so that his marginal product for that game is 0 In that case his batting average will fall 0 When the marginal product is below the average product the average will decrease In the nal example suppose the baseball player gets exactly 1 hit in 4 at bats His marginal product will be 25 which is equal to his batting average In this case his average will neither increase nor decrease 0 When the marginal product is exactly the same as the average product the average will stay the same Key Point The average product curve will always slope upwards whenever it is below the marginal product curve and will slope downwards whenever it is above the marginal product curve Your text shows you how would could calculate the average product curve and the marginal product curve from a total product curve It probably won t be very useful for the purposes of your HW or exams but its still nice to know gtTo nd the average product at any given point on the total product curve Simply draw a straight line connecting the origin to that point The slope of that line will be your average product gtTo nd the marginal product at any given point on the total product curve It will be the slope of the tangent line of that point C Production with Two Variable Inputs We ve assumed in the previous section a simple example where the producer only had to decide how much labor he has to employ in his production process Oftentimes the employer uses more than 1 input and has to choose between different combinations of factors of production in his production decision Assumptions 1 The rm uses two inputs which are variable The inputs are capital K and labor L The production function is FKL 2 Capital and labor are homogeneous respectively That is each unit of capital is exactly the same in terms of productivity and likewise with labor 3 Increasing the amount of both inputs strictly increases the amount of output that the firm can produce We can plot the various input combinations that efficiently produces a given level of output in an isoquant An isoquant is very similar to an indifference curve in that it tells you all the production bundles that give you the same level of output much like how an indifference curve told you all the consumption bundles that gave you the same level of satisfaction or utility Not surprisingly isoquants have properties which are identical to indifference curves 1 Isoquants are thin 2 Isoquants cannot slope upwards 3 Isoquants cannot cross 4 Higher level isoquants lie farther from the origin See your notes on indifference curves to see why this is true or read about the properties of isoquants on page 229 of your text We can further exploit the similarity between isoquants and indifference curves in terms of the substitution between inputs Recall that indifference curves told you that rate at which one is willing to sacrifice a good to gain an extra unit of another good Similarly for isoquants we can show that the slope of the isoquant tells us the rate at which one input can be substituted for another This is captured by the marginal rate of technical substitution MRTS for labor with capital MRTSLK Slope ofthe isoquant In words The MRTS tells us how much units of capital we would need to rent if we eliminate a unit of labor so that we can stay on the same isoquant Just like we were able to tie MRS with marginal utility concept we can do the same thing with MRTS and marginal product concept
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